CORD-19-Sentences  

CORD-19:90394841ad2cbaec78bf51646d5ca1ae26fadba6 JSONTXT 8 Projects

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Id Subject Object Predicate Lexical cue
TextSentencer_T1 0-56 Sentence denotes Bayesian Analysis for Inference of an Emerging Epidemic:
T32590 0-56 Sentence denotes Bayesian Analysis for Inference of an Emerging Epidemic:
TextSentencer_T2 57-90 Sentence denotes Citrus Canker in Urban Landscapes
T13114 57-90 Sentence denotes Citrus Canker in Urban Landscapes
TextSentencer_T3 92-100 Sentence denotes Abstract
T24615 92-100 Sentence denotes Abstract
TextSentencer_T4 101-178 Sentence denotes Outbreaks of infectious diseases require a rapid response from policy makers.
T20664 101-178 Sentence denotes Outbreaks of infectious diseases require a rapid response from policy makers.
TextSentencer_T5 179-387 Sentence denotes The choice of an adequate level of response relies upon available knowledge of the spatial and temporal parameters governing pathogen spread, affecting, amongst others, the predicted severity of the epidemic.
T45342 179-387 Sentence denotes The choice of an adequate level of response relies upon available knowledge of the spatial and temporal parameters governing pathogen spread, affecting, amongst others, the predicted severity of the epidemic.
TextSentencer_T6 388-595 Sentence denotes Yet, when a new pathogen is introduced into an alien environment, such information is often lacking or of no use, and epidemiological parameters must be estimated from the first observations of the epidemic.
T28029 388-595 Sentence denotes Yet, when a new pathogen is introduced into an alien environment, such information is often lacking or of no use, and epidemiological parameters must be estimated from the first observations of the epidemic.
TextSentencer_T7 596-706 Sentence denotes This poses a challenge to epidemiologists: how quickly can the parameters of an emerging disease be estimated?
T89397 596-706 Sentence denotes This poses a challenge to epidemiologists: how quickly can the parameters of an emerging disease be estimated?
TextSentencer_T8 707-778 Sentence denotes How soon can the future progress of the epidemic be reliably predicted?
T47681 707-778 Sentence denotes How soon can the future progress of the epidemic be reliably predicted?
TextSentencer_T9 779-939 Sentence denotes We investigate these issues using a unique, spatially and temporally resolved dataset for the invasion of a plant disease, Asiatic citrus canker in urban Miami.
T40190 779-939 Sentence denotes We investigate these issues using a unique, spatially and temporally resolved dataset for the invasion of a plant disease, Asiatic citrus canker in urban Miami.
TextSentencer_T10 940-1100 Sentence denotes We use epidemiological models, Bayesian Markov-chain Monte Carlo, and advanced spatial statistical methods to analyse rates and extent of spread of the disease.
T28308 940-1100 Sentence denotes We use epidemiological models, Bayesian Markov-chain Monte Carlo, and advanced spatial statistical methods to analyse rates and extent of spread of the disease.
TextSentencer_T11 1101-1151 Sentence denotes A rich and complex epidemic behaviour is revealed.
T4255 1101-1151 Sentence denotes A rich and complex epidemic behaviour is revealed.
TextSentencer_T12 1152-1334 Sentence denotes The spatial scale of spread is approximately constant over time and can be estimated rapidly with great precision (although the evidence for long-range transmission is inconclusive).
T61213 1152-1334 Sentence denotes The spatial scale of spread is approximately constant over time and can be estimated rapidly with great precision (although the evidence for long-range transmission is inconclusive).
TextSentencer_T13 1335-1464 Sentence denotes In contrast, the rate of infection is characterised by strong monthly fluctuations that we associate with extreme weather events.
T60022 1335-1464 Sentence denotes In contrast, the rate of infection is characterised by strong monthly fluctuations that we associate with extreme weather events.
TextSentencer_T14 1465-1660 Sentence denotes Uninformed predictions from the early stages of the epidemic, assuming complete ignorance of the future environmental drivers, fail because of the unpredictable variability of the infection rate.
T75581 1465-1660 Sentence denotes Uninformed predictions from the early stages of the epidemic, assuming complete ignorance of the future environmental drivers, fail because of the unpredictable variability of the infection rate.
TextSentencer_T15 1661-1808 Sentence denotes Conversely, predictions improve dramatically if we assume prior knowledge of either the main environmental trend, or the main environmental events.
T70145 1661-1808 Sentence denotes Conversely, predictions improve dramatically if we assume prior knowledge of either the main environmental trend, or the main environmental events.
TextSentencer_T16 1809-2021 Sentence denotes A contrast emerges between the high detail attained by modelling in the spatiotemporal description of the epidemic and the bottleneck imposed on epidemic prediction by the limits of meteorological predictability.
T37260 1809-2021 Sentence denotes A contrast emerges between the high detail attained by modelling in the spatiotemporal description of the epidemic and the bottleneck imposed on epidemic prediction by the limits of meteorological predictability.
TextSentencer_T17 2022-2140 Sentence denotes We argue that identifying such bottlenecks will be a fundamental step in future modelling of weather-driven epidemics.
T95766 2022-2140 Sentence denotes We argue that identifying such bottlenecks will be a fundamental step in future modelling of weather-driven epidemics.
TextSentencer_T18 2142-2201 Sentence denotes Emerging epidemics are of increasing topical interest [1] .
T51129 2142-2201 Sentence denotes Emerging epidemics are of increasing topical interest [1] .
TextSentencer_T19 2202-2448 Sentence denotes These emerging diseases pose new threats to human health [2] [3] [4] [5] [6] , livestock [7] [8] [9] [10] [11] and crop production [12] [13] [14] , as well as wildlife populations [15] [16] [17] and natural plant communities [18] [19] [20] [21] .
T80922 2202-2448 Sentence denotes These emerging diseases pose new threats to human health [2] [3] [4] [5] [6] , livestock [7] [8] [9] [10] [11] and crop production [12] [13] [14] , as well as wildlife populations [15] [16] [17] and natural plant communities [18] [19] [20] [21] .
TextSentencer_T20 2449-2650 Sentence denotes Such epidemics occur most frequently when exotic pathogens are introduced into new environments or when novel strains arise that enable a pathogen to grow in a previously unfavourable environment [1] .
T17324 2449-2650 Sentence denotes Such epidemics occur most frequently when exotic pathogens are introduced into new environments or when novel strains arise that enable a pathogen to grow in a previously unfavourable environment [1] .
TextSentencer_T21 2651-2855 Sentence denotes One of the principal challenges in managing emerging epidemics is to predict the likely future development of disease in order to assess the severity of the invasion prior to instituting control measures.
T48804 2651-2855 Sentence denotes One of the principal challenges in managing emerging epidemics is to predict the likely future development of disease in order to assess the severity of the invasion prior to instituting control measures.
TextSentencer_T22 2856-3100 Sentence denotes However, prediction is difficult when little is known about how a new pathogen is likely to continue to spread in an alien environment, and frequently the underlying epidemiological parameters that influence the spread of disease are not known.
T46489 2856-3100 Sentence denotes However, prediction is difficult when little is known about how a new pathogen is likely to continue to spread in an alien environment, and frequently the underlying epidemiological parameters that influence the spread of disease are not known.
TextSentencer_T23 3101-3407 Sentence denotes Even when there is prior knowledge of a pathogen, as for example foot and mouth epidemics in the UK in 1967, 1982 and 2001, different pathogen strains, changes in farming practices or environmental conditions can markedly change the extent and speed of disease spread through the landscape [7, 9, 22, 23] .
T19001 3101-3407 Sentence denotes Even when there is prior knowledge of a pathogen, as for example foot and mouth epidemics in the UK in 1967, 1982 and 2001, different pathogen strains, changes in farming practices or environmental conditions can markedly change the extent and speed of disease spread through the landscape [7, 9, 22, 23] .
TextSentencer_T24 3408-3715 Sentence denotes Whereas, for example, the spread of foot and mouth disease in the 1967 epidemic was relatively localised, occurring mainly by aerial dispersal [24] , changes in the frequency and distance of livestock movements over large distances [25] led to a strikingly, topologically different epidemic in 2001 [7, 9] .
T94735 3408-3715 Sentence denotes Whereas, for example, the spread of foot and mouth disease in the 1967 epidemic was relatively localised, occurring mainly by aerial dispersal [24] , changes in the frequency and distance of livestock movements over large distances [25] led to a strikingly, topologically different epidemic in 2001 [7, 9] .
TextSentencer_T25 3716-3837 Sentence denotes Numerous other examples have been reported of variability in epidemic outcome upon reintroductions of emerging pathogens.
T66000 3716-3837 Sentence denotes Numerous other examples have been reported of variability in epidemic outcome upon reintroductions of emerging pathogens.
TextSentencer_T26 3838-4002 Sentence denotes This is problematic, because rapid decisions about the introduction of disease control strategies often have to be made early in the course of an emerging epidemic.
T72354 3838-4002 Sentence denotes This is problematic, because rapid decisions about the introduction of disease control strategies often have to be made early in the course of an emerging epidemic.
TextSentencer_T27 4003-4032 Sentence denotes Sometimes, options are clear.
T87751 4003-4032 Sentence denotes Sometimes, options are clear.
TextSentencer_T28 4033-4151 Sentence denotes Immediate control aimed at eradication is initiated as soon as an outbreak is detected for certain statutory diseases.
T32311 4033-4151 Sentence denotes Immediate control aimed at eradication is initiated as soon as an outbreak is detected for certain statutory diseases.
TextSentencer_T29 4152-4414 Sentence denotes Actions against the H1N1-2009 pandemic influenza worldwide [26] , foot and mouth disease in the UK [8] , and Asian soya bean rust in several US states [27] are good examples amongst others of human, livestock and crop diseases that attract an immediate response.
T91553 4152-4414 Sentence denotes Actions against the H1N1-2009 pandemic influenza worldwide [26] , foot and mouth disease in the UK [8] , and Asian soya bean rust in several US states [27] are good examples amongst others of human, livestock and crop diseases that attract an immediate response.
TextSentencer_T30 4415-4660 Sentence denotes For other diseases, policy makers and disease control authorities may wish to wait to assess the likely severity of the infestation in order to consider the likely costs and benefits of control; delay may also be necessary to mobilise resources.
T97688 4415-4660 Sentence denotes For other diseases, policy makers and disease control authorities may wish to wait to assess the likely severity of the infestation in order to consider the likely costs and benefits of control; delay may also be necessary to mobilise resources.
TextSentencer_T31 4661-4890 Sentence denotes Informed decision making invokes a series of questions about how to make inferences about the emerging epidemic: what type of epidemiological model can be used to characterise the epidemic and to predict future spread of disease?
T49717 4661-4890 Sentence denotes Informed decision making invokes a series of questions about how to make inferences about the emerging epidemic: what type of epidemiological model can be used to characterise the epidemic and to predict future spread of disease?
TextSentencer_T32 4891-4969 Sentence denotes Where are the susceptible hosts and how are they distributed in the landscape?
T16754 4891-4969 Sentence denotes Where are the susceptible hosts and how are they distributed in the landscape?
TextSentencer_T33 4970-5086 Sentence denotes How is disease transmitted and what are the values of the epidemiological parameters for transmission and dispersal?
T84176 4970-5086 Sentence denotes How is disease transmitted and what are the values of the epidemiological parameters for transmission and dispersal?
TextSentencer_T34 5087-5171 Sentence denotes How soon during the course of the epidemic can the parameters be reliably estimated?
T74984 5087-5171 Sentence denotes How soon during the course of the epidemic can the parameters be reliably estimated?
TextSentencer_T35 5172-5214 Sentence denotes How should we take account of uncertainty?
T31098 5172-5214 Sentence denotes How should we take account of uncertainty?
TextSentencer_T36 5215-5435 Sentence denotes Here, we examine these questions using a combination of Bayesian statistical inference and a unique, spatially-and temporally-resolved data-set [28] for the invasion of a plant disease, Asiatic citrus canker, in Florida.
T36202 5215-5435 Sentence denotes Here, we examine these questions using a combination of Bayesian statistical inference and a unique, spatially-and temporally-resolved data-set [28] for the invasion of a plant disease, Asiatic citrus canker, in Florida.
TextSentencer_T37 5436-5530 Sentence denotes Asiatic citrus canker (ACC) is caused by the bacterium Xanthomonas axonopodis pv. citri (Xac).
T63682 5436-5530 Sentence denotes Asiatic citrus canker (ACC) is caused by the bacterium Xanthomonas axonopodis pv. citri (Xac).
TextSentencer_T38 5531-5697 Sentence denotes The pathogen can infect a very wide range of citrus and related hosts, causing defoliation, fruit blemishing and severe losses in quality and quantity of yield [29] .
T75230 5531-5697 Sentence denotes The pathogen can infect a very wide range of citrus and related hosts, causing defoliation, fruit blemishing and severe losses in quality and quantity of yield [29] .
TextSentencer_T39 5698-5762 Sentence denotes The pathogen is principally spread by wind-blown rain [29, 30] .
T41127 5698-5762 Sentence denotes The pathogen is principally spread by wind-blown rain [29, 30] .
TextSentencer_T40 5763-6003 Sentence denotes It is not vector borne, other than by anthropomorphic transmission on machinery [29] , but the spread is known to be exacerbated by leaf damage inflicted by the Asian leaf miner Phyllocnistis citrella that first appeared in Florida in 1993.
T63756 5763-6003 Sentence denotes It is not vector borne, other than by anthropomorphic transmission on machinery [29] , but the spread is known to be exacerbated by leaf damage inflicted by the Asian leaf miner Phyllocnistis citrella that first appeared in Florida in 1993.
TextSentencer_T41 6004-6103 Sentence denotes There have been several independent introductions of Xac into Florida up until the mid 1990s [31] .
T29217 6004-6103 Sentence denotes There have been several independent introductions of Xac into Florida up until the mid 1990s [31] .
TextSentencer_T42 6104-6284 Sentence denotes The pathogen was originally introduced on imported seedlings from Japan in 1910 and declared eradicated, after extensive removal of infected and exposed susceptible trees, in 1933.
T58210 6104-6284 Sentence denotes The pathogen was originally introduced on imported seedlings from Japan in 1910 and declared eradicated, after extensive removal of infected and exposed susceptible trees, in 1933.
TextSentencer_T43 6285-6454 Sentence denotes An outbreak in Manatee county on the west coast of Florida was thought to have been eradicated in the 1980s, but ACC reoccurred within two years from surviving inoculum.
T25978 6285-6454 Sentence denotes An outbreak in Manatee county on the west coast of Florida was thought to have been eradicated in the 1980s, but ACC reoccurred within two years from surviving inoculum.
TextSentencer_T44 6455-6580 Sentence denotes A new infestation of ACC from a genetically different strain of Xac was reported in urban Miami on residential trees in 1995.
T79774 6455-6580 Sentence denotes A new infestation of ACC from a genetically different strain of Xac was reported in urban Miami on residential trees in 1995.
TextSentencer_T45 6581-6833 Sentence denotes The disease spread rapidly through Eastern and central Florida [29] , triggering an extensive eradication programme, involving compulsory removal of ,7M commercial, .4M nursery and 0.8M residential trees around infected sites, at a cost of .$1 billion.
T22329 6581-6833 Sentence denotes The disease spread rapidly through Eastern and central Florida [29] , triggering an extensive eradication programme, involving compulsory removal of ,7M commercial, .4M nursery and 0.8M residential trees around infected sites, at a cost of .$1 billion.
TextSentencer_T46 6834-7068 Sentence denotes The eradication scheme was halted in 2006 following widespread dispersal of inoculum during several severe hurricanes in 2004 and the eventual determination that the disease had become endemic rendering eradication unattainable [32] .
T85235 6834-7068 Sentence denotes The eradication scheme was halted in 2006 following widespread dispersal of inoculum during several severe hurricanes in 2004 and the eventual determination that the disease had become endemic rendering eradication unattainable [32] .
TextSentencer_T47 7069-7322 Sentence denotes Here we focus on the early stage of the epidemic in urban Miami and, in particular, how to estimate the inherent spatial and temporal scales of the epidemic in order to predict the future course of an epidemic in a spatially heterogeneous urban setting.
T60862 7069-7322 Sentence denotes Here we focus on the early stage of the epidemic in urban Miami and, in particular, how to estimate the inherent spatial and temporal scales of the epidemic in order to predict the future course of an epidemic in a spatially heterogeneous urban setting.
TextSentencer_T48 7323-7478 Sentence denotes Infection on these trees constituted a potent source of inoculum that must be controlled were the disease threat to plantations to be economically managed.
T44674 7323-7478 Sentence denotes Infection on these trees constituted a potent source of inoculum that must be controlled were the disease threat to plantations to be economically managed.
TextSentencer_T49 7479-7669 Sentence denotes Accordingly, the USDA Agricultural Research Service initiated a detailed census of susceptible trees and the occurrence of ACC in five sites in Broward and Dade counties in the Miami region.
T39536 7479-7669 Sentence denotes Accordingly, the USDA Agricultural Research Service initiated a detailed census of susceptible trees and the occurrence of ACC in five sites in Broward and Dade counties in the Miami region.
TextSentencer_T50 7670-7720 Sentence denotes The sites ranged from 2.6 km 2 to 15.5 km 2 [28] .
T47508 7670-7720 Sentence denotes The sites ranged from 2.6 km 2 to 15.5 km 2 [28] .
TextSentencer_T51 7721-7848 Sentence denotes The data provide a full census of susceptible trees, with 24 successive monthly snapshots for the occurrence of new infections.
T39753 7721-7848 Sentence denotes The data provide a full census of susceptible trees, with 24 successive monthly snapshots for the occurrence of new infections.
TextSentencer_T52 7849-7916 Sentence denotes Retrospectively, the outcome of the epidemic at each site is known.
T2956 7849-7916 Sentence denotes Retrospectively, the outcome of the epidemic at each site is known.
TextSentencer_T53 7917-8067 Sentence denotes Here we use subsets of the data at different stages of the epidemic to recreate different levels of ignorance about the future course of the epidemic.
T51934 7917-8067 Sentence denotes Here we use subsets of the data at different stages of the epidemic to recreate different levels of ignorance about the future course of the epidemic.
TextSentencer_T54 8068-8200 Sentence denotes Then using Bayesian statistical inference and a stochastic model we compare model predictions with the known course of the epidemic.
T75552 8068-8200 Sentence denotes Then using Bayesian statistical inference and a stochastic model we compare model predictions with the known course of the epidemic.
TextSentencer_T55 8201-8221 Sentence denotes Specifically we ask:
T36411 8201-8221 Sentence denotes Specifically we ask:
TextSentencer_T56 8222-8418 Sentence denotes By using the citrus canker outbreak to address these broad questions, we introduce and test methodologies that are applicable to a much broader class of spatially-and temporally-complex epidemics.
T75532 8222-8418 Sentence denotes By using the citrus canker outbreak to address these broad questions, we introduce and test methodologies that are applicable to a much broader class of spatially-and temporally-complex epidemics.
TextSentencer_T57 8419-8456 Sentence denotes The methods are organised as follows.
T21483 8419-8456 Sentence denotes The methods are organised as follows.
TextSentencer_T58 8457-8718 Sentence denotes The first three sections set the general problem by describing the data used for parameter estimation and the data collection process (first section), the models fitted to the data (second section), and methods for Bayesian parameter estimation (third section).
T45119 8457-8718 Sentence denotes The first three sections set the general problem by describing the data used for parameter estimation and the data collection process (first section), the models fitted to the data (second section), and methods for Bayesian parameter estimation (third section).
TextSentencer_T59 8719-8779 Sentence denotes Model selection methods are explained in the fourth section.
T8003 8719-8779 Sentence denotes Model selection methods are explained in the fourth section.
TextSentencer_T60 8780-8971 Sentence denotes In the fifth section, we discuss temporal-window techniques for the change of parameter estimates with time; the sixth section describes techniques for parameter changes amongst census sites.
T70134 8780-8971 Sentence denotes In the fifth section, we discuss temporal-window techniques for the change of parameter estimates with time; the sixth section describes techniques for parameter changes amongst census sites.
TextSentencer_T61 8972-9024 Sentence denotes The seventh section describes goodness-of-fit tests.
T82693 8972-9024 Sentence denotes The seventh section describes goodness-of-fit tests.
TextSentencer_T62 9025-9135 Sentence denotes In the eighth and final section, we give details on simulating predictive distributions of epidemic outbreaks.
T50653 9025-9135 Sentence denotes In the eighth and final section, we give details on simulating predictive distributions of epidemic outbreaks.
TextSentencer_T63 9136-9327 Sentence denotes The data used for analysis consist of four sites in urban regions close to Miami ( Figure 1A) , with two sites in Broward County (labelled B1 and B2) and two in Miami Dade county (D1 and D2).
T26708 9136-9327 Sentence denotes The data used for analysis consist of four sites in urban regions close to Miami ( Figure 1A) , with two sites in Broward County (labelled B1 and B2) and two in Miami Dade county (D1 and D2).
TextSentencer_T64 9328-9457 Sentence denotes The spatial locations of susceptible citrus trees in the four sites were fully enumerated using a differential global positioning
T4524 9328-9457 Sentence denotes The spatial locations of susceptible citrus trees in the four sites were fully enumerated using a differential global positioning
TextSentencer_T65 9458-9560 Sentence denotes We consider emerging epidemics, arising, e.g., when a new pathogen is introduced in a host population.
T93926 9458-9560 Sentence denotes We consider emerging epidemics, arising, e.g., when a new pathogen is introduced in a host population.
TextSentencer_T66 9561-9744 Sentence denotes In face of the new threat, crucial control measures have to be implemented quickly, yet prior knowledge of the parameters underlying pathogen spread and transmission is often missing.
T39461 9561-9744 Sentence denotes In face of the new threat, crucial control measures have to be implemented quickly, yet prior knowledge of the parameters underlying pathogen spread and transmission is often missing.
TextSentencer_T67 9745-9883 Sentence denotes Predictive modelling can greatly help in informing decision making by estimating those parameters from early observations of the outbreak.
T73488 9745-9883 Sentence denotes Predictive modelling can greatly help in informing decision making by estimating those parameters from early observations of the outbreak.
TextSentencer_T68 9884-10055 Sentence denotes The important questions are then: can a modeller characterise the disease ''soon enough,'' i.e., within a useful time frame, in order to enact the proper control measures?
T58171 9884-10055 Sentence denotes The important questions are then: can a modeller characterise the disease ''soon enough,'' i.e., within a useful time frame, in order to enact the proper control measures?
TextSentencer_T69 10056-10141 Sentence denotes At what stage of the outbreak can the future epidemic progress be reliably predicted?
T24165 10056-10141 Sentence denotes At what stage of the outbreak can the future epidemic progress be reliably predicted?
TextSentencer_T70 10142-10241 Sentence denotes We analyse an outbreak of citrus canker, a wind-spread bacterial disease of citrus, in urban Miami.
T30716 10142-10241 Sentence denotes We analyse an outbreak of citrus canker, a wind-spread bacterial disease of citrus, in urban Miami.
TextSentencer_T71 10242-10356 Sentence denotes The model succeeds in capturing the main epidemiological features of the disease, but we find contrasting answers.
T37117 10242-10356 Sentence denotes The model succeeds in capturing the main epidemiological features of the disease, but we find contrasting answers.
TextSentencer_T72 10357-10458 Sentence denotes The spatial scale of disease spread can be identified quickly and accurately from early observations.
T88180 10357-10458 Sentence denotes The spatial scale of disease spread can be identified quickly and accurately from early observations.
TextSentencer_T73 10459-10626 Sentence denotes However, the rate of spread is rapidly changing in time, driven mainly by rare thunderstorms with very short-time predictability, which frustrates epidemic prediction.
T98745 10459-10626 Sentence denotes However, the rate of spread is rapidly changing in time, driven mainly by rare thunderstorms with very short-time predictability, which frustrates epidemic prediction.
TextSentencer_T74 10627-10634 Sentence denotes system.
T52067 10627-10634 Sentence denotes system.
TextSentencer_T75 10635-10719 Sentence denotes There were 4730, 1113, 6056 and 6072 trees at sites B1, B2, D1 and D2, respectively.
T26757 10635-10719 Sentence denotes There were 4730, 1113, 6056 and 6072 trees at sites B1, B2, D1 and D2, respectively.
TextSentencer_T76 10720-10827 Sentence denotes Each site was visited by teams of inspectors at successive intervals between October 1997 and October 1999.
T88513 10720-10827 Sentence denotes Each site was visited by teams of inspectors at successive intervals between October 1997 and October 1999.
TextSentencer_T77 10828-10996 Sentence denotes The locations of infected trees were identified and notional infection times were calculated by experienced personnel, from lesion size and other phenotypic characters.
T2940 10828-10996 Sentence denotes The locations of infected trees were identified and notional infection times were calculated by experienced personnel, from lesion size and other phenotypic characters.
TextSentencer_T78 10997-11191 Sentence denotes In order to account for errors in the assessment, the notional times were then grouped into 24 successive 30-day intervals (effectively used as censoring intervals for the true infection times).
T23082 10997-11191 Sentence denotes In order to account for errors in the assessment, the notional times were then grouped into 24 successive 30-day intervals (effectively used as censoring intervals for the true infection times).
TextSentencer_T79 11192-11351 Sentence denotes The data therefore provide spatial snapshots of the locations of susceptible and infected trees at successive 30-day intervals (see examples in Figures 1B,C) .
T12139 11192-11351 Sentence denotes The data therefore provide spatial snapshots of the locations of susceptible and infected trees at successive 30-day intervals (see examples in Figures 1B,C) .
TextSentencer_T80 11352-11529 Sentence denotes The incidence of disease increased rapidly at all sites during the first 18 intervals with little infection thereafter coincident with the onset of dry conditions ( Figure 1D ).
T40685 11352-11529 Sentence denotes The incidence of disease increased rapidly at all sites during the first 18 intervals with little infection thereafter coincident with the onset of dry conditions ( Figure 1D ).
TextSentencer_T81 11530-11591 Sentence denotes Further details of the collection of data are given in [28] .
T3545 11530-11591 Sentence denotes Further details of the collection of data are given in [28] .
TextSentencer_T82 11592-11816 Sentence denotes Disease was present in the area surrounding the census sites during the outbreak, with both susceptible and infected citrus trees between the sites ( Figure 1A ; see Figure S10 for a density map of citrus trees in the area).
T51960 11592-11816 Sentence denotes Disease was present in the area surrounding the census sites during the outbreak, with both susceptible and infected citrus trees between the sites ( Figure 1A ; see Figure S10 for a density map of citrus trees in the area).
TextSentencer_T83 11817-12097 Sentence denotes The data for an isolated small fifth site, also enumerated by the Agricultural Research Service (ARS) of the USDA, with a very small spread of infection around a single focus of three trees, are not analysed here because the small size of the outbreak precluded rigorous analysis.
T1502 11817-12097 Sentence denotes The data for an isolated small fifth site, also enumerated by the Agricultural Research Service (ARS) of the USDA, with a very small spread of infection around a single focus of three trees, are not analysed here because the small size of the outbreak precluded rigorous analysis.
TextSentencer_T84 12098-12226 Sentence denotes The effects of ingress of inoculum from infected trees outside the sites were incorporated into the rates for primary infection.
T91833 12098-12226 Sentence denotes The effects of ingress of inoculum from infected trees outside the sites were incorporated into the rates for primary infection.
TextSentencer_T85 12227-12424 Sentence denotes Hence, for the purposes of the analyses, in this paper each site was treated as an independent subpopulation subject to external inoculum, and parameters were assumed to be independent among sites.
T95638 12227-12424 Sentence denotes Hence, for the purposes of the analyses, in this paper each site was treated as an independent subpopulation subject to external inoculum, and parameters were assumed to be independent among sites.
TextSentencer_T86 12425-12596 Sentence denotes We consider a family of spatially-explicit, stochastic SI models for the spread of disease over time and space through a fixed population of trees (N) in each census site.
T98243 12425-12596 Sentence denotes We consider a family of spatially-explicit, stochastic SI models for the spread of disease over time and space through a fixed population of trees (N) in each census site.
TextSentencer_T87 12597-12716 Sentence denotes Sites are analysed independently and for notational simplicity the dependence of each parameter on the site is omitted.
T62681 12597-12716 Sentence denotes Sites are analysed independently and for notational simplicity the dependence of each parameter on the site is omitted.
TextSentencer_T88 12717-12761 Sentence denotes Infection sources and modes of transmission.
T62298 12717-12761 Sentence denotes Infection sources and modes of transmission.
TextSentencer_T89 12762-12949 Sentence denotes The model incorporates two sources of infection: secondary infection by tree to tree spread within census sites, and primary infection from external inoculum coming from outside the site.
T34738 12762-12949 Sentence denotes The model incorporates two sources of infection: secondary infection by tree to tree spread within census sites, and primary infection from external inoculum coming from outside the site.
TextSentencer_T90 12950-13147 Sentence denotes Secondary infection depends upon the relative locations of infected (I) and susceptible (S) trees within the site, whereas primary infection depends only upon the availability of susceptible trees.
T26815 12950-13147 Sentence denotes Secondary infection depends upon the relative locations of infected (I) and susceptible (S) trees within the site, whereas primary infection depends only upon the availability of susceptible trees.
TextSentencer_T91 13148-13343 Sentence denotes For any pair of infected (i) and susceptible (s) trees, the probability of secondary, tree-to-tree, infection within a census site depends upon the distance d is between i and s, and is given by:
T29414 13148-13343 Sentence denotes For any pair of infected (i) and susceptible (s) trees, the probability of secondary, tree-to-tree, infection within a census site depends upon the distance d is between i and s, and is given by:
TextSentencer_T92 13345-13602 Sentence denotes in which K(d; a) is a dispersal kernel with parameter a, and b is the transmission rate for infection given that inoculum from tree (i) arrives at tree (s), for a vanishingly small dt, so that no more than one infection event occurs in the interval (t,tzdt.
T59301 13345-13602 Sentence denotes in which K(d; a) is a dispersal kernel with parameter a, and b is the transmission rate for infection given that inoculum from tree (i) arrives at tree (s), for a vanishingly small dt, so that no more than one infection event occurs in the interval (t,tzdt.
TextSentencer_T93 13603-13669 Sentence denotes We extend the generic model to allow for external infection, thus:
T46152 13603-13669 Sentence denotes We extend the generic model to allow for external infection, thus:
TextSentencer_T94 13670-13761 Sentence denotes P s infected from within census site or by ð external inoculum in (t,tzdtÞ~Q s (t) dt; ð2aÞ
T84710 13670-13761 Sentence denotes P s infected from within census site or by ð external inoculum in (t,tzdtÞ~Q s (t) dt; ð2aÞ
TextSentencer_T95 13762-13903 Sentence denotes in which e is the rate of primary (external) infection per unit time and Q s (t) is the hazard, or infectious pressure, for host s at time t.
T31254 13762-13903 Sentence denotes in which e is the rate of primary (external) infection per unit time and Q s (t) is the hazard, or infectious pressure, for host s at time t.
TextSentencer_T96 13904-14041 Sentence denotes Initial inference is focused on three parameters, the primary and secondary transmission rates (e and b) and the dispersal parameter (a).
T79538 13904-14041 Sentence denotes Initial inference is focused on three parameters, the primary and secondary transmission rates (e and b) and the dispersal parameter (a).
TextSentencer_T97 14042-14100 Sentence denotes Later estimation allows for a change in b and e over time.
T73933 14042-14100 Sentence denotes Later estimation allows for a change in b and e over time.
TextSentencer_T98 14101-14268 Sentence denotes The latent period for citrus canker is short, ,7-21 days [28] relative to the timescale for infection, and shorter than the interval (30 days) used for data censoring.
T51973 14101-14268 Sentence denotes The latent period for citrus canker is short, ,7-21 days [28] relative to the timescale for infection, and shorter than the interval (30 days) used for data censoring.
TextSentencer_T99 14269-14336 Sentence denotes Hence, latent infection is not represented explicitly in our model.
T41176 14269-14336 Sentence denotes Hence, latent infection is not represented explicitly in our model.
TextSentencer_T100 14337-14395 Sentence denotes Asymptomatic infection was also not included in the model.
T45948 14337-14395 Sentence denotes Asymptomatic infection was also not included in the model.
TextSentencer_T101 14396-14540 Sentence denotes The period of asymptomatic infection has been estimated around 100 days [28] , which is not negligible compared with the timescale of infection.
T17228 14396-14540 Sentence denotes The period of asymptomatic infection has been estimated around 100 days [28] , which is not negligible compared with the timescale of infection.
TextSentencer_T102 14541-14925 Sentence denotes However, lags in the infection process due to the asymptomatic period were avoided in the analyses described here (see previous section): the dataset used for parameter estimation consists of censored infection times, estimated by pathologists at the time of detection by back calculating from symptom size and expression the likely day of infection with allowance for a 30-day error.
T97810 14541-14925 Sentence denotes However, lags in the infection process due to the asymptomatic period were avoided in the analyses described here (see previous section): the dataset used for parameter estimation consists of censored infection times, estimated by pathologists at the time of detection by back calculating from symptom size and expression the likely day of infection with allowance for a 30-day error.
TextSentencer_T103 14926-15041 Sentence denotes See the section ''Parameter estimation'' below for a test of our assumptions about latent and asymptomatic periods.
T18701 14926-15041 Sentence denotes See the section ''Parameter estimation'' below for a test of our assumptions about latent and asymptomatic periods.
TextSentencer_T104 15042-15060 Sentence denotes Spatial dispersal.
T73636 15042-15060 Sentence denotes Spatial dispersal.
TextSentencer_T105 15061-15380 Sentence denotes Here we consider a variety of models: a model with only primary infection (e.0, b = 0) in which the infected set at any time is therefore a random selection from the population, as well as spatially-structured models in which we consider dispersal kernels with and without allowance for contemporary external infection.
T59620 15061-15380 Sentence denotes Here we consider a variety of models: a model with only primary infection (e.0, b = 0) in which the infected set at any time is therefore a random selection from the population, as well as spatially-structured models in which we consider dispersal kernels with and without allowance for contemporary external infection.
TextSentencer_T106 15381-15555 Sentence denotes Several different models for dispersal (including the exponential, power law, Gaussian and Cauchy models) were screened for suitability in a preliminary analysis of the data.
T27487 15381-15555 Sentence denotes Several different models for dispersal (including the exponential, power law, Gaussian and Cauchy models) were screened for suitability in a preliminary analysis of the data.
TextSentencer_T107 15556-15743 Sentence denotes Two models, with qualitatively different behaviour, fitted substantially better than the others and were selected for comparison: these are the exponential and the Cauchy model, given by:
T58412 15556-15743 Sentence denotes Two models, with qualitatively different behaviour, fitted substantially better than the others and were selected for comparison: these are the exponential and the Cauchy model, given by:
TextSentencer_T108 15744-15860 Sentence denotes in which d is the Euclidean distance between a given pair of infected and susceptible trees, measured in kilometres.
T40014 15744-15860 Sentence denotes in which d is the Euclidean distance between a given pair of infected and susceptible trees, measured in kilometres.
TextSentencer_T109 15861-16133 Sentence denotes Both kernels in Equations 3 are isotropic, of the form K d,a ð Þ~1=(2pd)|f d; a ð Þ, where f d; a ð Þ is a one-dimensional kernel defined on the positive real axis (for the kernels in Equations 3, f d; a ð Þ is a negative exponential and half-Cauchy kernel, respectively).
T58664 15861-16133 Sentence denotes Both kernels in Equations 3 are isotropic, of the form K d,a ð Þ~1=(2pd)|f d; a ð Þ, where f d; a ð Þ is a one-dimensional kernel defined on the positive real axis (for the kernels in Equations 3, f d; a ð Þ is a negative exponential and half-Cauchy kernel, respectively).
TextSentencer_T110 16134-16230 Sentence denotes A cutoff at short distances was introduced (Text S1, Equations S5) to control kernel divergence.
T20561 16134-16230 Sentence denotes A cutoff at short distances was introduced (Text S1, Equations S5) to control kernel divergence.
TextSentencer_T111 16231-16474 Sentence denotes We remark that, owing to the kernel normalisation chosen in Equations 3, the secondary transmission rate b is measured in days 21 km 2 , while the primary transmission rate e is measured in days 21 (see Text S1 for a discussion of this point).
T6815 16231-16474 Sentence denotes We remark that, owing to the kernel normalisation chosen in Equations 3, the secondary transmission rate b is measured in days 21 km 2 , while the primary transmission rate e is measured in days 21 (see Text S1 for a discussion of this point).
TextSentencer_T112 16475-16543 Sentence denotes The dispersal models differ with respect to the patterns of disease.
T34759 16475-16543 Sentence denotes The dispersal models differ with respect to the patterns of disease.
TextSentencer_T113 16544-16795 Sentence denotes Whereas exponentially bounded models (such as the exponential) give rise to spreading waves of new infected sites (trees), heavier tailed kernels (such as the Cauchy) result in more dispersed daughter foci ahead of the initial site of infection [33] .
T9168 16544-16795 Sentence denotes Whereas exponentially bounded models (such as the exponential) give rise to spreading waves of new infected sites (trees), heavier tailed kernels (such as the Cauchy) result in more dispersed daughter foci ahead of the initial site of infection [33] .
TextSentencer_T114 16796-17064 Sentence denotes The introduction of an external infection rate was supported by the presence of infected hosts around the sites (see also Figure S10 for the population densities), and supplies the system with additional, randomly located primary infections throughout the entire plot.
T52536 16796-17064 Sentence denotes The introduction of an external infection rate was supported by the presence of infected hosts around the sites (see also Figure S10 for the population densities), and supplies the system with additional, randomly located primary infections throughout the entire plot.
TextSentencer_T115 17065-17217 Sentence denotes The transmission (e, b) and dispersal (a) parameters were estimated by Bayesian inference using Markov chain Monte Carlo methods with data augmentation.
T64143 17065-17217 Sentence denotes The transmission (e, b) and dispersal (a) parameters were estimated by Bayesian inference using Markov chain Monte Carlo methods with data augmentation.
TextSentencer_T116 17218-17375 Sentence denotes Let T min ,T max ½ be the time span of experimental observations, i a host infected at time t i (t i vT max ), and s a host still susceptible at time T max .
T56806 17218-17375 Sentence denotes Let T min ,T max ½ be the time span of experimental observations, i a host infected at time t i (t i vT max ), and s a host still susceptible at time T max .
TextSentencer_T117 17376-17461 Sentence denotes If infection times were known the likelihood function could be calculated as follows:
T20976 17376-17461 Sentence denotes If infection times were known the likelihood function could be calculated as follows:
TextSentencer_T118 17462-17538 Sentence denotes where Q j (t) is the infectious pressure for host j at time t (Equation 2b).
T70181 17462-17538 Sentence denotes where Q j (t) is the infectious pressure for host j at time t (Equation 2b).
TextSentencer_T119 17539-17741 Sentence denotes However, the data are actually censored, and the likelihood involves integrating over the unobserved infection times consistent with the data: f censored dataDa,b,e ð Þ Ð f uncensored dataDa,b,e ð Þ dt.
T56442 17539-17741 Sentence denotes However, the data are actually censored, and the likelihood involves integrating over the unobserved infection times consistent with the data: f censored dataDa,b,e ð Þ Ð f uncensored dataDa,b,e ð Þ dt.
TextSentencer_T120 17742-18039 Sentence denotes The posterior for a,b,e ð Þ can then be obtained by extending the parameter vector to a,b,e,t 1 ,t 2 , . . . ð Þ [H, i.e. including the unobserved event times as parameters, and using MCMC to explore the augmented parameter space H [34, 35] (for recent applications see e.g. [21, [36] [37] [38] ).
T61244 17742-18039 Sentence denotes The posterior for a,b,e ð Þ can then be obtained by extending the parameter vector to a,b,e,t 1 ,t 2 , . . . ð Þ [H, i.e. including the unobserved event times as parameters, and using MCMC to explore the augmented parameter space H [34, 35] (for recent applications see e.g. [21, [36] [37] [38] ).
TextSentencer_T121 18040-18091 Sentence denotes The marginal for a,b,e ð Þis the desired posterior.
T78745 18040-18091 Sentence denotes The marginal for a,b,e ð Þis the desired posterior.
TextSentencer_T122 18092-18232 Sentence denotes Independent uniform priors over the regions of interest were taken for all parameters, with support coinciding with the following intervals:
T87107 18092-18232 Sentence denotes Independent uniform priors over the regions of interest were taken for all parameters, with support coinciding with the following intervals:
TextSentencer_T123 18233-18298 Sentence denotes 0, 1 ½ km for a; 0, 1 ½ days 21 km 2 for b; 0, 1 ½ days 21 for e.
T57065 18233-18298 Sentence denotes 0, 1 ½ km for a; 0, 1 ½ days 21 km 2 for b; 0, 1 ½ days 21 for e.
TextSentencer_T124 18299-18527 Sentence denotes A Metropolis-Hastings algorithm with independent Gaussian proposal distributions [39] was used for parameters a, b, e, adjusting the width of the distributions to obtain an acceptance rate between 0.2 and 0.4 for each parameter.
T82106 18299-18527 Sentence denotes A Metropolis-Hastings algorithm with independent Gaussian proposal distributions [39] was used for parameters a, b, e, adjusting the width of the distributions to obtain an acceptance rate between 0.2 and 0.4 for each parameter.
TextSentencer_T125 18528-18640 Sentence denotes The proposal distribution for augmented infection times was constant over the corresponding censoring intervals.
T49600 18528-18640 Sentence denotes The proposal distribution for augmented infection times was constant over the corresponding censoring intervals.
TextSentencer_T126 18641-18913 Sentence denotes Each Monte Carlo chain was run for 100000-250000 steps (depending on the system size and the temporal window used, see below), and a burnin period corresponding to the initial 10% of the chain was discarded before the analysis, to ensure that convergence had been reached.
T85094 18641-18913 Sentence denotes Each Monte Carlo chain was run for 100000-250000 steps (depending on the system size and the temporal window used, see below), and a burnin period corresponding to the initial 10% of the chain was discarded before the analysis, to ensure that convergence had been reached.
TextSentencer_T127 18914-19202 Sentence denotes Sensitivity analysis was used to test the two assumptions: (i) that the existence of a latent period (,7-21 days) can be ignored; (ii) that the specific choice of a 30-day censoring interval for true infection times was appropriate given the length of the asymptomatic period (,100 days).
T89288 18914-19202 Sentence denotes Sensitivity analysis was used to test the two assumptions: (i) that the existence of a latent period (,7-21 days) can be ignored; (ii) that the specific choice of a 30-day censoring interval for true infection times was appropriate given the length of the asymptomatic period (,100 days).
TextSentencer_T128 19203-19331 Sentence denotes For the first assumption, we compared the fit of the default model with that of a model with a constant latent period (14 days).
T46151 19203-19331 Sentence denotes For the first assumption, we compared the fit of the default model with that of a model with a constant latent period (14 days).
TextSentencer_T129 19332-19574 Sentence denotes For the asymptomatic period, we compared the default model with a model fitted to a dataset where the censoring intervals for all infection times were artificially extended to 90 days (with the same midpoints as the original 30day intervals).
T68392 19332-19574 Sentence denotes For the asymptomatic period, we compared the default model with a model fitted to a dataset where the censoring intervals for all infection times were artificially extended to 90 days (with the same midpoints as the original 30day intervals).
TextSentencer_T130 19575-19689 Sentence denotes The candidate models were compared for each site separately using the deviance information criterion (DIC, [40] ).
T14884 19575-19689 Sentence denotes The candidate models were compared for each site separately using the deviance information criterion (DIC, [40] ).
TextSentencer_T131 19690-19992 Sentence denotes The objective is to consider whether or not there is evidence for spatially dependent secondary challenge rather than homogeneous primary challenge only, then to distinguish between kernels and whether or not there is evidence for a combination of external (primary) and internal (secondary) infection.
T44300 19690-19992 Sentence denotes The objective is to consider whether or not there is evidence for spatially dependent secondary challenge rather than homogeneous primary challenge only, then to distinguish between kernels and whether or not there is evidence for a combination of external (primary) and internal (secondary) infection.
TextSentencer_T132 19993-20089 Sentence denotes The adaptation (DIC 6 ) of the DIC suggested in [41] was used to account for the augmented data.
T36630 19993-20089 Sentence denotes The adaptation (DIC 6 ) of the DIC suggested in [41] was used to account for the augmented data.
TextSentencer_T133 20090-20289 Sentence denotes Following analysis of the entire dataset of 24 successive monthly snapshots of disease, parameters were estimated for subsets of the data in order to identify trends in parameter estimates over time.
T23101 20090-20289 Sentence denotes Following analysis of the entire dataset of 24 successive monthly snapshots of disease, parameters were estimated for subsets of the data in order to identify trends in parameter estimates over time.
TextSentencer_T134 20290-20446 Sentence denotes We also used the analyses to infer what effects additional snapshots or different starting times for data collection would have had on epidemic predictions.
T6903 20290-20446 Sentence denotes We also used the analyses to infer what effects additional snapshots or different starting times for data collection would have had on epidemic predictions.
TextSentencer_T135 20447-20681 Sentence denotes For subsequent analyses, we introduce a classification of the models (Table 1 ) based upon the temporal window used for the estimation (with no reference to the specific form of the dispersal kernel) and the number of parameters used.
T49808 20447-20681 Sentence denotes For subsequent analyses, we introduce a classification of the models (Table 1 ) based upon the temporal window used for the estimation (with no reference to the specific form of the dispersal kernel) and the number of parameters used.
TextSentencer_T136 20682-20774 Sentence denotes The original three-parameter model, fitted to the entire dataset, will be denoted with M 0 .
T17164 20682-20774 Sentence denotes The original three-parameter model, fitted to the entire dataset, will be denoted with M 0 .
TextSentencer_T137 20775-21009 Sentence denotes Cumulative windows (model M cum in Table 1 ) were used to identify the effect of recording more and more snapshots over time on the parameter estimates, by deriving estimates based upon snapshots for 0-3, 0-6, … 0-24 30-day intervals.
T24450 20775-21009 Sentence denotes Cumulative windows (model M cum in Table 1 ) were used to identify the effect of recording more and more snapshots over time on the parameter estimates, by deriving estimates based upon snapshots for 0-3, 0-6, … 0-24 30-day intervals.
TextSentencer_T138 21010-21363 Sentence denotes Sliding windows, for example 0-6, 3-9, …12-18 30-day intervals (model M DT slid in Table 1 , with DT equal to the window width), were used to assess the effects of different starting times for data collection and fixed periods of observation on parameter estimates (hence, they represent scenarios for later detection and initiation of data collection).
T52106 21010-21363 Sentence denotes Sliding windows, for example 0-6, 3-9, …12-18 30-day intervals (model M DT slid in Table 1 , with DT equal to the window width), were used to assess the effects of different starting times for data collection and fixed periods of observation on parameter estimates (hence, they represent scenarios for later detection and initiation of data collection).
TextSentencer_T139 21364-21420 Sentence denotes Two additional models were fitted to the entire dataset.
T87947 21364-21420 Sentence denotes Two additional models were fitted to the entire dataset.
TextSentencer_T140 21421-21615 Sentence denotes Rather than representing scenarios where observation is initiated at different times, as for the sliding-window estimates, these models, like model M 0 , are post facto analyses of the epidemic.
T92348 21421-21615 Sentence denotes Rather than representing scenarios where observation is initiated at different times, as for the sliding-window estimates, these models, like model M 0 , are post facto analyses of the epidemic.
TextSentencer_T141 21616-21956 Sentence denotes In a four parameter model, henceforth denoted with M V (cf. Table 1) , a and e are constant over time (as in model M 0 ), while the secondary transmission rate is a continuous, linearly decreasing Table 1 ) has heterogeneous time scales for the parameters, with a constant for the whole dataset and rates b and e changing by time intervals.
T98801 21616-21956 Sentence denotes In a four parameter model, henceforth denoted with M V (cf. Table 1) , a and e are constant over time (as in model M 0 ), while the secondary transmission rate is a continuous, linearly decreasing Table 1 ) has heterogeneous time scales for the parameters, with a constant for the whole dataset and rates b and e changing by time intervals.
TextSentencer_T142 21957-22178 Sentence denotes Essentially, this approach implies: choosing a time resolution (e.g., DT = six months) for the rates b t and e t ; partitioning the whole epidemic time span into regular intervals (e.g., for DT = 6 months, four intervals:
T93896 21957-22178 Sentence denotes Essentially, this approach implies: choosing a time resolution (e.g., DT = six months) for the rates b t and e t ; partitioning the whole epidemic time span into regular intervals (e.g., for DT = 6 months, four intervals:
TextSentencer_T143 22179-22381 Sentence denotes 0-6, 6-12, 12-18, and 18-24 months); fitting different b t and e t to each time interval (in the same example, four secondary rates b t and four primary rates e t ), but a single a to all the intervals.
T61474 22179-22381 Sentence denotes 0-6, 6-12, 12-18, and 18-24 months); fitting different b t and e t to each time interval (in the same example, four secondary rates b t and four primary rates e t ), but a single a to all the intervals.
TextSentencer_T144 22382-22463 Sentence denotes We assess the hypothesis that parameters vary spatially between sites as follows.
T29690 22382-22463 Sentence denotes We assess the hypothesis that parameters vary spatially between sites as follows.
TextSentencer_T145 22464-22697 Sentence denotes The model is fitted to pairs of sites J and K independently (J, K = B1, B2, D1, D2), yielding a sample from the marginal distribution, e.g., for b J and b K (and similarly for the other parameters) for each of the sites respectively.
T60254 22464-22697 Sentence denotes The model is fitted to pairs of sites J and K independently (J, K = B1, B2, D1, D2), yielding a sample from the marginal distribution, e.g., for b J and b K (and similarly for the other parameters) for each of the sites respectively.
TextSentencer_T146 22698-22937 Sentence denotes Under the prior assumption of independence of parameters amongst sites, we can then build a joint posterior distribution for b J and b K , and empirically evaluate the probability p JK b ð Þ~Pr b J wb K Dcensored ð data for sites J and KÞ.
T52433 22698-22937 Sentence denotes Under the prior assumption of independence of parameters amongst sites, we can then build a joint posterior distribution for b J and b K , and empirically evaluate the probability p JK b ð Þ~Pr b J wb K Dcensored ð data for sites J and KÞ.
TextSentencer_T147 22938-23186 Sentence denotes Should p JK b ð Þ be near 1 or 0, there is evidence that there is a difference in parameter values between sites; if intermediate, the joint posterior straddles the line of equality and we cannot conclude in which location the parameter is greater.
T18684 22938-23186 Sentence denotes Should p JK b ð Þ be near 1 or 0, there is evidence that there is a difference in parameter values between sites; if intermediate, the joint posterior straddles the line of equality and we cannot conclude in which location the parameter is greater.
TextSentencer_T148 23187-23222 Sentence denotes Further details are given in [42] .
T19319 23187-23222 Sentence denotes Further details are given in [42] .
TextSentencer_T149 23223-23362 Sentence denotes Goodness-of-fit was tested for parameter estimates from different types of temporal windows using posterior predictive distributions [43] .
T24709 23223-23362 Sentence denotes Goodness-of-fit was tested for parameter estimates from different types of temporal windows using posterior predictive distributions [43] .
TextSentencer_T150 23363-23756 Sentence denotes For each time window (delimited by times t 0 and t 1 , with t 0~0 for cumulative windows), a stochastic, spatially explicit model, based upon Equations 2, with parameter values sampled from the posterior distribution, was used to generate a large number (1000) of replicate epidemics, running from time t 0 (with initial conditions set according to the recorded infection status) to time t 1 .
T30352 23363-23756 Sentence denotes For each time window (delimited by times t 0 and t 1 , with t 0~0 for cumulative windows), a stochastic, spatially explicit model, based upon Equations 2, with parameter values sampled from the posterior distribution, was used to generate a large number (1000) of replicate epidemics, running from time t 0 (with initial conditions set according to the recorded infection status) to time t 1 .
TextSentencer_T151 23757-23987 Sentence denotes Three summary statistics were stored for each simulation: the count of infected trees, I(t), and two spatial statistics, the autocorrelation function C t (d) and the ''time-lagged'' statistic R t t0 (d), described in detail below.
T26240 23757-23987 Sentence denotes Three summary statistics were stored for each simulation: the count of infected trees, I(t), and two spatial statistics, the autocorrelation function C t (d) and the ''time-lagged'' statistic R t t0 (d), described in detail below.
TextSentencer_T152 23988-24321 Sentence denotes The posterior predictive distributions for stored values of I(t), C t (d), and R t t0 (d) (henceforth, simulated summary statistics), at times t corresponding to experimental snapshots, were then compared with the corresponding summary statistics extracted from the experimental dataset (henceforth, experimental summary statistics).
T39217 23988-24321 Sentence denotes The posterior predictive distributions for stored values of I(t), C t (d), and R t t0 (d) (henceforth, simulated summary statistics), at times t corresponding to experimental snapshots, were then compared with the corresponding summary statistics extracted from the experimental dataset (henceforth, experimental summary statistics).
TextSentencer_T153 24322-24347 Sentence denotes Autocorrelation function.
T76354 24322-24347 Sentence denotes Autocorrelation function.
TextSentencer_T154 24348-24479 Sentence denotes We introduce the following definitions: n(d) is the number of all tree-tree pairs separated by a distance d in a given census site;
T53320 24348-24479 Sentence denotes We introduce the following definitions: n(d) is the number of all tree-tree pairs separated by a distance d in a given census site;
TextSentencer_T155 24480-24559 Sentence denotes is the corresponding fraction of infected-infected pairs a distance d Table 1 .
T76877 24480-24559 Sentence denotes is the corresponding fraction of infected-infected pairs a distance d Table 1 .
TextSentencer_T156 24560-24726 Sentence denotes Main models used in the paper, classified according to the time-dependence of parameters. apart at time T; r I (T)~I(T)=N is the fraction of infected hosts at time T.
T71786 24560-24726 Sentence denotes Main models used in the paper, classified according to the time-dependence of parameters. apart at time T; r I (T)~I(T)=N is the fraction of infected hosts at time T.
TextSentencer_T157 24727-24813 Sentence denotes The spatial autocorrelation function at distance d can be defined (see e.g. [44] ) as:
T7946 24727-24813 Sentence denotes The spatial autocorrelation function at distance d can be defined (see e.g. [44] ) as:
TextSentencer_T158 24814-24897 Sentence denotes The non-parametric estimator used here for C T (d) is the spline correlogram [45] .
T75473 24814-24897 Sentence denotes The non-parametric estimator used here for C T (d) is the spline correlogram [45] .
TextSentencer_T159 24898-25100 Sentence denotes A 95% confidence interval for the estimated experimental autocorrelation function was calculated from 1000 bootstrapped datasets, generated from the experimental data, using a dedicated algorithm [45] .
T13995 24898-25100 Sentence denotes A 95% confidence interval for the estimated experimental autocorrelation function was calculated from 1000 bootstrapped datasets, generated from the experimental data, using a dedicated algorithm [45] .
TextSentencer_T160 25101-25303 Sentence denotes Finally, the statistical significance of autocorrelation functions was evaluated by generating 1000 simulated datasets where the infection status of each host was re-allocated randomly (see e.g. [46] ).
T54184 25101-25303 Sentence denotes Finally, the statistical significance of autocorrelation functions was evaluated by generating 1000 simulated datasets where the infection status of each host was re-allocated randomly (see e.g. [46] ).
TextSentencer_T161 25304-25417 Sentence denotes We refer the reader to Text S1 for a brief introduction to spline correlogram calculation and related techniques.
T51787 25304-25417 Sentence denotes We refer the reader to Text S1 for a brief introduction to spline correlogram calculation and related techniques.
TextSentencer_T162 25418-25448 Sentence denotes Time-lagged spatial statistic.
T9467 25418-25448 Sentence denotes Time-lagged spatial statistic.
TextSentencer_T163 25449-25669 Sentence denotes When t 0 w0, the spatial autocorrelation function between all infected trees at time T is inevitably offset by the spatial configuration of trees already infected at time t 0 , especially in later stages of the epidemic.
T74482 25449-25669 Sentence denotes When t 0 w0, the spatial autocorrelation function between all infected trees at time T is inevitably offset by the spatial configuration of trees already infected at time t 0 , especially in later stages of the epidemic.
TextSentencer_T164 25670-25902 Sentence denotes It is then useful to introduce a statistic that measures the spatial association between ''mother foci'' (henceforth, M), i.e., trees infected at t 0 , and ''daughter foci'' (henceforth, D), i.e., trees becoming infected after t 0 .
T34884 25670-25902 Sentence denotes It is then useful to introduce a statistic that measures the spatial association between ''mother foci'' (henceforth, M), i.e., trees infected at t 0 , and ''daughter foci'' (henceforth, D), i.e., trees becoming infected after t 0 .
TextSentencer_T165 25903-26051 Sentence denotes We define n MS (d; t 0 ) as the number of pairs at time t 0 that comprise an infected tree (mother focus) and a susceptible tree a distance d apart.
T55112 25903-26051 Sentence denotes We define n MS (d; t 0 ) as the number of pairs at time t 0 that comprise an infected tree (mother focus) and a susceptible tree a distance d apart.
TextSentencer_T166 26052-26192 Sentence denotes At time Twt 0 , a number n MD (d; T) of those initial infected-susceptible pairs have turned into infected-infected (mother-daughter) pairs.
T93544 26052-26192 Sentence denotes At time Twt 0 , a number n MD (d; T) of those initial infected-susceptible pairs have turned into infected-infected (mother-daughter) pairs.
TextSentencer_T167 26193-26402 Sentence denotes If spatial dependence is ignored, the probability for any M-S pair at time t 0 to become an M-D pair by time T coincides with the probability for an initially susceptible host to be infected between t 0 and T:
T66204 26193-26402 Sentence denotes If spatial dependence is ignored, the probability for any M-S pair at time t 0 to become an M-D pair by time T coincides with the probability for an initially susceptible host to be infected between t 0 and T:
TextSentencer_T168 26403-26579 Sentence denotes If there is spatial dependence, the probability of observing an M-D pair is affected by d, and the observed number n MD (d; T) can differ significantly from the expected value.
T90909 26403-26579 Sentence denotes If there is spatial dependence, the probability of observing an M-D pair is affected by d, and the observed number n MD (d; T) can differ significantly from the expected value.
TextSentencer_T169 26580-26648 Sentence denotes Such difference is measured by the time-lagged statistic R T t0 (d):
T85957 26580-26648 Sentence denotes Such difference is measured by the time-lagged statistic R T t0 (d):
TextSentencer_T170 26649-26654 Sentence denotes where
T23818 26649-26654 Sentence denotes where
TextSentencer_T171 26655-26657 Sentence denotes ).
T39568 26655-26657 Sentence denotes ).
TextSentencer_T172 26658-26907 Sentence denotes The same techniques described above for spline correlogram estimation were used to obtain smoothed, non-parametric estimates of R T t 0 (d), confidence intervals for experimental estimates, and regions of significance (see Text S1 for more details).
T22144 26658-26907 Sentence denotes The same techniques described above for spline correlogram estimation were used to obtain smoothed, non-parametric estimates of R T t 0 (d), confidence intervals for experimental estimates, and regions of significance (see Text S1 for more details).
TextSentencer_T173 26908-27078 Sentence denotes A stochastic, spatially-explicit model, based upon Equations 2, with parameters estimated from different time periods, was used to predict future progress of the disease.
T61369 26908-27078 Sentence denotes A stochastic, spatially-explicit model, based upon Equations 2, with parameters estimated from different time periods, was used to predict future progress of the disease.
TextSentencer_T174 27079-27342 Sentence denotes Large numbers (1000) of replicate epidemics were generated in each of the census sites, with the susceptible trees located according to the original map for each site and initial conditions set according to the recorded infection status at the time of prediction.
T23906 27079-27342 Sentence denotes Large numbers (1000) of replicate epidemics were generated in each of the census sites, with the susceptible trees located according to the original map for each site and initial conditions set according to the recorded infection status at the time of prediction.
TextSentencer_T175 27343-27483 Sentence denotes A variety of models were compared, comprising secondary infection kernels with and without external infection, and external infection alone.
T56695 27343-27483 Sentence denotes A variety of models were compared, comprising secondary infection kernels with and without external infection, and external infection alone.
TextSentencer_T176 27484-27650 Sentence denotes The deviance information criterion (DIC 6 ) strongly supported spatially structured models with additional external infection as the most plausible at all four sites.
T68457 27484-27650 Sentence denotes The deviance information criterion (DIC 6 ) strongly supported spatially structured models with additional external infection as the most plausible at all four sites.
TextSentencer_T177 27651-27914 Sentence denotes We conclude that, while the epidemic is largely driven by secondary infection between infected and susceptible trees within each site, there are sufficient numbers of isolated new foci at each site to infer that external infection continues to perturb the system.
T88687 27651-27914 Sentence denotes We conclude that, while the epidemic is largely driven by secondary infection between infected and susceptible trees within each site, there are sufficient numbers of isolated new foci at each site to infer that external infection continues to perturb the system.
TextSentencer_T178 27915-28031 Sentence denotes Such disturbance is consistent with long distance dispersal that is known to occur during tropical storms [29, 32] .
T62510 27915-28031 Sentence denotes Such disturbance is consistent with long distance dispersal that is known to occur during tropical storms [29, 32] .
TextSentencer_T179 28032-28297 Sentence denotes While DIC 6 did clearly select for the exponential and Cauchy models with external infection as the most plausible at all sites, amongst all models tested in post hoc analysis of the data, it did not give decisive overall support for either (Text S1 and Table S1 ).
T5597 28032-28297 Sentence denotes While DIC 6 did clearly select for the exponential and Cauchy models with external infection as the most plausible at all sites, amongst all models tested in post hoc analysis of the data, it did not give decisive overall support for either (Text S1 and Table S1 ).
TextSentencer_T180 28298-28527 Sentence denotes The main reason for this, for which we refer the reader to the Discussion and Text S1, is the difficulty in discriminating between long-range dispersal, occurring within a census site, and primary infection incoming from outside.
T21549 28298-28527 Sentence denotes The main reason for this, for which we refer the reader to the Discussion and Text S1, is the difficulty in discriminating between long-range dispersal, occurring within a census site, and primary infection incoming from outside.
TextSentencer_T181 28528-28646 Sentence denotes All subsequent analyses apply to the more conservative model with exponential dispersal kernel and external infection.
T70847 28528-28646 Sentence denotes All subsequent analyses apply to the more conservative model with exponential dispersal kernel and external infection.
TextSentencer_T182 28647-28780 Sentence denotes We remark, however, that the results shown below are very similar when using estimates from the Cauchy model with external infection.
T67366 28647-28780 Sentence denotes We remark, however, that the results shown below are very similar when using estimates from the Cauchy model with external infection.
TextSentencer_T183 28781-28929 Sentence denotes Having selected the exponential model from a post hoc analysis, we now investigate parameter estimation for this model from early disease snapshots.
T53188 28781-28929 Sentence denotes Having selected the exponential model from a post hoc analysis, we now investigate parameter estimation for this model from early disease snapshots.
TextSentencer_T184 28930-28998 Sentence denotes The kernel type itself could not be identified from early snapshots.
T19853 28930-28998 Sentence denotes The kernel type itself could not be identified from early snapshots.
TextSentencer_T185 28999-29337 Sentence denotes Our situation is therefore analogous to a broad class of epidemics in which prior evidence would favour a particular model (here the exponential, or equivalently the Cauchy kernel) and the question is then how soon can the parameters be estimated during an emerging epidemics (see Discussion for further consideration of model selection).
T37603 28999-29337 Sentence denotes Our situation is therefore analogous to a broad class of epidemics in which prior evidence would favour a particular model (here the exponential, or equivalently the Cauchy kernel) and the question is then how soon can the parameters be estimated during an emerging epidemics (see Discussion for further consideration of model selection).
TextSentencer_T186 29338-29531 Sentence denotes The posterior distributions for the dispersal kernel (a), transmission rate (b), and the ingress of external inoculum (e) are summarised in Figure 2 for one of the sites (B2) in Broward county.
T60507 29338-29531 Sentence denotes The posterior distributions for the dispersal kernel (a), transmission rate (b), and the ingress of external inoculum (e) are summarised in Figure 2 for one of the sites (B2) in Broward county.
TextSentencer_T187 29532-29710 Sentence denotes The results show the sensitivity of the posterior distributions of the parameters to the observation time window (cf. Table 1 ); similar results were obtained for all four sites.
T59414 29532-29710 Sentence denotes The results show the sensitivity of the posterior distributions of the parameters to the observation time window (cf. Table 1 ); similar results were obtained for all four sites.
TextSentencer_T188 29711-29892 Sentence denotes Initial inferences were done for cumulative windows (model M cum , Table 1 ), in which successively more monthly snapshots of the locations of infected and healthy trees were added.
T57357 29711-29892 Sentence denotes Initial inferences were done for cumulative windows (model M cum , Table 1 ), in which successively more monthly snapshots of the locations of infected and healthy trees were added.
TextSentencer_T189 29893-30041 Sentence denotes These results show how the availability of additional information during the epidemic affects the precision of the parameter estimates (Figure 2A) .
T42660 29893-30041 Sentence denotes These results show how the availability of additional information during the epidemic affects the precision of the parameter estimates (Figure 2A) .
TextSentencer_T190 30042-30082 Sentence denotes The estimate for a is remarkably robust.
T80272 30042-30082 Sentence denotes The estimate for a is remarkably robust.
TextSentencer_T191 30083-30258 Sentence denotes There is a short, initial transient period (0-3 30-day periods) for which the parameter is not well estimated, by the end of which there are fewer than 21/1113 infected trees.
T94188 30083-30258 Sentence denotes There is a short, initial transient period (0-3 30-day periods) for which the parameter is not well estimated, by the end of which there are fewer than 21/1113 infected trees.
TextSentencer_T192 30259-30442 Sentence denotes Later estimates were remarkably close both in expectation and precision, with no further gain in precision after six months (Figure 2A) , when 69/1113 trees were recorded as infected.
T93872 30259-30442 Sentence denotes Later estimates were remarkably close both in expectation and precision, with no further gain in precision after six months (Figure 2A) , when 69/1113 trees were recorded as infected.
TextSentencer_T193 30443-30561 Sentence denotes There were clear trends in both the expectation and the precision of estimates for the secondary transmission rate, b.
T65194 30443-30561 Sentence denotes There were clear trends in both the expectation and the precision of estimates for the secondary transmission rate, b.
TextSentencer_T194 30562-30780 Sentence denotes As in the case of a, the posterior distribution for b had a large variance when based upon data for the first three months, and adding extra monthly snapshots decreased the variance of the posterior (cf Figures 2B,E) .
T1885 30562-30780 Sentence denotes As in the case of a, the posterior distribution for b had a large variance when based upon data for the first three months, and adding extra monthly snapshots decreased the variance of the posterior (cf Figures 2B,E) .
TextSentencer_T195 30781-30891 Sentence denotes In contrast with the case of a, there was also a trend in the posteriors for b to decrease as time progressed.
T58949 30781-30891 Sentence denotes In contrast with the case of a, there was also a trend in the posteriors for b to decrease as time progressed.
TextSentencer_T196 30892-31120 Sentence denotes The trend in b is more appropriately characterised by the sliding windows ( Figure 2E ), in which estimates are averaged over successive but overlapping six 30-day intervals (cf. model M DT slid in Table 1 , with DT = 6 months).
T81531 30892-31120 Sentence denotes The trend in b is more appropriately characterised by the sliding windows ( Figure 2E ), in which estimates are averaged over successive but overlapping six 30-day intervals (cf. model M DT slid in Table 1 , with DT = 6 months).
TextSentencer_T197 31121-31257 Sentence denotes Similar results were obtained for e ( Figures 2C,F) , suggesting that both forms of transmission were driven by environmental variables.
T46437 31121-31257 Sentence denotes Similar results were obtained for e ( Figures 2C,F) , suggesting that both forms of transmission were driven by environmental variables.
TextSentencer_T198 31258-31398 Sentence denotes Epidemics were dominated by secondary over primary infection: the forces of infection corresponding to b were much greater than those for e.
T79851 31258-31398 Sentence denotes Epidemics were dominated by secondary over primary infection: the forces of infection corresponding to b were much greater than those for e.
TextSentencer_T199 31399-31502 Sentence denotes Hence, in the following we will focus our analysis of environmental trends on the time dependence of b.
T22647 31399-31502 Sentence denotes Hence, in the following we will focus our analysis of environmental trends on the time dependence of b.
TextSentencer_T200 31503-31816 Sentence denotes The robustness of sliding-window estimates for a to different estimation periods motivates the following assumption: environmental fluctuations affect the model only through primary and secondary infection rates, while the short-range dispersal scale a remains constant at each census site all along the epidemic.
T79671 31503-31816 Sentence denotes The robustness of sliding-window estimates for a to different estimation periods motivates the following assumption: environmental fluctuations affect the model only through primary and secondary infection rates, while the short-range dispersal scale a remains constant at each census site all along the epidemic.
TextSentencer_T201 31817-32112 Sentence denotes We integrated this assumption into our estimations, and fitted to the entire dataset model M DT a , with heterogeneous time scales for the parameters (cf. model Table 1 and Methods), where a was kept constant for the whole epidemic history, while the rates b t and e t changed with frequency DT.
T16181 31817-32112 Sentence denotes We integrated this assumption into our estimations, and fitted to the entire dataset model M DT a , with heterogeneous time scales for the parameters (cf. model Table 1 and Methods), where a was kept constant for the whole epidemic history, while the rates b t and e t changed with frequency DT.
TextSentencer_T202 32113-32263 Sentence denotes All the analyses from now on concern model M DT a , and focus on two different time intervals for the infection rates, obeying two different purposes.
T16162 32113-32263 Sentence denotes All the analyses from now on concern model M DT a , and focus on two different time intervals for the infection rates, obeying two different purposes.
TextSentencer_T203 32264-32488 Sentence denotes The first, DT = 6 months, is intended to capture the main temporal trend in rates; the second, DT = 1 month (corresponding to the highest possible resolution given data censoring), is used to analyse short-time fluctuations.
T39081 32264-32488 Sentence denotes The first, DT = 6 months, is intended to capture the main temporal trend in rates; the second, DT = 1 month (corresponding to the highest possible resolution given data censoring), is used to analyse short-time fluctuations.
TextSentencer_T204 32489-32520 Sentence denotes In Figure 3A , (Figures 3F-I) .
T65015 32489-32520 Sentence denotes In Figure 3A , (Figures 3F-I) .
TextSentencer_T205 32521-32730 Sentence denotes The decreasing trend in b can be partly explained by previous investigations [28] , which suggested that the epidemic slowed down after ,12 months because of the onset of an unusually prolonged drought period.
T21206 32521-32730 Sentence denotes The decreasing trend in b can be partly explained by previous investigations [28] , which suggested that the epidemic slowed down after ,12 months because of the onset of an unusually prolonged drought period.
TextSentencer_T206 32731-33044 Sentence denotes Moreover, there is compelling evidence [28] that the three main peaks in the monthly time series for b t (see e.g. months 6, 11, and 15 in Figure 3H for site D1, and similar times for the other three sites) were associated with major rainstorm events (strong wind gusts, combined with rainfall) in the Miami area.
T95697 32731-33044 Sentence denotes Moreover, there is compelling evidence [28] that the three main peaks in the monthly time series for b t (see e.g. months 6, 11, and 15 in Figure 3H for site D1, and similar times for the other three sites) were associated with major rainstorm events (strong wind gusts, combined with rainfall) in the Miami area.
TextSentencer_T207 33045-33090 Sentence denotes For each census site, the decreasing trend is
T1435 33045-33090 Sentence denotes For each census site, the decreasing trend is
TextSentencer_T208 33092-33175 Sentence denotes There was evidence of strong consistency for posterior distributions amongst sites.
T4522 33092-33175 Sentence denotes There was evidence of strong consistency for posterior distributions amongst sites.
TextSentencer_T209 33176-33349 Sentence denotes This is shown in Figure 4A correspondence of magnitudes and trends in b t between the two Broward sites (Figure 4A ), which are located close to each other (cf. Figure 1A) .
T94009 33176-33349 Sentence denotes This is shown in Figure 4A correspondence of magnitudes and trends in b t between the two Broward sites (Figure 4A ), which are located close to each other (cf. Figure 1A) .
TextSentencer_T210 33350-33533 Sentence denotes The more distant Dade sites ( Figure 4B ) are themselves more distantly separated than the Broward sites (cf. Figure 1A) and show at first a less consistent pattern (see Figure S8 ).
T40347 33350-33533 Sentence denotes The more distant Dade sites ( Figure 4B ) are themselves more distantly separated than the Broward sites (cf. Figure 1A) and show at first a less consistent pattern (see Figure S8 ).
TextSentencer_T211 33534-33682 Sentence denotes However, if we allow for a 1-month lag in the rates between D1 and D2, the two series of estimates display again a strong correlation ( Figure 4B ).
T26304 33534-33682 Sentence denotes However, if we allow for a 1-month lag in the rates between D1 and D2, the two series of estimates display again a strong correlation ( Figure 4B ).
TextSentencer_T212 33683-33816 Sentence denotes Such a time lag would be consistent with delayed introduction of the pathogen or the vector, but awaits further analysis and testing.
T34844 33683-33816 Sentence denotes Such a time lag would be consistent with delayed introduction of the pathogen or the vector, but awaits further analysis and testing.
TextSentencer_T213 33817-33947 Sentence denotes Similar, yet more regular patterns at all four sites emerge when comparing estimates at resolution DT = 6 months (see Figure S9 ).
T34254 33817-33947 Sentence denotes Similar, yet more regular patterns at all four sites emerge when comparing estimates at resolution DT = 6 months (see Figure S9 ).
TextSentencer_T214 33948-34182 Sentence denotes In Figure 5 , we show the results of goodness-of-fit tests for the constant-dispersal model M DT a , DT = 6 months (cf. Table 1 ), for one of the Dade sites (D1; analogous results for the other sites are shown in Figures S2, S3, S4) .
T84260 33948-34182 Sentence denotes In Figure 5 , we show the results of goodness-of-fit tests for the constant-dispersal model M DT a , DT = 6 months (cf. Table 1 ), for one of the Dade sites (D1; analogous results for the other sites are shown in Figures S2, S3, S4) .
TextSentencer_T215 34183-34267 Sentence denotes Intervals (t 0 ,t 1 ) shown are for t 0~0 , 6, 9, 12 months, with t 1~t0 z 6 months.
T92826 34183-34267 Sentence denotes Intervals (t 0 ,t 1 ) shown are for t 0~0 , 6, 9, 12 months, with t 1~t0 z 6 months.
TextSentencer_T216 34268-34386 Sentence denotes Simulated disease progress curves are able to reproduce on average the observed epidemic progress (Figures 5A,C,F,I) .
T28906 34268-34386 Sentence denotes Simulated disease progress curves are able to reproduce on average the observed epidemic progress (Figures 5A,C,F,I) .
TextSentencer_T217 34387-34516 Sentence denotes The spatial autocorrelation function calculated at the end of each interval, C t1 (d) (Equation 5) is shown in Figures 5B,D ,G,J.
T81463 34387-34516 Sentence denotes The spatial autocorrelation function calculated at the end of each interval, C t1 (d) (Equation 5) is shown in Figures 5B,D ,G,J.
TextSentencer_T218 34517-34661 Sentence denotes Predictive distributions of C t1 (d) (gray shaded areas) agree well with the autocorrelation estimated from experimental data (thick red lines).
T15358 34517-34661 Sentence denotes Predictive distributions of C t1 (d) (gray shaded areas) agree well with the autocorrelation estimated from experimental data (thick red lines).
TextSentencer_T219 34662-34918 Sentence denotes Some deviations emerge for the intervals [6, 12] and [9, 15] months ( Figures 5G,J) , where the experimental function appears to decay faster than the simulated function between 100 m and 250 m ( Figure 5G ) and 200 m and 600 m ( Figure 5J ), respectively.
T20083 34662-34918 Sentence denotes Some deviations emerge for the intervals [6, 12] and [9, 15] months ( Figures 5G,J) , where the experimental function appears to decay faster than the simulated function between 100 m and 250 m ( Figure 5G ) and 200 m and 600 m ( Figure 5J ), respectively.
TextSentencer_T220 34919-35200 Sentence denotes The spatial structure of the hosts infected at the beginning of the window (time t 0 ) can significantly bias the values of C t1 (d): such an effect emerges at short distances in Figure 5J , as the value 0 lies out of the 95% significance interval for C t1 (d) (dashed cyan lines).
T20680 34919-35200 Sentence denotes The spatial structure of the hosts infected at the beginning of the window (time t 0 ) can significantly bias the values of C t1 (d): such an effect emerges at short distances in Figure 5J , as the value 0 lies out of the 95% significance interval for C t1 (d) (dashed cyan lines).
TextSentencer_T221 35201-35420 Sentence denotes A statistic free from this bias is the time-lagged function R t1 t0 (d) (Equation 6, Figures 5E,H,K) , which measures the excess of newly infected trees at time t 1 at distance d from the trees already infected at t 0 .
T91430 35201-35420 Sentence denotes A statistic free from this bias is the time-lagged function R t1 t0 (d) (Equation 6, Figures 5E,H,K) , which measures the excess of newly infected trees at time t 1 at distance d from the trees already infected at t 0 .
TextSentencer_T222 35421-35496 Sentence denotes Significance intervals (dashed cyan lines) are always distributed around 0.
T20339 35421-35496 Sentence denotes Significance intervals (dashed cyan lines) are always distributed around 0.
TextSentencer_T223 35497-35778 Sentence denotes Predictive distributions of R t1 t0 (d) (gray shaded areas) are in very good agreement with R t1 t0 (d) from observational data (thick solid red lines), except again for the interval [9,15] months ( Figure 5K ; for a possible origin of the disagreement see Text S1 and Figure S5 ).
T67669 35497-35778 Sentence denotes Predictive distributions of R t1 t0 (d) (gray shaded areas) are in very good agreement with R t1 t0 (d) from observational data (thick solid red lines), except again for the interval [9,15] months ( Figure 5K ; for a possible origin of the disagreement see Text S1 and Figure S5 ).
TextSentencer_T224 35779-35874 Sentence denotes Overall, the spatial pattern of the epidemic is broadly well reproduced by the model estimates.
T5337 35779-35874 Sentence denotes Overall, the spatial pattern of the epidemic is broadly well reproduced by the model estimates.
TextSentencer_T225 35875-36006 Sentence denotes We remark (cf. the beginning of this section) that very similar results were found for a model with Cauchy kernel (not shown here).
T29928 35875-36006 Sentence denotes We remark (cf. the beginning of this section) that very similar results were found for a model with Cauchy kernel (not shown here).
TextSentencer_T226 36007-36244 Sentence denotes Deviations appear when using different dispersal kernels (considered at the preliminary stage, see Methods), and extreme discrepancies with the data arise when testing models without primary infection (an example is given in Figure S7 ).
T1993 36007-36244 Sentence denotes Deviations appear when using different dispersal kernels (considered at the preliminary stage, see Methods), and extreme discrepancies with the data arise when testing models without primary infection (an example is given in Figure S7 ).
TextSentencer_T227 36245-36364 Sentence denotes Strategic decisions about how to react to emerging epidemics are inevitably made early on, when few data are available.
T95779 36245-36364 Sentence denotes Strategic decisions about how to react to emerging epidemics are inevitably made early on, when few data are available.
TextSentencer_T228 36365-36681 Sentence denotes However, it is strongly suspected [28] that the main drivers of the epidemic (responsible for the fluctuations and the final slowing down of transmission rates found in our post hoc analyses, cf. Figures 3B-I and related discussion) were major weather events that could not be known at the beginning of the outbreak.
T65793 36365-36681 Sentence denotes However, it is strongly suspected [28] that the main drivers of the epidemic (responsible for the fluctuations and the final slowing down of transmission rates found in our post hoc analyses, cf. Figures 3B-I and related discussion) were major weather events that could not be known at the beginning of the outbreak.
TextSentencer_T229 36682-36775 Sentence denotes Such lack of knowledge affects epidemic forecasts made from the early stages of the outbreak.
T46813 36682-36775 Sentence denotes Such lack of knowledge affects epidemic forecasts made from the early stages of the outbreak.
TextSentencer_T230 36776-37024 Sentence denotes In the following, we investigate three different hypothetical scenarios for early prediction: when no prior information is given about the future conditions of the epidemic (scenario A), and when some prior knowledge is assumed (scenarios B and C).
T98061 36776-37024 Sentence denotes In the following, we investigate three different hypothetical scenarios for early prediction: when no prior information is given about the future conditions of the epidemic (scenario A), and when some prior knowledge is assumed (scenarios B and C).
TextSentencer_T231 37025-37266 Sentence denotes For each scenario, the parameters were estimated using observation windows of increasing size, all starting at t = 0, and then used to predict future trajectories of the epidemics up to 18 months (i.e. for the pre-drought period; see above).
T28805 37025-37266 Sentence denotes For each scenario, the parameters were estimated using observation windows of increasing size, all starting at t = 0, and then used to predict future trajectories of the epidemics up to 18 months (i.e. for the pre-drought period; see above).
TextSentencer_T232 37267-37386 Sentence denotes The results are shown in Figure 6 for one of the Miami Dade sites (D1), with observation windows of 3, 6, and 9 months.
T14317 37267-37386 Sentence denotes The results are shown in Figure 6 for one of the Miami Dade sites (D1), with observation windows of 3, 6, and 9 months.
TextSentencer_T233 37387-37505 Sentence denotes Scenario A. (Figures 6A1-A3) The cumulative-window model M cum (Table 1 ) was fitted to the three observation windows.
T19076 37387-37505 Sentence denotes Scenario A. (Figures 6A1-A3) The cumulative-window model M cum (Table 1 ) was fitted to the three observation windows.
TextSentencer_T234 37506-37645 Sentence denotes The posterior distributions for a, b and e were used to generate epidemic trajectories, which were then compared with the true realisation.
T36157 37506-37645 Sentence denotes The posterior distributions for a, b and e were used to generate epidemic trajectories, which were then compared with the true realisation.
TextSentencer_T235 37646-37841 Sentence denotes Predictions based upon initial estimates during the first three months ( Figure 6A1 ) capture the overall trend, although with very wide credible intervals for the ensemble of possible epidemics.
T8514 37646-37841 Sentence denotes Predictions based upon initial estimates during the first three months ( Figure 6A1 ) capture the overall trend, although with very wide credible intervals for the ensemble of possible epidemics.
TextSentencer_T236 37842-38097 Sentence denotes As new data for estimation are included ( Figures 6A2-A3) , the credible intervals tighten, but at the same time the predictions systematically and increasingly overestimate the real epidemic, as they fail in capturing the slowing down of epidemic spread.
T34109 37842-38097 Sentence denotes As new data for estimation are included ( Figures 6A2-A3) , the credible intervals tighten, but at the same time the predictions systematically and increasingly overestimate the real epidemic, as they fail in capturing the slowing down of epidemic spread.
TextSentencer_T237 38098-38361 Sentence denotes As the differences are mainly driven by changes in the transmission rate, b ( Figures 3D,H) , we tested whether the epidemics could be adequately predicted using model M V , which incorporates a long-term decreasing linear trend: b(t) = b 0 (12vt) (cf. Table 1 ).
T23555 38098-38361 Sentence denotes As the differences are mainly driven by changes in the transmission rate, b ( Figures 3D,H) , we tested whether the epidemics could be adequately predicted using model M V , which incorporates a long-term decreasing linear trend: b(t) = b 0 (12vt) (cf. Table 1 ).
TextSentencer_T238 38362-38654 Sentence denotes However, the linear trend is confounded by large monthly fluctuations (Figure 3H) , and a reliable estimate of the decay rate v was only possible when at least 12 snapshots were Table 1 ) are shown for four different intervals (each delimited by times t 0 and t 1 , with t 1 = t 0 +6 months).
T22107 38362-38654 Sentence denotes However, the linear trend is confounded by large monthly fluctuations (Figure 3H) , and a reliable estimate of the decay rate v was only possible when at least 12 snapshots were Table 1 ) are shown for four different intervals (each delimited by times t 0 and t 1 , with t 1 = t 0 +6 months).
TextSentencer_T239 38655-38838 Sentence denotes Parameter estimates obtained for each interval are used to run the model 1000 times between t 0 and t 1 , and summary statistics calculated from the output are compared with the data.
T43472 38655-38838 Sentence denotes Parameter estimates obtained for each interval are used to run the model 1000 times between t 0 and t 1 , and summary statistics calculated from the output are compared with the data.
TextSentencer_T240 38839-39131 Sentence denotes A, C, F, I Distributions of simulated disease progress between t 0 and t 1 (shaded areas, with black corresponding to the median and different levels of gray to different quantiles) compared to observed disease progress (red circles; empty black circles mark data not used in the comparison).
T69258 38839-39131 Sentence denotes A, C, F, I Distributions of simulated disease progress between t 0 and t 1 (shaded areas, with black corresponding to the median and different levels of gray to different quantiles) compared to observed disease progress (red circles; empty black circles mark data not used in the comparison).
TextSentencer_T241 39132-39181 Sentence denotes The total number of hosts in site D1 is N = 6056.
T69997 39132-39181 Sentence denotes The total number of hosts in site D1 is N = 6056.
TextSentencer_T242 39182-39492 Sentence denotes B, D, G, J The autocorrelation function at time t 1 , C t1 (d), estimated from observed data (thick red line), together with the 95% bootstrapped confidence interval (thin red lines), is compared with the distribution of C t1 (d) estimated from simulated epidemics (shaded gray, same as for panels A, C, F, I).
T92021 39182-39492 Sentence denotes B, D, G, J The autocorrelation function at time t 1 , C t1 (d), estimated from observed data (thick red line), together with the 95% bootstrapped confidence interval (thin red lines), is compared with the distribution of C t1 (d) estimated from simulated epidemics (shaded gray, same as for panels A, C, F, I).
TextSentencer_T243 39493-39590 Sentence denotes Dashed cyan lines represent the 95% significance interval found with random labelling techniques.
T30438 39493-39590 Sentence denotes Dashed cyan lines represent the 95% significance interval found with random labelling techniques.
TextSentencer_T244 39591-39673 Sentence denotes E, H, K Time-lagged statistics calculated between times t 0 and t 1 , R t1 t0 (d).
T83347 39591-39673 Sentence denotes E, H, K Time-lagged statistics calculated between times t 0 and t 1 , R t1 t0 (d).
TextSentencer_T245 39674-40077 Sentence denotes Thick red lines are R t1 t0 (d) estimated from observed data, thin red lines mark the 95% confidence interval, dashed cyan lines mark the 95% significance intervals, and distributions of R t1 t0 (d) estimated from simulated epidemics are shown in shaded gray. doi:10.1371/journal.pcbi.1003587.g005 from the ''full'' estimation, cf. solid gray line in Figures 3D, H) , and estimating only a, b 0 , and e.
T78247 39674-40077 Sentence denotes Thick red lines are R t1 t0 (d) estimated from observed data, thin red lines mark the 95% confidence interval, dashed cyan lines mark the 95% significance intervals, and distributions of R t1 t0 (d) estimated from simulated epidemics are shown in shaded gray. doi:10.1371/journal.pcbi.1003587.g005 from the ''full'' estimation, cf. solid gray line in Figures 3D, H) , and estimating only a, b 0 , and e.
TextSentencer_T246 40078-40299 Sentence denotes While very early predictions ( Figure 6B1 ) slightly under-estimate disease (with a very large credible interval), including more snapshots for estimation leads to consistent improvement of the forecast (Figures 6B2,B3) .
T8914 40078-40299 Sentence denotes While very early predictions ( Figure 6B1 ) slightly under-estimate disease (with a very large credible interval), including more snapshots for estimation leads to consistent improvement of the forecast (Figures 6B2,B3) .
TextSentencer_T247 40300-40399 Sentence denotes Hence, information about a single parameter, v, leads to a stark improvement of disease prediction.
T32416 40300-40399 Sentence denotes Hence, information about a single parameter, v, leads to a stark improvement of disease prediction.
TextSentencer_T248 40400-40624 Sentence denotes We remark, however, that it was not possible to identify a single, clear environmental factor responsible for the overall decreasing trend of the time series (henceforth, we refer to the monthly series only, cf. Figure 3H) .
T24498 40400-40624 Sentence denotes We remark, however, that it was not possible to identify a single, clear environmental factor responsible for the overall decreasing trend of the time series (henceforth, we refer to the monthly series only, cf. Figure 3H) .
TextSentencer_T249 40625-40731 Sentence denotes Hence, knowing v implies advance knowledge of the behaviour of b t along the whole course of the epidemic.
T36692 40625-40731 Sentence denotes Hence, knowing v implies advance knowledge of the behaviour of b t along the whole course of the epidemic.
TextSentencer_T250 40732-40862 Sentence denotes It is desirable to test epidemic predictions under alternative, more parsimonious assumptions about our prior information on b t .
T8747 40732-40862 Sentence denotes It is desirable to test epidemic predictions under alternative, more parsimonious assumptions about our prior information on b t .
TextSentencer_T251 40863-41078 Sentence denotes Scenario C. (Figures 6C1-C3 , 6D1-D3) We assumed to have prior information about the time of occurrence and values of the three peaks of b t (cf. Figure 3H) ; no prior information was given about the drought period.
T12491 40863-41078 Sentence denotes Scenario C. (Figures 6C1-C3 , 6D1-D3) We assumed to have prior information about the time of occurrence and values of the three peaks of b t (cf. Figure 3H) ; no prior information was given about the drought period.
TextSentencer_T252 41079-41128 Sentence denotes We fitted to the observation windows a Table 1 ).
T80535 41079-41128 Sentence denotes We fitted to the observation windows a Table 1 ).
TextSentencer_T253 41129-41198 Sentence denotes A1-A3 Predictions based on model M 0 , assuming no prior information.
T45412 41129-41198 Sentence denotes A1-A3 Predictions based on model M 0 , assuming no prior information.
TextSentencer_T254 41199-41348 Sentence denotes The probability distributions for predicted trajectories are shown by gray shading, with intensity of shading representing probability of occurrence.
T60431 41199-41348 Sentence denotes The probability distributions for predicted trajectories are shown by gray shading, with intensity of shading representing probability of occurrence.
TextSentencer_T255 41349-41571 Sentence denotes The observational data (disease snapshots) used for prediction are marked by orange circles, the last snapshot used (the prediction time) by a larger red circle, and the observational data to be predicted by white circles.
T51335 41349-41571 Sentence denotes The observational data (disease snapshots) used for prediction are marked by orange circles, the last snapshot used (the prediction time) by a larger red circle, and the observational data to be predicted by white circles.
TextSentencer_T256 41572-41622 Sentence denotes The total number of hosts in the site is N = 6056.
T38607 41572-41622 Sentence denotes The total number of hosts in the site is N = 6056.
TextSentencer_T257 41623-41834 Sentence denotes B1-B3 Predictions (same conventions as for panels A1-A3) based upon model M V , with the assumption that the value of v (the linear decay rate of b(t), cf. gray line in Figure 3D ,H) is known from the beginning.
T93873 41623-41834 Sentence denotes B1-B3 Predictions (same conventions as for panels A1-A3) based upon model M V , with the assumption that the value of v (the linear decay rate of b(t), cf. gray line in Figure 3D ,H) is known from the beginning.
TextSentencer_T258 41835-42001 Sentence denotes C1-C3, D1-D3 Predictions based upon model M DT a (DT = 1 month), with constant dispersal parameter a, and monthly rates of transmission (b t , e t ) (cf. Figure 3H ).
T5612 41835-42001 Sentence denotes C1-C3, D1-D3 Predictions based upon model M DT a (DT = 1 month), with constant dispersal parameter a, and monthly rates of transmission (b t , e t ) (cf. Figure 3H ).
TextSentencer_T259 42002-42075 Sentence denotes C1-C3 Predicted and observed trajectories (same conventions as in A1-A3).
T92531 42002-42075 Sentence denotes C1-C3 Predicted and observed trajectories (same conventions as in A1-A3).
TextSentencer_T260 42076-42248 Sentence denotes D1-D3 The associated secondary infection rates b t , estimated from observed data, marked by orange circles (coinciding with the mode of the distributions; cf. Figure 3H ).
T29384 42076-42248 Sentence denotes D1-D3 The associated secondary infection rates b t , estimated from observed data, marked by orange circles (coinciding with the mode of the distributions; cf. Figure 3H ).
TextSentencer_T261 42249-42446 Sentence denotes Predictions are made under the assumption that the positions and values of the peaks in the time series for b t (blue circles in panels D1-D3, same as the peaks in Figure 3H ) are known in advance.
T14683 42249-42446 Sentence denotes Predictions are made under the assumption that the positions and values of the peaks in the time series for b t (blue circles in panels D1-D3, same as the peaks in Figure 3H ) are known in advance.
TextSentencer_T262 42447-42674 Sentence denotes A spline interpolator (dark red line in panels D1-D3) is used to impute missing values of b t . doi:10.1371/journal.pcbi.1003587.g006 constant-dispersal model M DT a with monthly-varying rates (DT = 1 month, cf. Figures 3F-I) .
T63169 42447-42674 Sentence denotes A spline interpolator (dark red line in panels D1-D3) is used to impute missing values of b t . doi:10.1371/journal.pcbi.1003587.g006 constant-dispersal model M DT a with monthly-varying rates (DT = 1 month, cf. Figures 3F-I) .
TextSentencer_T263 42675-42908 Sentence denotes In Figures 6D1-D3 , the modes of the estimated monthly values of b t (orange circles) are shown for each observation window together with the peak values of b t (blue circles) that are known in advance (same values as in Figure 3H ).
T67241 42675-42908 Sentence denotes In Figures 6D1-D3 , the modes of the estimated monthly values of b t (orange circles) are shown for each observation window together with the peak values of b t (blue circles) that are known in advance (same values as in Figure 3H ).
TextSentencer_T264 42909-43052 Sentence denotes In order to impute the missing values of b t , a spline interpolator (dark red line) was built from all the known and estimated values of b t .
T94781 42909-43052 Sentence denotes In order to impute the missing values of b t , a spline interpolator (dark red line) was built from all the known and estimated values of b t .
TextSentencer_T265 43053-43167 Sentence denotes The missing values of e t were assumed to be constant and equal to the average of e t over the observation window.
T46686 43053-43167 Sentence denotes The missing values of e t were assumed to be constant and equal to the average of e t over the observation window.
TextSentencer_T266 43168-43403 Sentence denotes Predictions based on the first three months ( Figure 6C1 , with corresponding estimates for b t in Figure 6D1 ) capture the future progress of disease, with a smaller credible interval than for scenarios A and B (cf. Figures 6A1, B1) .
T77562 43168-43403 Sentence denotes Predictions based on the first three months ( Figure 6C1 , with corresponding estimates for b t in Figure 6D1 ) capture the future progress of disease, with a smaller credible interval than for scenarios A and B (cf. Figures 6A1, B1) .
TextSentencer_T267 43404-43743 Sentence denotes Increasing the observation window to six and nine snapshots does not have a significant effect on forecast ( Figures 6C2-C3) , as most of the additional true values of b t (orange circles starting from month 4 in Figures 6D2-D3 ) are already well imputed from the first three months (cf. corresponding times in Figure 6D1 , dark red line).
T13217 43404-43743 Sentence denotes Increasing the observation window to six and nine snapshots does not have a significant effect on forecast ( Figures 6C2-C3) , as most of the additional true values of b t (orange circles starting from month 4 in Figures 6D2-D3 ) are already well imputed from the first three months (cf. corresponding times in Figure 6D1 , dark red line).
TextSentencer_T268 43744-43919 Sentence denotes We conclude that knowledge of the peak values of b t , supplemented by a few early stage observations, provide enough information to predict the future course of the epidemic.
T76105 43744-43919 Sentence denotes We conclude that knowledge of the peak values of b t , supplemented by a few early stage observations, provide enough information to predict the future course of the epidemic.
TextSentencer_T269 43920-44145 Sentence denotes Among the different scenarios we investigated (including several not discussed here), we found scenario C to correspond to the minimal amount of extra information that could produce reliable predictions from the early stages.
T45178 43920-44145 Sentence denotes Among the different scenarios we investigated (including several not discussed here), we found scenario C to correspond to the minimal amount of extra information that could produce reliable predictions from the early stages.
TextSentencer_T270 44146-44287 Sentence denotes Chief amongst the concerns of policy makers concerned with managing an emerging epidemic are: how far and how fast is the epidemic spreading?
T69245 44146-44287 Sentence denotes Chief amongst the concerns of policy makers concerned with managing an emerging epidemic are: how far and how fast is the epidemic spreading?
TextSentencer_T271 44288-44349 Sentence denotes How reliable are future predictions of the epidemic severity?
T82943 44288-44349 Sentence denotes How reliable are future predictions of the epidemic severity?
TextSentencer_T272 44350-44434 Sentence denotes Does the epidemic merit the deployment of control, and how should this be optimised?
T42700 44350-44434 Sentence denotes Does the epidemic merit the deployment of control, and how should this be optimised?
TextSentencer_T273 44435-44626 Sentence denotes Here we have focused on the first two questions about estimation and prediction, using a combination of Bayesian statistical inference and data for the spread of citrus canker in urban Miami.
T20531 44435-44626 Sentence denotes Here we have focused on the first two questions about estimation and prediction, using a combination of Bayesian statistical inference and data for the spread of citrus canker in urban Miami.
TextSentencer_T274 44627-44765 Sentence denotes We assumed that little was known about the pathogen, using non-informative priors for the parameters and a selection of dispersal kernels.
T68691 44627-44765 Sentence denotes We assumed that little was known about the pathogen, using non-informative priors for the parameters and a selection of dispersal kernels.
TextSentencer_T275 44766-44957 Sentence denotes Our analyses have shown that the same spatio-temporal, stochastic model is able to capture the temporal trends and spatial statistics characterising the spread of infection in all four sites.
T14776 44766-44957 Sentence denotes Our analyses have shown that the same spatio-temporal, stochastic model is able to capture the temporal trends and spatial statistics characterising the spread of infection in all four sites.
TextSentencer_T276 44958-45135 Sentence denotes Pathogen spread within sites is described by an exponential dispersal kernel with a time-varying transmission rate augmented by a small, time-varying rate of external infection.
T2534 44958-45135 Sentence denotes Pathogen spread within sites is described by an exponential dispersal kernel with a time-varying transmission rate augmented by a small, time-varying rate of external infection.
TextSentencer_T277 45136-45308 Sentence denotes We show, therefore, that epidemics were not self-contained within sites but new foci of infection also arose from external inoculum, a phenomenon evident at all four sites.
T91279 45136-45308 Sentence denotes We show, therefore, that epidemics were not self-contained within sites but new foci of infection also arose from external inoculum, a phenomenon evident at all four sites.
TextSentencer_T278 45309-45469 Sentence denotes The estimation of dispersal and transmission parameters for stochastic models from spatial snap-shots of disease is not new [21, [47] [48] [49] [50] [51] [52] .
T95928 45309-45469 Sentence denotes The estimation of dispersal and transmission parameters for stochastic models from spatial snap-shots of disease is not new [21, [47] [48] [49] [50] [51] [52] .
TextSentencer_T279 45470-45897 Sentence denotes While Gibson and Austin [51] first used likelihood estimation to estimate dispersal parameters from snapshots of citrus tristeza disease in plantations, the current analyses are based upon subsequent MCMC methods to deal with unobserved infection times [34, 35] , estimate the most likely chain of infections between successive snapshots [48, 49] , and account for temporal variability in transmission parameters [21, 36, 38] .
T3540 45470-45897 Sentence denotes While Gibson and Austin [51] first used likelihood estimation to estimate dispersal parameters from snapshots of citrus tristeza disease in plantations, the current analyses are based upon subsequent MCMC methods to deal with unobserved infection times [34, 35] , estimate the most likely chain of infections between successive snapshots [48, 49] , and account for temporal variability in transmission parameters [21, 36, 38] .
TextSentencer_T280 45898-46083 Sentence denotes What is different in the current investigation is the quantification of precision and bias of the parameters associated with taking different snapshots of disease over time (Figure 2) .
T22000 45898-46083 Sentence denotes What is different in the current investigation is the quantification of precision and bias of the parameters associated with taking different snapshots of disease over time (Figure 2) .
TextSentencer_T281 46084-46285 Sentence denotes Models with short-range dispersal (exponential kernel) and longrange dispersal (Cauchy kernel) together with external primary infection were compared using DIC tests (DIC 6 , cf. Table S1 and Text S1).
T71040 46084-46285 Sentence denotes Models with short-range dispersal (exponential kernel) and longrange dispersal (Cauchy kernel) together with external primary infection were compared using DIC tests (DIC 6 , cf. Table S1 and Text S1).
TextSentencer_T282 46286-46435 Sentence denotes Table S1 shows no significant differences between the exponential and Cauchy models, except for site D1, for which the exponential model is favoured.
T36211 46286-46435 Sentence denotes Table S1 shows no significant differences between the exponential and Cauchy models, except for site D1, for which the exponential model is favoured.
TextSentencer_T283 46436-46506 Sentence denotes For the other census sites, the two models are essentially equivalent.
T2391 46436-46506 Sentence denotes For the other census sites, the two models are essentially equivalent.
TextSentencer_T284 46507-46704 Sentence denotes This result can be explained in two steps, first by analysing dispersal at short distances (Figure 7) , then by considering the contribution of external infection at longer distances ( Figure S1 ).
T32871 46507-46704 Sentence denotes This result can be explained in two steps, first by analysing dispersal at short distances (Figure 7) , then by considering the contribution of external infection at longer distances ( Figure S1 ).
TextSentencer_T285 46705-46840 Sentence denotes Figure 7 shows a direct comparison of estimated exponential and Cauchy kernels, plotted as a function of distance for each census site.
T24636 46705-46840 Sentence denotes Figure 7 shows a direct comparison of estimated exponential and Cauchy kernels, plotted as a function of distance for each census site.
TextSentencer_T286 46841-47014 Sentence denotes The pattern is qualitatively similar for all census sites: the two kernels are substantially identical up to distances of a few hundred metres (''plus'' signs in Figure 7) :
T52711 46841-47014 Sentence denotes The pattern is qualitatively similar for all census sites: the two kernels are substantially identical up to distances of a few hundred metres (''plus'' signs in Figure 7) :
TextSentencer_T287 47015-47173 Sentence denotes 250-300 m for all the sites bar D1, and ,150 m for site D1 ( Figure 7C : this may be a reason why the DIC tests favours the exponential kernel for this site).
T16093 47015-47173 Sentence denotes 250-300 m for all the sites bar D1, and ,150 m for site D1 ( Figure 7C : this may be a reason why the DIC tests favours the exponential kernel for this site).
TextSentencer_T288 47174-47339 Sentence denotes Beyond those distances, which correspond to a fraction of the size of the census site (1 km-4 km), the relative difference between the two kernels increases rapidly.
T11018 47174-47339 Sentence denotes Beyond those distances, which correspond to a fraction of the size of the census site (1 km-4 km), the relative difference between the two kernels increases rapidly.
TextSentencer_T289 47340-47478 Sentence denotes Hence, in principle it should still be possible to detect the effect of such difference in estimates from spatio-temporal maps of disease.
T62898 47340-47478 Sentence denotes Hence, in principle it should still be possible to detect the effect of such difference in estimates from spatio-temporal maps of disease.
TextSentencer_T290 47479-47585 Sentence denotes However, the long-distance divergence between the two kernels is balanced by the primary infection rate e.
T93875 47479-47585 Sentence denotes However, the long-distance divergence between the two kernels is balanced by the primary infection rate e.
TextSentencer_T291 47586-47835 Sentence denotes This is shown with an illustrative example in Figure S1 (see also Text S1 for details), where exponential and Cauchy kernels are used to generate spatial maps of the infectious pressure from a given experimental snapshot of site D2 ( Figure S1(A) ).
T25867 47586-47835 Sentence denotes This is shown with an illustrative example in Figure S1 (see also Text S1 for details), where exponential and Cauchy kernels are used to generate spatial maps of the infectious pressure from a given experimental snapshot of site D2 ( Figure S1(A) ).
TextSentencer_T292 47836-48110 Sentence denotes When only secondary infection is considered, clear differences between the two kernels emerge at long distances ( Figures S1(B-C) ), but the differences disappear, yielding virtually identical maps, when adding the effect of the external infection rate e (Figures S1(D-E) ).
T20056 47836-48110 Sentence denotes When only secondary infection is considered, clear differences between the two kernels emerge at long distances ( Figures S1(B-C) ), but the differences disappear, yielding virtually identical maps, when adding the effect of the external infection rate e (Figures S1(D-E) ).
TextSentencer_T293 48111-48373 Sentence denotes We draw the following conclusion: that the scale of our observations is too small to choose unambiguously between the two dispersal kernels, as the potential effect of long-range dispersal within a census site is confounded by the presence of external infection.
T28646 48111-48373 Sentence denotes We draw the following conclusion: that the scale of our observations is too small to choose unambiguously between the two dispersal kernels, as the potential effect of long-range dispersal within a census site is confounded by the presence of external infection.
TextSentencer_T294 48374-48569 Sentence denotes Gottwald et al. [53] found that a power law dispersal model was superior to an exponential model for the spread of ACC in 203 citrus plots in Brazil, following the introduction of the leaf miner.
T64527 48374-48569 Sentence denotes Gottwald et al. [53] found that a power law dispersal model was superior to an exponential model for the spread of ACC in 203 citrus plots in Brazil, following the introduction of the leaf miner.
TextSentencer_T295 48570-48797 Sentence denotes In the absence of the leaf miner, however, dispersal of ACC was adequately described by an exponential model, which is in agreement with our findings; moreover, none of the models considered in [53] included external infection.
T13669 48570-48797 Sentence denotes In the absence of the leaf miner, however, dispersal of ACC was adequately described by an exponential model, which is in agreement with our findings; moreover, none of the models considered in [53] included external infection.
TextSentencer_T296 48798-48918 Sentence denotes We remarked in the results that support for the exponential and Cauchy model was found in post hoc analyses of the data.
T27594 48798-48918 Sentence denotes We remarked in the results that support for the exponential and Cauchy model was found in post hoc analyses of the data.
TextSentencer_T297 48919-49141 Sentence denotes Model comparison from early snapshots supported in general spatially structured models with external infection, but could not select a dispersal kernel (most of the kernels tried, see e.g. Text S1, performed equally well).
T65207 48919-49141 Sentence denotes Model comparison from early snapshots supported in general spatially structured models with external infection, but could not select a dispersal kernel (most of the kernels tried, see e.g. Text S1, performed equally well).
TextSentencer_T298 49142-49352 Sentence denotes The choice of an exponential kernel for early estimations (Figure 2 ) would then be motivated by a strong prior belief on disease dispersal (for example, from results in the absence of the leaf miner in [53] ).
T71101 49142-49352 Sentence denotes The choice of an exponential kernel for early estimations (Figure 2 ) would then be motivated by a strong prior belief on disease dispersal (for example, from results in the absence of the leaf miner in [53] ).
TextSentencer_T299 49353-49536 Sentence denotes Here, we also note that, in our case, the absence of such a prior belief would be of little importance, as the exact form of the kernel would not affect the main results of Figure 2 .
T91324 49353-49536 Sentence denotes Here, we also note that, in our case, the absence of such a prior belief would be of little importance, as the exact form of the kernel would not affect the main results of Figure 2 .
TextSentencer_T300 49537-49782 Sentence denotes Of the several kernels tried for the first few snapshots, most (e.g. the Gaussian, Text S1) produced estimates of dispersal scale and infection rates with patterns in time qualitatively very similar to those in Figure 2 (results not shown here).
T71928 49537-49782 Sentence denotes Of the several kernels tried for the first few snapshots, most (e.g. the Gaussian, Text S1) produced estimates of dispersal scale and infection rates with patterns in time qualitatively very similar to those in Figure 2 (results not shown here).
TextSentencer_T301 49783-49934 Sentence denotes Successful control of disease depends upon matching the scale of control with the inherent spatial and temporal scales of the epidemic [54] [55] [56] .
T68359 49783-49934 Sentence denotes Successful control of disease depends upon matching the scale of control with the inherent spatial and temporal scales of the epidemic [54] [55] [56] .
TextSentencer_T302 49935-50140 Sentence denotes For our dataset, we have identified a short initial transient period at all four sites for which a and b are not well estimated, with comparatively wider posterior distributions than for later assessments.
T55498 49935-50140 Sentence denotes For our dataset, we have identified a short initial transient period at all four sites for which a and b are not well estimated, with comparatively wider posterior distributions than for later assessments.
TextSentencer_T303 50141-50327 Sentence denotes Clearly, relying upon data for the first three 30-d intervals leads to great uncertainty in estimates of the dispersal scale, and hence decisions about the scale of control ( Figure 2 ).
T54287 50141-50327 Sentence denotes Clearly, relying upon data for the first three 30-d intervals leads to great uncertainty in estimates of the dispersal scale, and hence decisions about the scale of control ( Figure 2 ).
TextSentencer_T304 50328-50543 Sentence denotes The use of sliding windows shows that fewer but later snapshots could be as precise in estimating dispersal parameters (measured by posterior distributions) as cumulative windows with more snapshots (Figures 2A,D) .
T82871 50328-50543 Sentence denotes The use of sliding windows shows that fewer but later snapshots could be as precise in estimating dispersal parameters (measured by posterior distributions) as cumulative windows with more snapshots (Figures 2A,D) .
TextSentencer_T305 50544-50753 Sentence denotes Estimates for the dispersal parameter changed very little over time ( Figure 2D ): this motivated consideration of a new, simpler model where dispersal was constant throughout the epidemic (M DT a , Table 1 ).
T24384 50544-50753 Sentence denotes Estimates for the dispersal parameter changed very little over time ( Figure 2D ): this motivated consideration of a new, simpler model where dispersal was constant throughout the epidemic (M DT a , Table 1 ).
TextSentencer_T306 50754-51010 Sentence denotes The robustness of the results for the dispersal scale was confirmed by goodness of fit tests, in which the posterior predictive distribution of several test statistics showed close concordance with the observed statistics ( Figure 5 and Figures S2,S3,S4 ).
T43359 50754-51010 Sentence denotes The robustness of the results for the dispersal scale was confirmed by goodness of fit tests, in which the posterior predictive distribution of several test statistics showed close concordance with the observed statistics ( Figure 5 and Figures S2,S3,S4 ).
TextSentencer_T307 51011-51383 Sentence denotes The evidence that the dispersal parameter (almost identical for three out of four census sites, Figure 3A ) did not change significantly over time, and the fact that this parameter was estimated with substantial precision with few snapshots, are encouraging results in view of control decisions where the scale of control depends on the scale of dispersal [54] [55] [56] .
T9940 51011-51383 Sentence denotes The evidence that the dispersal parameter (almost identical for three out of four census sites, Figure 3A ) did not change significantly over time, and the fact that this parameter was estimated with substantial precision with few snapshots, are encouraging results in view of control decisions where the scale of control depends on the scale of dispersal [54] [55] [56] .
TextSentencer_T308 51384-51627 Sentence denotes In contrast with the dispersal parameter, estimates for the transmission rates (b, e) were not constant ( Figures 2E,F and Figures 3B-I) , with the secondary transmission rate b showing substantial month to month fluctuations ( Figures 3F-H) .
T36256 51384-51627 Sentence denotes In contrast with the dispersal parameter, estimates for the transmission rates (b, e) were not constant ( Figures 2E,F and Figures 3B-I) , with the secondary transmission rate b showing substantial month to month fluctuations ( Figures 3F-H) .
TextSentencer_T309 51628-51775 Sentence denotes This result bears two consequences: first, it can frustrate control efforts based on the assumption of a single, intrinsic transmission rate [56] .
T73055 51628-51775 Sentence denotes This result bears two consequences: first, it can frustrate control efforts based on the assumption of a single, intrinsic transmission rate [56] .
TextSentencer_T310 51776-51929 Sentence denotes Second, prediction of future disease severity (upon which the decision to apply control is made) is difficult and prone to systematic error ( Figure 6 ).
T4484 51776-51929 Sentence denotes Second, prediction of future disease severity (upon which the decision to apply control is made) is difficult and prone to systematic error ( Figure 6 ).
TextSentencer_T311 51930-52076 Sentence denotes We suggested that both b and e were driven by environmental variables that affected the infectivity, and possibly the susceptibility, of the host.
T75426 51930-52076 Sentence denotes We suggested that both b and e were driven by environmental variables that affected the infectivity, and possibly the susceptibility, of the host.
TextSentencer_T312 52077-52236 Sentence denotes Accordingly, we found strong evidence of a time pattern similar among all the census sites for the transmission rate b (Figures 3-4 ; see also Figures S8, S9).
T18585 52077-52236 Sentence denotes Accordingly, we found strong evidence of a time pattern similar among all the census sites for the transmission rate b (Figures 3-4 ; see also Figures S8, S9).
TextSentencer_T313 52237-52467 Sentence denotes Savill et al. [55] explored analogous problems for the infectiousness of infected premises in the 2001 UK foot and mouth epidemic, and identified missing and inaccurate data as a rate-limiting step in refining parameter estimates.
T56076 52237-52467 Sentence denotes Savill et al. [55] explored analogous problems for the infectiousness of infected premises in the 2001 UK foot and mouth epidemic, and identified missing and inaccurate data as a rate-limiting step in refining parameter estimates.
TextSentencer_T314 52468-52642 Sentence denotes For ACC, the principal environmental variables that are likely to influence the pathogen, Xac, and the disease are known to be wind-speed, rain and temperature [29, 30, 32] .
T15370 52468-52642 Sentence denotes For ACC, the principal environmental variables that are likely to influence the pathogen, Xac, and the disease are known to be wind-speed, rain and temperature [29, 30, 32] .
TextSentencer_T315 52643-53032 Sentence denotes Extreme weather events have indeed been identified, with robust statistical evidence [28] , as the main determinants of the pattern of b (Figures 3F-H) : major rainstorm events, acting as environmental pulses, were linked to peaks in the monthly series of transmission rates, and a drought was responsible for the strong quenching of the rates in the second half of the observation period.
T19756 52643-53032 Sentence denotes Extreme weather events have indeed been identified, with robust statistical evidence [28] , as the main determinants of the pattern of b (Figures 3F-H) : major rainstorm events, acting as environmental pulses, were linked to peaks in the monthly series of transmission rates, and a drought was responsible for the strong quenching of the rates in the second half of the observation period.
TextSentencer_T316 53033-53215 Sentence denotes The existence of a common external driver is also supported (Figure 4 and Figure S9 ) by the close similarities in the temporal patterns of transmission rates across different sites.
T22157 53033-53215 Sentence denotes The existence of a common external driver is also supported (Figure 4 and Figure S9 ) by the close similarities in the temporal patterns of transmission rates across different sites.
TextSentencer_T317 53216-53411 Sentence denotes Nevertheless, extensive exploratory analysis using environmental data for temperature, wind and rain as covariates did not succeed in identifying a mechanistic environmentally-driven model for b.
T71805 53216-53411 Sentence denotes Nevertheless, extensive exploratory analysis using environmental data for temperature, wind and rain as covariates did not succeed in identifying a mechanistic environmentally-driven model for b.
TextSentencer_T318 53412-53529 Sentence denotes This was due in part to the (largely unknown) time-lags in the effect of weather events on the pathogen and the host.
T88659 53412-53529 Sentence denotes This was due in part to the (largely unknown) time-lags in the effect of weather events on the pathogen and the host.
TextSentencer_T319 53530-53687 Sentence denotes It is also reasonable to assume that environmental, weather-related forcing was just one, if the most important, of the factors affecting the behaviour of b.
T85440 53530-53687 Sentence denotes It is also reasonable to assume that environmental, weather-related forcing was just one, if the most important, of the factors affecting the behaviour of b.
TextSentencer_T320 53688-53865 Sentence denotes Factors intrinsic to the host population might also have played an important role: tree age, cultivar, and horticultural care can affect the susceptibility to the disease [28] .
T86854 53688-53865 Sentence denotes Factors intrinsic to the host population might also have played an important role: tree age, cultivar, and horticultural care can affect the susceptibility to the disease [28] .
TextSentencer_T321 53866-54033 Sentence denotes In a population of residential trees, the distribution of such individual factors is extremely heterogeneous in space at several scales, and also fluctuates over time.
T46459 53866-54033 Sentence denotes In a population of residential trees, the distribution of such individual factors is extremely heterogeneous in space at several scales, and also fluctuates over time.
TextSentencer_T322 54034-54167 Sentence denotes In the present case, as a result, there was a high degree of spatio-temporal variability in the response of hosts to weather drivers.
T63623 54034-54167 Sentence denotes In the present case, as a result, there was a high degree of spatio-temporal variability in the response of hosts to weather drivers.
TextSentencer_T323 54168-54450 Sentence denotes Fitting models with explicit individual factors is unfeasible in such a highly heterogeneous scenario; however, such a class of models might be very useful in future analyses of outbreaks within commercial citrus plantations, where host properties are more consistently distributed.
T31790 54168-54450 Sentence denotes Fitting models with explicit individual factors is unfeasible in such a highly heterogeneous scenario; however, such a class of models might be very useful in future analyses of outbreaks within commercial citrus plantations, where host properties are more consistently distributed.
TextSentencer_T324 54451-54595 Sentence denotes We showed that, in retrospect, advance knowledge of major weather events would have been required in order to forecast future epidemic progress.
T87011 54451-54595 Sentence denotes We showed that, in retrospect, advance knowledge of major weather events would have been required in order to forecast future epidemic progress.
TextSentencer_T325 54596-54784 Sentence denotes Our methods, based on limitedinformation forecast scenarios, should be applicable more generally, e.g., to windborne diseases where transmission is mostly driven by strong weather changes.
T56987 54596-54784 Sentence denotes Our methods, based on limitedinformation forecast scenarios, should be applicable more generally, e.g., to windborne diseases where transmission is mostly driven by strong weather changes.
TextSentencer_T326 54785-55089 Sentence denotes In our analysis ( Figure 6 ), predictions based upon initial estimates, ignoring large weatherrelated fluctuations in transmission rates ( Figures 3E-I) , showed progressively more deviation from the actual outcome as more epidemic snapshots were included in the estimation (scenario A, Figures 6A1-A3) .
T50296 54785-55089 Sentence denotes In our analysis ( Figure 6 ), predictions based upon initial estimates, ignoring large weatherrelated fluctuations in transmission rates ( Figures 3E-I) , showed progressively more deviation from the actual outcome as more epidemic snapshots were included in the estimation (scenario A, Figures 6A1-A3) .
TextSentencer_T327 55090-55454 Sentence denotes Post facto predictions were effective only when the assumption of complete ignorance of the future was waived (scenarios B and C, Figures 6B1-B3, 6C1-C6 ), and some extra information, corresponding to major environmental events, was known in advance (i.e., the drought period and the amplitude of the fluctuations in b in scenario B; the peaks of b in scenario C).
T36283 55090-55454 Sentence denotes Post facto predictions were effective only when the assumption of complete ignorance of the future was waived (scenarios B and C, Figures 6B1-B3, 6C1-C6 ), and some extra information, corresponding to major environmental events, was known in advance (i.e., the drought period and the amplitude of the fluctuations in b in scenario B; the peaks of b in scenario C).
TextSentencer_T328 55455-55574 Sentence denotes At the same time, of course, meteorological predictability imposes drastic constraints on prior knowledge of that kind.
T42741 55455-55574 Sentence denotes At the same time, of course, meteorological predictability imposes drastic constraints on prior knowledge of that kind.
TextSentencer_T329 55575-55843 Sentence denotes For example, the evolution of position, intensity, and heavier rainfall areas of supercell thunderstorms (two of which were most likely responsible for the first two peaks in the time series for b) can currently not be predicted with more than 2 hours lead time [57] .
T14450 55575-55843 Sentence denotes For example, the evolution of position, intensity, and heavier rainfall areas of supercell thunderstorms (two of which were most likely responsible for the first two peaks in the time series for b) can currently not be predicted with more than 2 hours lead time [57] .
TextSentencer_T330 55844-56134 Sentence denotes We can then draw a more general conclusion from our results: that the spatial and temporal scales for prediction must be chosen carefully, not only to match the scales of disease spread [54] [55] [56] , but also with respect to the scales of the weather events that might affect the spread.
T34025 55844-56134 Sentence denotes We can then draw a more general conclusion from our results: that the spatial and temporal scales for prediction must be chosen carefully, not only to match the scales of disease spread [54] [55] [56] , but also with respect to the scales of the weather events that might affect the spread.
TextSentencer_T331 56135-56435 Sentence denotes The spatial and temporal scales considered here (a few km and ,1 y, respectively) proved to be ''too small'' for prediction: at those scales, the model output is extremely sensitive to the number and timing of isolated rare weather events (i.e., the effect of those events could not be averaged out).
T25793 56135-56435 Sentence denotes The spatial and temporal scales considered here (a few km and ,1 y, respectively) proved to be ''too small'' for prediction: at those scales, the model output is extremely sensitive to the number and timing of isolated rare weather events (i.e., the effect of those events could not be averaged out).
TextSentencer_T332 56436-56772 Sentence denotes An important question that arises is whether or not our results could be up-scaled: that is, how prediction would perform over larger (e.g., state-wide) spatial scales and longer (e.g., decadal) temporal scales, using the parameter values calculated here and weather templates (cf. [58] ) to generate time series for transmission rates.
T52063 56436-56772 Sentence denotes An important question that arises is whether or not our results could be up-scaled: that is, how prediction would perform over larger (e.g., state-wide) spatial scales and longer (e.g., decadal) temporal scales, using the parameter values calculated here and weather templates (cf. [58] ) to generate time series for transmission rates.
TextSentencer_T333 56773-56817 Sentence denotes This is the object of ongoing investigation.
T47529 56773-56817 Sentence denotes This is the object of ongoing investigation.
TextSentencer_T334 56818-57211 Sentence denotes Finally, while the lack of predictability is disappointing, it bears an important broader warning, namely that if a component of an epidemic-pathogen, vector or host-is affected by weather, or climate, but that relationship is poorly understood and there are insufficient long-term data, prediction of the future evolution of the epidemic can be both challenging and prone to systematic error.
T81731 56818-57211 Sentence denotes Finally, while the lack of predictability is disappointing, it bears an important broader warning, namely that if a component of an epidemic-pathogen, vector or host-is affected by weather, or climate, but that relationship is poorly understood and there are insufficient long-term data, prediction of the future evolution of the epidemic can be both challenging and prone to systematic error.
TextSentencer_T335 57212-57306 Sentence denotes Our system was mainly driven by stochastic weather events occurring on very short time scales.
T73394 57212-57306 Sentence denotes Our system was mainly driven by stochastic weather events occurring on very short time scales.
TextSentencer_T336 57307-57416 Sentence denotes At longer scales, we can consider influenza and mosquito-borne diseases as further contrasting illustrations.
T94329 57307-57416 Sentence denotes At longer scales, we can consider influenza and mosquito-borne diseases as further contrasting illustrations.
TextSentencer_T337 57417-57639 Sentence denotes Following recent evidence [59] that absolute humidity is a strong driver of the rates of transmission and survival of the influenza virus, a framework to predict seasonal outbreaks of influenza was recently proposed [60] .
T45609 57417-57639 Sentence denotes Following recent evidence [59] that absolute humidity is a strong driver of the rates of transmission and survival of the influenza virus, a framework to predict seasonal outbreaks of influenza was recently proposed [60] .
TextSentencer_T338 57640-57847 Sentence denotes With daily climatological data and real-time population disease status as inputs, retrospective forecasts could predict historical peaks of influenza outbreak with good accuracy seven weeks in advance [60] .
T36489 57640-57847 Sentence denotes With daily climatological data and real-time population disease status as inputs, retrospective forecasts could predict historical peaks of influenza outbreak with good accuracy seven weeks in advance [60] .
TextSentencer_T339 57848-57992 Sentence denotes While this case concerns short-term seasonal changes in weather, longer-term changes are also known to influence the risk and spread of disease.
T72226 57848-57992 Sentence denotes While this case concerns short-term seasonal changes in weather, longer-term changes are also known to influence the risk and spread of disease.
TextSentencer_T340 57993-58156 Sentence denotes The importance of climate on the spread of mosquito-borne diseases is broadly accepted [61] [62] [63] though very complex and not fully understood [64] [65] [66] .
T76012 57993-58156 Sentence denotes The importance of climate on the spread of mosquito-borne diseases is broadly accepted [61] [62] [63] though very complex and not fully understood [64] [65] [66] .
TextSentencer_T341 58157-58349 Sentence denotes Large scale weather anomalies, such as unusually long rain [67] or drought periods [68, 69] , can lead to unpredictable vector densities, which in turn frustrates public health planning [70] .
T91854 58157-58349 Sentence denotes Large scale weather anomalies, such as unusually long rain [67] or drought periods [68, 69] , can lead to unpredictable vector densities, which in turn frustrates public health planning [70] .
TextSentencer_T342 58350-58536 Sentence denotes Global climate change is expected to increase the frequency and intensity of unpredictable extreme weather events, with a far-reaching projected impact on many infectious diseases [70] .
T20913 58350-58536 Sentence denotes Global climate change is expected to increase the frequency and intensity of unpredictable extreme weather events, with a far-reaching projected impact on many infectious diseases [70] .
TextSentencer_T343 58537-58726 Sentence denotes In the face of such future challenges, it will be increasingly important for epidemiologists to explore and identify the external factors limiting the predictive capability of their models.
T34957 58537-58726 Sentence denotes In the face of such future challenges, it will be increasingly important for epidemiologists to explore and identify the external factors limiting the predictive capability of their models.
TextSentencer_T344 58727-58800 Sentence denotes Figure S1 Mapping infectious pressure from primary and secondary sources.
T60474 58727-58800 Sentence denotes Figure S1 Mapping infectious pressure from primary and secondary sources.
TextSentencer_T345 58801-58842 Sentence denotes A Snapshot of census site D2 at 150 days.
T66474 58801-58842 Sentence denotes A Snapshot of census site D2 at 150 days.
TextSentencer_T346 58843-58936 Sentence denotes The density of susceptible hosts is in gray scale; overlapped red circles are infected hosts.
T22686 58843-58936 Sentence denotes The density of susceptible hosts is in gray scale; overlapped red circles are infected hosts.
TextSentencer_T347 58937-59065 Sentence denotes The infectious pressure on susceptible hosts comes from two contributions: secondary sources (red circles) and external sources.
T21415 58937-59065 Sentence denotes The infectious pressure on susceptible hosts comes from two contributions: secondary sources (red circles) and external sources.
TextSentencer_T348 59066-59119 Sentence denotes B, C Infectious pressure from secondary sources only.
T9148 59066-59119 Sentence denotes B, C Infectious pressure from secondary sources only.
TextSentencer_T349 59120-59293 Sentence denotes Maps of the infectious pressure integrated over 30 days (equal to the expected density of new infections), estimated for the E model (panel B) and for the C model (panel C).
T61726 59120-59293 Sentence denotes Maps of the infectious pressure integrated over 30 days (equal to the expected density of new infections), estimated for the E model (panel B) and for the C model (panel C).
TextSentencer_T350 59294-59410 Sentence denotes Differences between the two models are evident in the top region of the system, far away from the secondary sources.
T9346 59294-59410 Sentence denotes Differences between the two models are evident in the top region of the system, far away from the secondary sources.
TextSentencer_T351 59411-59471 Sentence denotes D, E Infectious pressure from primary and secondary sources.
T71462 59411-59471 Sentence denotes D, E Infectious pressure from primary and secondary sources.
TextSentencer_T352 59472-59582 Sentence denotes Maps of the integrated infectious pressure, estimated for the E model (panel D) and for the C model (panel E).
T2428 59472-59582 Sentence denotes Maps of the integrated infectious pressure, estimated for the E model (panel D) and for the C model (panel E).
TextSentencer_T353 59583-59677 Sentence denotes The differences between the two models disappear when primary infection is taken into account.
T35515 59583-59677 Sentence denotes The differences between the two models disappear when primary infection is taken into account.
TextSentencer_T354 59678-59879 Sentence denotes See Text S1 for a description of the methods used to build the maps and a detailed discussion. (TIF) (3, 9) months, at two (A, D), four (B, E), and six months (C, F) from the beginning of the interval.
T9375 59678-59879 Sentence denotes See Text S1 for a description of the methods used to build the maps and a detailed discussion. (TIF) (3, 9) months, at two (A, D), four (B, E), and six months (C, F) from the beginning of the interval.
TextSentencer_T355 59880-60189 Sentence denotes Discrepancies between experimental (red lines) and simulated (grey shaded area) spatial statistics, explained by a lag of the experimental statistics, are solved by artificially shifting forward by two months the experimental autocorrelation function (J, H) and the experimental time-lagged statistics (I, J).
T45575 59880-60189 Sentence denotes Discrepancies between experimental (red lines) and simulated (grey shaded area) spatial statistics, explained by a lag of the experimental statistics, are solved by artificially shifting forward by two months the experimental autocorrelation function (J, H) and the experimental time-lagged statistics (I, J).
TextSentencer_T356 60190-60331 Sentence denotes See Text S1 for a detailed explanation. (TIF) Figure S7 Posterior predictive distributions from a model with negligible background infection.
T85159 60190-60331 Sentence denotes See Text S1 for a detailed explanation. (TIF) Figure S7 Posterior predictive distributions from a model with negligible background infection.
TextSentencer_T357 60332-60592 Sentence denotes Predictive distributions for site D1 are calculated from estimates for model M DT a , DT = 6 months (same census site and intervals as in Figure 5 ), with Cauchy kernel (cf. Text S1, Equation S5b) and background infection e kept at a very small constant value.
T94065 60332-60592 Sentence denotes Predictive distributions for site D1 are calculated from estimates for model M DT a , DT = 6 months (same census site and intervals as in Figure 5 ), with Cauchy kernel (cf. Text S1, Equation S5b) and background infection e kept at a very small constant value.
TextSentencer_T358 60593-60914 Sentence denotes Predictive distributions for disease progress (A, C, F, I; the total number of hosts being N = 6056), spatial autocorrelation function C t1 (B, D, G, J), and time-lagged statistic R t1 t0 (E, H, K) are shown, for intervals (0, 6) months (A, B), (3, 9) months (C, D, E), (6, 12) months (F, G, H), (9, 15) months (I, J, K).
T48146 60593-60914 Sentence denotes Predictive distributions for disease progress (A, C, F, I; the total number of hosts being N = 6056), spatial autocorrelation function C t1 (B, D, G, J), and time-lagged statistic R t1 t0 (E, H, K) are shown, for intervals (0, 6) months (A, B), (3, 9) months (C, D, E), (6, 12) months (F, G, H), (9, 15) months (I, J, K).
TextSentencer_T359 60915-60969 Sentence denotes Symbols and conventions are the same as for Figure 5 .
T23614 60915-60969 Sentence denotes Symbols and conventions are the same as for Figure 5 .
TextSentencer_T360 60970-61272 Sentence denotes For the last three periods (C-K), the progress of the epidemic is well reproduced (C,F,I), but simulated spatial statistics (D,G,J and E,H,K) clearly and consistently overestimate experimental spatial statistics (compare with Figure 5 , same panels, for the exponential kernel with external infection).
T85061 60970-61272 Sentence denotes For the last three periods (C-K), the progress of the epidemic is well reproduced (C,F,I), but simulated spatial statistics (D,G,J and E,H,K) clearly and consistently overestimate experimental spatial statistics (compare with Figure 5 , same panels, for the exponential kernel with external infection).
TextSentencer_T361 61273-61374 Sentence denotes See Text S1 for more details. (TIF) Figure S8 Temporal pattern of secondary rates in sites D1 and D2:
T37156 61273-61374 Sentence denotes See Text S1 for more details. (TIF) Figure S8 Temporal pattern of secondary rates in sites D1 and D2:
TextSentencer_T362 61375-61391 Sentence denotes Effect of shift.
T38007 61375-61391 Sentence denotes Effect of shift.
TextSentencer_T363 61392-61674 Sentence denotes Joint posterior distributions for the transmission rate, b t (model M DT a , DT = 1 month) for sites D1 and D2 (cf. Figure 4B ), plotted with no artificial shift in time (A) and with a 1-month shift in the rates for site D2 (B, same as Figure 4B and reproduced here for comparison).
T22884 61392-61674 Sentence denotes Joint posterior distributions for the transmission rate, b t (model M DT a , DT = 1 month) for sites D1 and D2 (cf. Figure 4B ), plotted with no artificial shift in time (A) and with a 1-month shift in the rates for site D2 (B, same as Figure 4B and reproduced here for comparison).
TextSentencer_T364 61675-61913 Sentence denotes While the joint densities in A lack a clear correlation pattern, consistency for the two sites emerges in B upon introducing a 1-month lag for the parameters of D2. (TIF) Figure S9 Consistency of longer-term secondary rates amongst sites:
T34753 61675-61913 Sentence denotes While the joint densities in A lack a clear correlation pattern, consistency for the two sites emerges in B upon introducing a 1-month lag for the parameters of D2. (TIF) Figure S9 Consistency of longer-term secondary rates amongst sites:
TextSentencer_T365 61914-61933 Sentence denotes 6-month resolution.
T97260 61914-61933 Sentence denotes 6-month resolution.
TextSentencer_T366 61934-62228 Sentence denotes Joint posterior distributions for the transmission rate, b t (model M DT a , DT = 6 months; cf. Figure 4 and Figure S8 for DT = 1 month) for sites B1 and B2 (A), sites D1 and D2 plotted with no artificial shift in time (B), and sites D1 and D2 with a 1-month shift in the rates for site D2 (C).
T53043 61934-62228 Sentence denotes Joint posterior distributions for the transmission rate, b t (model M DT a , DT = 6 months; cf. Figure 4 and Figure S8 for DT = 1 month) for sites B1 and B2 (A), sites D1 and D2 plotted with no artificial shift in time (B), and sites D1 and D2 with a 1-month shift in the rates for site D2 (C).
TextSentencer_T367 62229-62440 Sentence denotes Here, using a lower time resolution for rates, the consistency in the pattern of b t among census sites emerges with more regularity, although the qualitative behaviour is the same as in Figure 4 and Figure S8 .
T16427 62229-62440 Sentence denotes Here, using a lower time resolution for rates, the consistency in the pattern of b t among census sites emerges with more regularity, although the qualitative behaviour is the same as in Figure 4 and Figure S8 .
TextSentencer_T368 62441-62453 Sentence denotes Figure 1A) .
T15377 62441-62453 Sentence denotes Figure 1A) .
TextSentencer_T369 62454-62594 Sentence denotes For each polygon (small sub-areas delimited by gray lines), the human population density and number of households is known from census data.
T6306 62454-62594 Sentence denotes For each polygon (small sub-areas delimited by gray lines), the human population density and number of households is known from census data.
TextSentencer_T370 62595-62783 Sentence denotes The estimated density of residential citrus trees (colour-coded) was found using an empirical relationship between the number of citrus trees per household and human population density (W.
T36493 62595-62783 Sentence denotes The estimated density of residential citrus trees (colour-coded) was found using an empirical relationship between the number of citrus trees per household and human population density (W.
TextSentencer_T371 62784-62794 Sentence denotes Luo and T.
T67985 62784-62794 Sentence denotes Luo and T.
TextSentencer_T372 62795-62828 Sentence denotes Gottwald, private communication).
T88286 62795-62828 Sentence denotes Gottwald, private communication).
TextSentencer_T373 62829-62946 Sentence denotes The estimate shows that the host population was distributed with high spatial heterogeneity around every census site.
T74008 62829-62946 Sentence denotes The estimate shows that the host population was distributed with high spatial heterogeneity around every census site.
TextSentencer_T374 62947-63161 Sentence denotes Moreover, new infections were found in the area, and outside census sites, during all the epidemic (see Methods), which motivates the use of a primary infection rate e in the model (Equation (2b)). (TIF) Table 1 ).
T88490 62947-63161 Sentence denotes Moreover, new infections were found in the area, and outside census sites, during all the epidemic (see Methods), which motivates the use of a primary infection rate e in the model (Equation (2b)). (TIF) Table 1 ).
TextSentencer_T375 63162-63386 Sentence denotes Pairwise differences between DIC values for E and C models (columns with header E-C) show that the two models are essentially equivalent, with a trend for E to perform better than C as the frequency of rate change increases.
T52947 63162-63386 Sentence denotes Pairwise differences between DIC values for E and C models (columns with header E-C) show that the two models are essentially equivalent, with a trend for E to perform better than C as the frequency of rate change increases.
TextSentencer_T376 63387-63439 Sentence denotes Only for census site D1 is model E clearly favoured.
T82462 63387-63439 Sentence denotes Only for census site D1 is model E clearly favoured.
TextSentencer_T377 63440-63475 Sentence denotes See Text S1 for more details. (PDF)
T5009 63440-63475 Sentence denotes See Text S1 for more details. (PDF)
TextSentencer_T378 63476-63536 Sentence denotes Text S1 Dispersal kernels and spatial goodness-of-fit tests:
T7036 63476-63536 Sentence denotes Text S1 Dispersal kernels and spatial goodness-of-fit tests:
TextSentencer_T379 63537-63646 Sentence denotes Definitions, basic theory and discussion of further results (including selected supplementary figures). (PDF)
T75738 63537-63646 Sentence denotes Definitions, basic theory and discussion of further results (including selected supplementary figures). (PDF)