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Id Subject Object Predicate Lexical cue
T1 0-97 Sentence denotes Quantifying the impact of COVID-19 control measures using a Bayesian model of physical distancing
T2 98-195 Sentence denotes Quantifying the impact of COVID-19 control measures using a Bayesian model of physical distancing
T3 197-205 Sentence denotes Abstract
T4 206-362 Sentence denotes Extensive non-pharmaceutical and physical distancing measures are currently the primary interventions against coronavirus disease 2019 (COVID-19) worldwide.
T5 363-434 Sentence denotes It is therefore urgent to estimate the impact such measures are having.
T6 435-672 Sentence denotes We introduce a Bayesian epidemiological model in which a proportion of individuals are willing and able to participate in distancing, with the timing of distancing measures informed by survey data on attitudes to distancing and COVID-19.
T7 673-897 Sentence denotes We fit our model to reported COVID-19 cases in British Columbia (BC), Canada, and five other jurisdictions, using an observation model that accounts for both underestimation and the delay between symptom onset and reporting.
T8 898-1061 Sentence denotes We estimated the impact that physical distancing (social distancing) has had on the contact rate and examined the projected impact of relaxing distancing measures.
T9 1062-1377 Sentence denotes We found that, as of April 11 2020, distancing had a strong impact in BC, consistent with declines in reported cases and in hospitalization and intensive care unit numbers; individuals practising physical distancing experienced approximately 0.22 (0.11–0.34 90% CI [credible interval]) of their normal contact rate.
T10 1378-1445 Sentence denotes The threshold above which prevalence was expected to grow was 0.55.
T11 1446-1642 Sentence denotes We define the “contact ratio” to be the ratio of the estimated contact rate to the threshold rate at which cases are expected to grow; we estimated this contact ratio to be 0.40 (0.19–0.60) in BC.
T12 1643-1792 Sentence denotes We developed an R package ‘covidseir’ to make our model available, and used it to quantify the impact of distancing in five additional jurisdictions.
T13 1793-2148 Sentence denotes As of May 7, 2020, we estimated that New Zealand was well below its threshold value (contact ratio of 0.22 [0.11–0.34]), New York (0.60 [0.43–0.74]), Washington (0.84 [0.79–0.90]) and Florida (0.86 [0.76–0.96]) were progressively closer to theirs yet still below, but California (1.15 [1.07–1.23]) was above its threshold overall, with cases still rising.
T14 2149-2369 Sentence denotes Accordingly, we found that BC, New Zealand, and New York may have had more room to relax distancing measures than the other jurisdictions, though this would need to be done cautiously and with total case volumes in mind.
T15 2370-2514 Sentence denotes Our projections indicate that intermittent distancing measures—if sufficiently strong and robustly followed—could control COVID-19 transmission.
T16 2515-2728 Sentence denotes This approach provides a useful tool for jurisdictions to monitor and assess current levels of distancing relative to their threshold, which will continue to be essential through subsequent waves of this pandemic.
T17 2730-2742 Sentence denotes Introduction
T18 2743-2993 Sentence denotes Coronavirus disease 2019 (COVID-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has now spread worldwide and resulted in over 20 million diagnosed cases and 700,000 confirmed deaths globally as of August 11, 2020 [1].
T19 2994-3241 Sentence denotes Estimates of COVID-19 case fatality rates from Hubei, China, the rest of China, and other countries range from 0.3% to above 5% in different populations at various times [2, 3], with an estimate of 1.4% [4] currently favoured in some analyses [5].
T20 3242-3398 Sentence denotes Age [6] and comorbidities (hypertension, cardiovascular and respiratory disease [7]) are strong risk factors for severe illness, hospitalization, and death.
T21 3399-3594 Sentence denotes Furthermore, COVID-19 poses severe challenges for health care, with risks that requirements will exceed hospital bed, critical care, and ICU capacities even in well-resourced health care systems.
T22 3595-3929 Sentence denotes In the current absence of a vaccine or effective therapeutic options, widespread non-pharmaceutical interventions including testing, contact tracing, isolation and quarantine, hand hygiene, and physician distancing, along with broad physical or social distancing, are the main interventions currently available to reduce transmission.
T23 3930-4127 Sentence denotes Countries have used a variety of such physical or social distancing measures including cancelling mass gatherings, closing restaurants, work-from-home orders, and “lockdowns” of varying strictness.
T24 4128-4331 Sentence denotes In British Columbia (BC), Canada, for example, the first case of infection was detected on January 26, 2020 with sporadic cases related to travel until March 8, followed by a sustained increase in cases.
T25 4332-4426 Sentence denotes A number of measures were implemented over the following weeks to reduce transmission (Fig 1).
T26 4427-4501 Sentence denotes However, the direct impact of these measures on transmission is not known.
T27 4502-4569 Sentence denotes Distancing measures have high economic, health, and social impacts.
T28 4570-4709 Sentence denotes Thus, there is an urgent need to understand what level of contact rate and physical distancing measures are optimal to reduce transmission.
T29 4710-4924 Sentence denotes Once initial transmission has been brought under control, as in China and Korea [8, 9] as of March/April 2020, there remains the question of what relaxation in social measures could keep transmission under control.
T30 4925-4991 Sentence denotes Fig 1 Information regarding COVID-19 in British Columbia, Canada.
T31 4992-5065 Sentence denotes (A) Key physical distancing measures implemented in response to COVID-19.
T32 5066-5295 Sentence denotes Schools closed for an annual two-week break on March 14 and then were declared indefinitely closed on March 17. (B) Time from symptom onset to reporting from case-specific data as of April 11, 2020 and (C) reported cases per day.
T33 5296-5404 Sentence denotes The dashed line in panel B represents the line above which cases, by definition, have not been reported yet.
T34 5405-5523 Sentence denotes Boxes indicate interquartile range and median values. (D) Hospitalization and ICU (Intensive Care Unit) census counts.
T35 5524-5581 Sentence denotes All data are from the BC Centre for Disease Control [10].
T36 5582-5688 Sentence denotes There have been a number of models simulating the impact of broad physical distancing measures [8, 11–13].
T37 5689-5888 Sentence denotes Direct estimates of the strength and impact of distancing measures have focused on the effective reproduction number over time, using approaches based on reported deaths [14] or confirmed cases [15].
T38 5889-6039 Sentence denotes These estimates are influenced by the assumed serial interval distribution, the infection fatality rate and the delay between symptom onset and death.
T39 6040-6205 Sentence denotes In comparisons among European Union countries, estimates assume that physical-distancing measures impact each location equally and that all deaths are reported [14].
T40 6206-6445 Sentence denotes Estimates of the effective reproduction number based on reported cases have been adjusted for the delay between symptom onset and reporting [15, 16], but do not accommodate underestimation or asymptomatic or weakly symptomatic individuals.
T41 6446-6666 Sentence denotes Furthermore, the effective reproduction number is a broad summary of the overall growth of the epidemic, and is not a direct estimate of the impact of physical distancing on the contact patterns relevant to transmission.
T42 6667-6886 Sentence denotes Here, we introduce an epidemiological model of physical distancing and assess the degree to which contact rates have changed—for the population that is participating in physical distancing—due to recent policy measures.
T43 6887-6992 Sentence denotes We focus on BC, and also apply our methods to New York, Florida, Washington, California, and New Zealand.
T44 6993-7144 Sentence denotes We quantify how close jurisdictions are to the threshold at which cases begin to rise, and we explore the impact of reducing distancing measures in BC.
T45 7146-7153 Sentence denotes Methods
T46 7155-7159 Sentence denotes Data
T47 7160-7383 Sentence denotes We fit the physical distancing model to case-count data from British Columbia from March 1, 2020 (when a total of eight cases had been detected in the province) to April 11, 2020 at which time 1445 cases had been confirmed.
T48 7384-7573 Sentence denotes These data are available in press releases from the BC Centre for Disease Control (BCCDC) [10], from the public data dashboard [17], and from the code repository associated with this paper.
T49 7574-7638 Sentence denotes Testing procedures were adapted over the course of the outbreak.
T50 7639-7879 Sentence denotes In particular, lab testing criteria were changed on March 16 to focus on hospitalized patients, healthcare workers, long-term care facility residents/staff, and those people part of an existing cluster and experiencing respiratory symptoms.
T51 7880-8004 Sentence denotes This led to high variability in case counts in the surrounding days with some large jumps in the number of identified cases.
T52 8005-8201 Sentence denotes We accounted for this in the model by adjusting the testing fraction ψr to accommodate widening the testing pool and thereby increasing the fraction of infected individuals being tested (Table 1).
T53 8202-8255 Sentence denotes There was also variability in the daily testing rate.
T54 8256-8385 Sentence denotes During March, the daily number of completed tests ranged from approximately 100 to 3500, and did not strictly increase over time.
T55 8386-8539 Sentence denotes Table 1 Values and sources for British Columbia parameterization of the model (see Supplemental Methods and Table B in S1 Text for other jurisdictions).
T56 8540-8682 Sentence denotes The duration of the infectious period is shorter than the duration of severe illness, accounting for self-isolation and less severe illnesses.
T57 8683-8832 Sentence denotes The quarantine parameter q reflects approximately 1/5 of severe cases either ceasing to transmit due to hospitalization or completely self-isolating.
T58 8833-8972 Sentence denotes The model depends on the combination ur/(ur + ud), the fraction engaged in physical distancing, estimated from the survey data cited above.
T59 8973-9124 Sentence denotes The testing patterns have changed over time, with laboratories increasing the numbers of tests on approximately March 14 (motivating our change in ψr).
T60 9125-9182 Sentence denotes Symbol Definition Specified/fitted value Justification
T61 9183-9218 Sentence denotes N Population size 5,100,000 [23]
T62 9219-9278 Sentence denotes D Mean duration of the infectious period 5 days [24, 25]
T63 9279-9342 Sentence denotes k 1 (time to infectiousness)−1 (E1 to E2) 0.2 days−1 [26–28]
T64 9343-9429 Sentence denotes k 2 (time period of pre-symptomatic transmissibility)−1 (E2 to I) 1 days−1 [27, 28]
T65 9430-9460 Sentence denotes q Quarantine rate 0.05 [29]
T66 9461-9521 Sentence denotes u d Rate of people moving to physical distancing 0.1 [20]
T67 9522-9589 Sentence denotes u r Rate of people returning from physical distancing 0.02 [20]
T68 9590-9687 Sentence denotes ψ r Proportion of anticipated cases on day r that are tested and reported 0.1 Before March 14
T69 9688-9714 Sentence denotes 0.3 On and after March 14
T70 9715-9824 Sentence denotes Shape Weibull parameter in delay-to-reporting distribution 1.73 (1.60–1.86 95% CI) Fit to data from Fig 1B
T71 9825-9935 Sentence denotes Scale Weibull parameter in delay-to-reporting distribution 9.85 (9.30–10.46 95% CI) Fit to data from Fig 1B
T72 9936-10017 Sentence denotes R 0b Basic reproductive number 2.95 (2.88–3.02 95% CI) Fit to data from Fig 1C
T73 10018-10128 Sentence denotes f 2 Fraction of normal contacts during physical distancing 0.22 (0.08– 0.36 95% CI) Fit to data from Fig 1C
T74 10129-10342 Sentence denotes ϕ Inverse dispersion from negative binomial (NB2) observation model 6.86 (3.39–12.37 95% CI) Fit to data from Fig 1C For some confirmed cases in BC, estimates of the date of symptom onset are available (Fig 1).
T75 10343-10455 Sentence denotes We used the delays between symptom onset and cases being reported to parameterize the physical distancing model.
T76 10456-10598 Sentence denotes In this case-specific data set there were only seven cases reported before February 29, and a decline in reported cases after April 2 (Fig 1).
T77 10599-10745 Sentence denotes Therefore we used only the 535 cases in the case-specific data that were reported between these dates to parameterize the delay part of the model.
T78 10746-10940 Sentence denotes For California (CA), New York (NY), and Florida (FL) we used reported case and testing data from The COVID Tracking Project, and assumed a BC-like delay between symptom onset and case reporting.
T79 10941-11028 Sentence denotes For New Zealand (NZ) we used reported cases from the NZ Ministry of Health [18], and A.
T80 11029-11042 Sentence denotes Lustig and M.
T81 11043-11222 Sentence denotes Plank (pers. comm.) fit the delay distribution to NZ case-reporting data using our package [19], since these data are not publicly available (see Supplemental Methods in S1 Text).
T82 11223-11300 Sentence denotes For our main analysis with BC, we fit our model to data until April 11, 2020.
T83 11301-11544 Sentence denotes When demonstrating the application of our model to other jurisdictions, we included data until May 6 or 7, 2020, the date we completed this portion of the analysis and before these jurisdictions had begun relaxing physical distancing measures.
T84 11545-11834 Sentence denotes An outbreak at a poultry plant in BC, combined with an expansion of testing in mid April, meant that in order to extend the BC model to May 6 or 7, we would have had to introduce changes to the methodology that would not be straightforward and would not be possible in other jurisdictions.
T85 11835-12032 Sentence denotes These include, for example, modelling the poultry workforce’s interventions and contacts and the links between the outbreak and general community transmission, in concert with differential testing.
T86 12033-12097 Sentence denotes We therefore limited the data used for the BC model to April 11.
T87 12098-12302 Sentence denotes We motivated the structure of our model based on a survey conducted by the Angus Reid Institute to examine how physical distancing measures changed behaviour in Canada (March 20–23, 2020; n = 1664; [20]).
T88 12303-12504 Sentence denotes Responses indicated that there was a subset of the population believing that the response to the COVID-19 epidemic was “overblown”, who were less willing than others to engage in distancing behaviours.
T89 12505-12683 Sentence denotes This motivated treating the distancing and non-distancing compartments of our model separately and assuming that ∼80% of individuals were able and willing to physically distance.
T90 12684-12869 Sentence denotes We used the timing of known government interventions to inform the timing of behavioural changes, and verified these dates against publicly available mobility data for each region [21].
T91 12871-12892 Sentence denotes Epidemiological model
T92 12893-12957 Sentence denotes We used a susceptible-exposed-infectious-recovered (SEIR) model.
T93 12958-13123 Sentence denotes Our model allows for self-isolation and quarantine through a quarantine compartment and a reduced duration of infection (compared to the clinical course of disease).
T94 13124-13356 Sentence denotes We modelled a fixed portion of the population that was able to participate in physical distancing; each of the SEIR compartments has an analogous compartment in the distancing group (Fig 2; Table 1; Supplemental Methods in S1 Text).
T95 13357-13403 Sentence denotes Fig 2 Schematic of the epidemiological model.
T96 13404-13592 Sentence denotes Compartments are: susceptible to the virus (S); exposed (E1); exposed, pre-symptomatic, and infectious (E2); symptomatic and infectious (I); quarantined (Q); and recovered or deceased (R).
T97 13593-13640 Sentence denotes Recovered individuals are assumed to be immune.
T98 13641-13727 Sentence denotes The model includes analogous variables for individuals practising physical distancing:
T99 13728-13757 Sentence denotes Sd, E1d, E2d, Id, Qd, and Rd.
T100 13758-13905 Sentence denotes Solid arrows represent flow of individuals between compartments at rates indicated by the mathematical terms (see Supplement for full definitions).
T101 13906-13972 Sentence denotes Dashed lines show which compartments contribute to new infections.
T102 13973-14086 Sentence denotes An individual in some compartment X can begin distancing and move to the corresponding compartment Xd at rate ud.
T103 14087-14128 Sentence denotes The reverse transition occurs at rate ur.
T104 14129-14288 Sentence denotes The model quickly settles on a fraction e = ud/(ud + ur) participating in distancing, and dynamics depend on this fraction, rather than on the rates ud and ur.
T105 14289-14443 Sentence denotes The physical distancing compartments contribute a reduced amount (a fraction f) to the force of infection, with f = 1 representing no physical distancing.
T106 14444-14513 Sentence denotes We made f time-dependent to represent changes in physical distancing.
T107 14514-14869 Sentence denotes We modelled the change in physical distancing by a simple linear function whereby physical distancing increases (f(t) decreases from 1 to a final value f2, which we estimated) over one week between March 15 (t = t1) and March 22 (t = t2) in BC, and as informed by policy and mobility data in the other jurisdictions (Table B in S1 Text; Eq. 3 in S1 Text).
T108 14870-15040 Sentence denotes We fixed f(t) = f2 until the final day of observed data and changed f(t) for any future days to represent different scenarios regarding relaxation of physical distancing.
T109 15041-15220 Sentence denotes The number of people per day who become symptomatic is the number per day moving from the pre-symptomatic E2 and E2d compartments to the symptomatic I and Id compartments (Fig 2).
T110 15221-15424 Sentence denotes Due to the delay between symptom onset and reporting, the model’s predicted number of reported cases, μr, on day r is comprised of contributions from previous days weighted by a delay, which we estimate.
T111 15425-15594 Sentence denotes We used a negative binomial model combined with information about testing changes over time to form a likelihood function, linking observed cases to the model (S1 Text).
T112 15595-15759 Sentence denotes The proportion of anticipated cases on day r that are tested and reported varies over time due to changes in the testing protocols, lab capacity, and other factors.
T113 15760-15906 Sentence denotes In our BC data, the number of tests performed each day jumped dramatically on March 14; we modelled this with a sharp increase in ψr on that date.
T114 15907-15973 Sentence denotes We fit a random walk to this function as a supplementary analysis.
T115 15974-16009 Sentence denotes In other jurisdictions we fixed ψr.
T116 16010-16248 Sentence denotes We used a Weibull distribution for the delay function w(s), based on [22], and fit the shape and scale parameters using the case-specific data of reported cases and time of symptom onset (Fig 1), accounting for right truncation (S1 Text).
T117 16250-16260 Sentence denotes Estimation
T118 16261-16441 Sentence denotes We used a Bayesian statistical model to condition our inference about R0b, f2, and expected case counts on the number of reported cases, where R0b is the basic reproductive number.
T119 16442-16576 Sentence denotes We related the expected number of cases to the observations through a negative binomial observation model with dispersion parameter ϕ.
T120 16577-16641 Sentence denotes We placed weakly informative priors on R0b, f2, and ϕ (S1 Text).
T121 16642-16789 Sentence denotes Outside of BC, we estimated the start and end times of the ramp-up of social distancing using priors informed by policy and transit data (S1 Text).
T122 16790-16969 Sentence denotes We fit our models with Stan 2.19.1 [30, 31] and R 3.6.2 [32]; Stan implements the No-U-Turn Hamiltonian Markov chain Monte Carlo algorithm [33] for Bayesian statistical inference.
T123 16970-17113 Sentence denotes In our main model run, we sampled from eight chains with 2000 iterations each and discarded the first 1000 iterations of each chain as warm-up.
T124 17114-17378 Sentence denotes We assessed chain convergence visually via trace plots (Figure G in S1 Text) and via ensuring that R^≤1.01 (the potential scale reduction factor) and that ESS > 200 (the effective sample size), as calculated by the rstan R package [31] (Tables C and D in S1 Text).
T125 17379-17442 Sentence denotes We represent uncertainty via quantile-based credible intervals.
T126 17443-17500 Sentence denotes We validated our approach using simulated data (S1 Text).
T127 17501-17704 Sentence denotes We developed two R packages for this analysis: ‘rightTruncation’ [19] and ‘covidseir’ [34]. ‘rightTruncation’ performs maximum likelihood estimates of delay distributions accounting for right truncation.
T128 17705-17806 Sentence denotes We used this approach to estimate the time between symptom onset and reporting in BC and New Zealand.
T129 17807-17893 Sentence denotes The ‘covidseir’ package facilitates the SEIR model fitting of case-count data in Stan.
T130 17895-17902 Sentence denotes Results
T131 17903-18008 Sentence denotes We found that, as of April 11, 2020, physical distancing had considerably reduced the contact rate in BC.
T132 18009-18259 Sentence denotes We estimated that individuals practising physical distancing experienced approximately 0.22 (0.11–0.34 90% CI [credible interval]) of their normal contact rate, which was below the critical threshold (0.55; Fig 3; Figures E–H and Table C in S1 Text).
T133 18260-18428 Sentence denotes The model described the count data well, with reported cases showing a peak in late March, approximately two weeks after the initiation of distancing measures (Fig 3A).
T134 18429-18581 Sentence denotes The data were informative with respect to both main parameters with the posteriors distinctly different and more peaked than the priors (Fig 3B and 3D).
T135 18582-18707 Sentence denotes We used a fixed value of e, the fraction engaged in distancing; this choice was motivated by the survey and behavioural data.
T136 18708-18810 Sentence denotes If e were lower, the estimated strength of distancing would be higher to achieve the same case counts.
T137 18811-18950 Sentence denotes We found this trade-off analytically using the basic reproduction number for the full model (Supplemental Methods and Figure A in S1 Text).
T138 18951-19124 Sentence denotes Fig 3 (A) Observed and estimated case counts, (C) estimated prevalence, and posterior estimates for (B) R0b and (D) fraction of normal contacts (f2) among those distancing.
T139 19125-19261 Sentence denotes These projections do not account for introduced cases from other jurisdictions and they assume that distancing measures remain in place.
T140 19262-19392 Sentence denotes The fraction of normal contacts is the model’s portion of contacts that remain among those who are engaged in physical distancing.
T141 19393-19533 Sentence denotes In panel A, the blue line represents the posterior mean and the shaded ribbons represent 50% and 90% credible intervals on new observations.
T142 19534-19583 Sentence denotes Dots and black lines represent the reported data.
T143 19584-19621 Sentence denotes Grey region indicates the projection.
T144 19622-19683 Sentence denotes In panel C, lines represent example draws from the posterior.
T145 19684-19751 Sentence denotes In panels B and D, priors are shown in grey and posteriors in blue.
T146 19752-19899 Sentence denotes In panel D, the dashed vertical line denotes the threshold above which an exponential increase in prevalence is expected (see Figure J in S1 Text).
T147 19900-19905 Sentence denotes Note:
T148 19906-20092 Sentence denotes Model prevalence depends on assumptions about underestimation, incubation period, and the duration of infection, none of which we can estimate well from these data (Figure M in S1 Text).
T149 20093-20159 Sentence denotes Much higher values of the prevalence are consistent with our data.
T150 20160-20526 Sentence denotes We found that with a shorter incubation period and duration of infectiousness, a lower reproduction number would fit the same overall growth rate, and conversely if the infectious duration and serial interval were longer, a higher reproduction number would be required but the fit to data would be similar (Figure K in S1 Text); this relationship is well known [35].
T151 20527-20637 Sentence denotes The conclusion that distancing measures reduced contact is robust to these alternatives (Figure K in S1 Text).
T152 20638-20847 Sentence denotes The model depends on the fraction engaged in distancing, but not strongly on the rates ud and ur; Figure L in S1 Text illustrates that we obtained the same results with these rates increased by a factor of 10.
T153 20848-21156 Sentence denotes We also explored the robustness to the unknown underestimation fractions (Figure M in S1 Text), and a random walk pattern in the fraction of cases sampled (Figure N in S1 Text); again, the data are consistent with a range of underestimation fractions, but the conclusion about the contact fraction is robust.
T154 21157-21604 Sentence denotes Our estimates suggest that, as of April 11, 2020, some relaxation of current distancing measures in BC would have been possible without bringing the growth rate above zero, but if measures were relaxed too much (in the absence of monitoring and re-starting measures), the prevalence and case counts would begin to increase exponentially (Fig 4A and 4B), reaching high levels by June 2020 if distancing were to cease entirely (Figure I in S1 Text).
T155 21605-21769 Sentence denotes These are illustrative scenarios only; public health responses with renewed or revised measures would likely be put in place rapidly were such rises to be observed.
T156 21770-21873 Sentence denotes The speed of growth depends on how close the system is to the epidemic threshold (Figure J in S1 Text).
T157 21874-22062 Sentence denotes If strong enough measures are not maintained, the model predicts a range of possible epidemic curves (Figure I in S1 Text) consistent with simple and complex published models [11, 12, 14].
T158 22063-22112 Sentence denotes Fig 4 Scenarios of relaxing distancing measures.
T159 22113-22329 Sentence denotes Distancing measures are relaxed to (A) 60% (A) and (B) 80% levels of normal contacts and exponential growth is observed at moderate and rapid rates. (C, D) Two scenarios of cycling between physical distancing levels.
T160 22330-22481 Sentence denotes Here, the percentage of normal contacts alternates between 80% (dark-grey shading) and 22% (light-grey shading) at (C) 3-week and (D) 4-week intervals.
T161 22482-22575 Sentence denotes Reducing contacts to 22% of normal is approximately the level estimated by our model (Fig 3).
T162 22576-22653 Sentence denotes Note the lag between changes in physical distancing and reported case counts.
T163 22654-22716 Sentence denotes Figure description is otherwise the same as for Fig 3A and 3C.
T164 22717-22892 Sentence denotes There has been interest in relaxing distancing measures and re-introducing them when a threshold has been reached, such as when intensive care capacity is nearly reached [36].
T165 22893-23040 Sentence denotes We did not explore a dynamic trigger, but did explore the behaviour when distancing measures are introduced and relaxed repeatedly (Fig 4C and 4D).
T166 23041-23249 Sentence denotes If the relaxation period is such that the outbreak remains contained throughout (with an effective reproduction number less than one), then the prevalence would decline at alternating faster and slower rates.
T167 23250-23438 Sentence denotes In a scenario of switching between the current mean estimate (22% of normal contacts) and 80% of normal contacts, reported cases rise, lagging the relaxation of distancing (Fig 4C and 4D).
T168 23439-23693 Sentence denotes Illustrative simulations in which distancing alternates every three or four weeks allows an overall continued decline; however, the longer the period of relaxation, the more the prevalence is able to rise in between periods of distancing (Fig 4C and 4D).
T169 23694-23891 Sentence denotes Control of delayed feedback systems is challenging [37], and ideally if a dynamic trigger such as reported cases or ICU admissions were to be used, monitoring would need to be as rapid as possible.
T170 23892-24011 Sentence denotes Monitoring of distancing behaviour and population contact patterns would be important, in addition to monitoring cases.
T171 24012-24318 Sentence denotes We estimated the fraction of normal contact rate in five additional jurisdictions as of May 7, 2020 (Fig 5), and give numerical results as the median (and 90% CI) of the “contact ratio”: the ratio of the fraction of normal contacts to the threshold (above which prevalence increases) for each jurisdiction.
T172 24319-24615 Sentence denotes We found that while New York had a high peak in reported cases, overall control there was strong as of May 7 and there may have been room to relax distancing measures while remaining below the threshold above which cases would be expected to increase, since the contact ratio is 0.60 (0.43–0.74).
T173 24616-24724 Sentence denotes We estimated contact ratios of 0.86 (0.76–0.96) for Florida and 0.84 (0.79–0.90) for Washington as of May 7.
T174 24725-24864 Sentence denotes These are not far below 1.0, and so any re-opening or relaxation of distancing measures would be expected to result in rising case numbers.
T175 24865-25217 Sentence denotes In contrast, while some areas in California experienced strong distancing and mobility data suggest movement on par with Florida, New York, and Washington (Fig 5F), overall case counts in California had not declined as of May 7, and our model estimated that contacts were exceeding the critical threshold on average (contact ratio of 1.15 [1.07–1.23]).
T176 25218-25422 Sentence denotes In contrast, New Zealand had extremely effective control measures and we estimated that nearly all contacts were removed among those distancing as of May 6, 2020, with a contact ratio of 0.22 (0.11–0.34).
T177 25423-25555 Sentence denotes This left considerable room for re-opening (in concert with careful border measures and continued contact tracing and case finding).
T178 25556-25681 Sentence denotes Fig 5 Observed and estimated case counts for (A) New York, (B) Florida, (C) Washington, (D) California, and (E) New Zealand.
T179 25682-25805 Sentence denotes Solid curves represent the posterior means and shaded ribbons represent 50% and 90% credible intervals of estimated counts.
T180 25806-25855 Sentence denotes Dots and black lines represent the reported data.
T181 25856-26180 Sentence denotes Inset histograms show the posterior distributions of the fraction of normal contacts (f2), with the vertical lines denoting the threshold above which an exponential increase in prevalence is expected (as in Fig 3D). (F) Reduction in movement from Google mobility transit-station data [21] colour-coded for each jurisdiction.
T182 26181-26272 Sentence denotes Thin lines are raw data; thick lines are smoothed values from a generalized additive model.
T183 26273-26389 Sentence denotes See Table B and Supplemental Methods in S1 Text for details on the regional modelling parameters and initialization.
T184 26391-26401 Sentence denotes Discussion
T185 26402-26680 Sentence denotes Our results suggest that physical distancing measures were effective in British Columbia; we estimated that individuals practising physical distancing in British Columbia to be experiencing approximately 0.22 (0.11–0.34 90% CI) of their normal contact rate as of April 11, 2020.
T186 26681-26810 Sentence denotes This was below the threshold of 0.55 at which prevalence was expected to grow, which left some room to relax distancing measures.
T187 26811-26891 Sentence denotes These results were supported by declines in hospitalizations and ICU admissions.
T188 26892-26988 Sentence denotes We estimated that there was varying room to relax measures in other locations as of May 7, 2020.
T189 26989-27079 Sentence denotes Strong control in New Zealand suggested considerable scope for restrictions to be relaxed.
T190 27080-27191 Sentence denotes However, we found that there was relatively little room to relax measures in New York, Florida, and Washington.
T191 27192-27410 Sentence denotes The overall picture in California, as of May 7, 2020, appeared to be that contacts were above the threshold that leads to increasing prevalence, and hence restrictions were not sufficient to curb spread of the disease.
T192 27411-27550 Sentence denotes We note that in California, and all locations considered, it is likely that there was strong regional variation around our broad estimates.
T193 27551-27672 Sentence denotes Our estimates for BC are consistent with local mobility data, and with contact patterns in other international locations.
T194 27673-27857 Sentence denotes For example, survey data from the UK [39] suggested a 73% reduction in contacts, and a modelling study found that a 70–80% reduction in contacts is consistent with data in France [13].
T195 27858-28014 Sentence denotes Our estimate of the effect of distancing on contact patterns in BC is consistent with independent lines of evidence for the strength of distancing measures.
T196 28015-28178 Sentence denotes Local rail (SkyTrain) station crowding data, provided by Metro Vancouver’s transportation authority TransLink, gives a proxy for reduction in public transport use.
T197 28179-28309 Sentence denotes Overall daytime travel was reduced by 16% for the week of March 9, 64% for the week of March 16, and 73% for the week of March 23.
T198 28310-28430 Sentence denotes Estimates on adhering to physical distancing are also available from a publicly available respondent-driven survey [20].
T199 28431-28602 Sentence denotes The survey found the rate of respondents stating that there was a serious threat of a coronavirus outbreak in Canada increased from 42% on March 5–6 to 88% on March 20–23.
T200 28603-28784 Sentence denotes For individuals who stated there was a serious threat, 89% stated they were keeping personal distance compared to 66% for individuals who did not believe there was a serious threat.
T201 28785-29068 Sentence denotes Mobile phone location data from BlueDot [39] suggested that the maximum and cumulative distance travelled from home fell by approximately 90%, the portion of mobile phone check-ins at home rose by over 10%, and the portion of devices for which every check-in was at home rose by 60%.
T202 29069-29184 Sentence denotes These estimates are also consistent with Google mobility [21], Citymapper index [40], and Apple mobility data [41].
T203 29185-29322 Sentence denotes These are indirect reflections of the contact rate but are supportive of a dramatic change in contact patterns as reflected in our model.
T204 29323-29393 Sentence denotes Furthermore, similar data are widely available for many jurisdictions.
T205 29394-29483 Sentence denotes Our results provide a direct estimate of contact rates in conjunction with mobility data.
T206 29484-29691 Sentence denotes Our results suggest that some relaxation of distancing measures may have been possible in BC and New York, considerably so in New Zealand, but that relaxation would have been risky in Washington and Florida.
T207 29692-29842 Sentence denotes In BC, we simulated fixed and dynamic measures—less stringent than the measures in place at present—which would continue to maintain low case numbers.
T208 29843-29950 Sentence denotes This is feasible either through continual strong distancing, or via well-monitored dynamic on/off measures.
T209 29951-30197 Sentence denotes We have illustrated the model’s high case volumes and long time frames that would result from cessation of distancing and the absence of continued strong public health and behavioural intervention in BC; the dynamics would look similar elsewhere.
T210 30198-30412 Sentence denotes In all jurisdictions, we found that immunity has not built up in the model; our estimates of the decline are not due to a natural peak in an epidemic curve, but are the direct effect of changes in contact patterns.
T211 30413-30531 Sentence denotes Seasonal transmission could even amplify a peak in the winter season, if control and monitoring were ceased then [12].
T212 30532-30679 Sentence denotes The delays between exposure and reporting present obvious challenges for monitoring the success of control measures using reported case-count data.
T213 30680-30987 Sentence denotes We suggest that two different kinds of monitoring will be important if distancing measures are to be relaxed: (1) monitoring cases through testing, contact tracing, and other case finding, and (2) monitoring contact patterns and distancing behaviour in the population, in a “distancing surveillance” effort.
T214 30988-31304 Sentence denotes This latter form of monitoring, derived from mobile phones, surveys and apps, could be available rapidly, whereas the incubation period places an unavoidable delay between control measures and detecting their impact in reported cases—even if testing of symptomatic cases were widespread and reporting were immediate.
T215 31305-31471 Sentence denotes There is considerable interest in real-time monitoring of mobile phone movements, population surveys on the uptake of physical distancing, and other behavioural data.
T216 31472-31566 Sentence denotes While these are potentially promising avenues, the outcome of interest is incident infections.
T217 31567-31673 Sentence denotes Locations of mobile phones, traffic patterns, and survey information are proxies for this outcome at best.
T218 31674-31848 Sentence denotes The work we have presented here could help to calibrate distancing surveillance measurements, to understand how they relate to changes in contact rates for modelling efforts.
T219 31849-31911 Sentence denotes Our modelling framework has a number of important limitations.
T220 31912-32054 Sentence denotes We do not model age and contact structure explicitly, except to distinguish between two populations: those participating in distancing or not.
T221 32055-32235 Sentence denotes This has the advantage that we do not require data on age-specific contact patterns, responses to distancing measures, or infectiousness; these data are not available at this time.
T222 32236-32348 Sentence denotes It also limits our ability to provide guidance on where and how contact reduction measures could be implemented.
T223 32349-32600 Sentence denotes It is a simplification of behaviour in many ways; true distancing responses are a continuum, and the measures in place (e.g., no mass gatherings or dine-in services) also mean that the whole population is experiencing some changes in contact patterns.
T224 32601-32770 Sentence denotes Our model is deterministic, and so does not capture the possibility of extinction; in addition, we have not simulated introductions of COVID-19 from other jurisdictions.
T225 32771-32948 Sentence denotes We have not accounted for geographic structure; differences in distancing behaviour, health care practices, and demographics in different jurisdictions could impact the results.
T226 32949-33162 Sentence denotes We have also not modelled either conventional or automated contact tracing [42, 43]; in our model these would decrease the duration of the infectious period and change the transitions for some exposed individuals.
T227 33163-33202 Sentence denotes There are also limitations in our data.
T228 33203-33357 Sentence denotes We have used an observation model to link reported cases to the modelled prevalence, and we included variation in the portion of cases detected over time.
T229 33358-33572 Sentence denotes Modelling and forecasting based on reported cases faces challenges when testing is driven by clinical needs, testing capacities, and other constraints (and in particular is not designed to test population samples).
T230 33573-33697 Sentence denotes Cases in long-term care facilities (LTCF) represent a substantial fraction of the cases, and particularly the deaths, in BC.
T231 33698-33802 Sentence denotes Along with the low number of deaths in total, this is one rationale for not modelling deaths explicitly.
T232 33803-33908 Sentence denotes We included LTCF cases but also modelled a wide range of under-reporting to account for potential biases.
T233 33909-34061 Sentence denotes If many cases in an LTCF cluster were all reported on the same day (or within a short time frame) this could increase the noise in reported case counts.
T234 34062-34387 Sentence denotes We have modelled case counts as over-dispersed compared to a Poisson distribution to account for such variation; we have developed the R package to model a range of data types individually or in combination (e.g., reported cases, hospitalizations, ICU admissions), which could help to overcome limitations of particular data.
T235 34388-34468 Sentence denotes The testing criteria include a number of categories that have changed over time.
T236 34469-34573 Sentence denotes Testing volume increased sharply in mid March in BC and most jurisdictions have changed testing volumes.
T237 34574-34624 Sentence denotes The base population being tested has also changed.
T238 34625-34833 Sentence denotes In BC, testing first focused primarily on those hospitalized or likely to be hospitalized, health care workers, residents of long-term care facilities, and other cluster investigations (mid-March to April 9).
T239 34834-35017 Sentence denotes Testing was then expanded to include residents of remote, isolated, or Indigenous communities, people who are homeless or have unstable housing, and by physicians’ clinical judgement.
T240 35018-35185 Sentence denotes There is likely some inconsistency in the application of these guidelines across hospitals and facilities, and base populations differ in across jurisdictions as well.
T241 35186-35316 Sentence denotes As a consequence, the base population being tested changes with time and contributes a changing portion of the force of infection.
T242 35317-35422 Sentence denotes Underestimation is therefore complex and is comprised of varying under-ascertainment and under-reporting.
T243 35423-35590 Sentence denotes There remain important unknowns about COVID-19 that give rise to additional limitations for modelling efforts; immunity and asymptomatic transmission are two of these.
T244 35591-35816 Sentence denotes We have included pre-symptomatic transmission but we have not explicitly modelled asymptomatic individuals, who may have few or no symptoms but nonetheless be transmitting, and who may or may not be building lasting immunity.
T245 35817-35944 Sentence denotes Recent work suggests that both pre- and asymptomatic individuals may be contributing considerably to transmission [27, 28, 44].
T246 35945-36092 Sentence denotes We have indirectly approached this uncertainty, exploring variable underestimation fractions and duration of the incubation and infectious periods.
T247 36093-36181 Sentence denotes A wide range for underestimation and duration is consistent with the reported case data.
T248 36182-36411 Sentence denotes Our conclusion about the impact of distancing measures appears to be robust to these uncertainties, although the basic reproductive number and the model prevalence vary according to assumptions about underestimation and duration.
T249 36412-36640 Sentence denotes Model predictions for the peak timing and size of prevalence without strong public health interventions will depend strongly on the dynamics of immunity, including the numbers of asymptomatic individuals and their immunity [12].
T250 36641-36842 Sentence denotes Our model suggests that distancing measures were working well in British Columbia as of April, 2020, that some relaxation of these measures may have been possible, but that this must be done carefully.
T251 36843-37005 Sentence denotes More broadly, we estimated a range of effectiveness of physical distancing in other locations (from very strong in New Zealand to weak in California as of May 7).
T252 37006-37118 Sentence denotes Given the likely low levels of immunity, long-term public health measures will be necessary to control COVID-19.
T253 37119-37462 Sentence denotes If data were available describing contact patterns and transmissibility by age, along with data describing the impact of specific activities on these contact patterns, then models could be effective tools to determine how to safely relax distancing measures—for example, restarting specific activities such as particular workplaces or schools.
T254 37463-37726 Sentence denotes Without knowledge of prevalence and transmissibility in children, of the extent of asymptomatic infection, and of the contact patterns that would result from restarting specific activities, models aiming to simulate these activities will have large uncertainties.
T255 37727-37923 Sentence denotes We therefore suggest that there is an urgent need for longitudinal measurements of population-level prevalence and immunity via viral testing and serological studies, even where prevalence is low.
T256 37924-38189 Sentence denotes Furthermore, if distancing measures are to be relaxed, it will be crucial to have strong surveillance through widespread testing, contact tracing, and isolation of new cases, as well as strong compliance with potentially shifting public health policy and messaging.
T257 38191-38213 Sentence denotes Supporting information
T258 38214-38345 Sentence denotes S1 Text Model specification, validation and analysis, likelihood parameter estimation, supplemental results, sensitivity analysis.
T259 38346-38351 Sentence denotes (PDF)
T260 38352-38388 Sentence denotes Click here for additional data file.
T261 38390-38527 Sentence denotes We thank TransLink for providing data on transportation and Bluedot for descriptive summary statistics on mobile-phone mobility patterns.
T262 38528-38654 Sentence denotes The research and analysis are based on data from TransLink and the opinions expressed do not represent the views of TransLink.
T263 38655-38737 Sentence denotes The opinions and conclusions expressed also do not represent the views of Bluedot.
T264 38738-38751 Sentence denotes We thank J.A.
T265 38752-38821 Sentence denotes Otte for providing details on testing-criteria changes in BC and C.L.
T266 38822-38873 Sentence denotes Cahill for assistance simulation testing the model.
T267 38874-38887 Sentence denotes We thank J.A.
T268 38888-38901 Sentence denotes Otte and L.A.
T269 38902-38974 Sentence denotes Rogers for insightful comments on an earlier version of this manuscript.
T270 38975-38986 Sentence denotes We thank A.
T271 38987-39000 Sentence denotes Lustig and M.
T272 39001-39077 Sentence denotes Plank for fitting the delay distribution to New Zealand case reporting data.