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Id Subject Object Predicate Lexical cue
T1 0-135 Sentence denotes The Epidemiological Signature of Pathogen Populations That Vary in the Relationship between Free-Living Parasite Survival and Virulence
T2 137-145 Sentence denotes Abstract
T3 146-282 Sentence denotes The relationship between parasite virulence and transmission is a pillar of evolutionary theory that has implications for public health.
T4 283-462 Sentence denotes Part of this canon involves the idea that virulence and free-living survival (a key component of transmission) may have different relationships in different host–parasite systems.
T5 463-668 Sentence denotes Most examinations of the evolution of virulence-transmission relationships—Theoretical or empirical in nature—Tend to focus on the evolution of virulence, with transmission being a secondary consideration.
T6 669-847 Sentence denotes Even within transmission studies, the focus on free-living survival is a smaller subset, though recent studies have examined its importance in the ecology of infectious diseases.
T7 848-981 Sentence denotes Few studies have examined the epidemic-scale consequences of variation in survival across different virulence–survival relationships.
T8 982-1261 Sentence denotes In this study, we utilize a mathematical model motivated by aspects of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) natural history to investigate how evolutionary changes in survival may influence several aspects of disease dynamics at the epidemiological scale.
T9 1262-1580 Sentence denotes Across virulence–survival relationships (where these traits are either positively or negatively correlated), we found that small changes (5% above and below the nominal value) in survival can have a meaningful effect on certain outbreak features, including R0, and on the size of the infectious peak in the population.
T10 1581-1860 Sentence denotes These results highlight the importance of properly understanding the mechanistic relationship between virulence and parasite survival, as the evolution of increased survival across different relationships with virulence may have considerably different epidemiological signatures.
T11 1862-1864 Sentence denotes 1.
T12 1865-1877 Sentence denotes Introduction
T13 1878-2007 Sentence denotes Interactions between the life history of a pathogen and the environment in which it is embedded drive the evolution of virulence.
T14 2008-2160 Sentence denotes These interactions thus dictate both the experience of disease at the individual host level and the shape of disease dynamics in host populations [1,2].
T15 2161-2308 Sentence denotes The nature of the interaction between virulence and transmission has been the object of both theoretical and empirical examination [2,3,4,5,6,7,8].
T16 2309-2479 Sentence denotes Free-living survival, here defined as the ability of a pathogen to persist outside of its host, is one of many transmission life-history traits associated with virulence.
T17 2480-2586 Sentence denotes The relationship between the two varies between host–pathogen types and different environments [4,8,9,10].
T18 2587-2709 Sentence denotes Several hypotheses serve as the canon in the evolution of virulence, theorizing its relationship with transmission traits.
T19 2710-3062 Sentence denotes The Curse of the Pharaoh hypothesis—Named after a tale about a mythical curse that torments individuals who dig up tombs of Egyptian pharaohs [11]—Suggests that, if a parasite has high free-living survival, then it is far less dependent on its host for transmission and, consequently, will have no evolutionary incentive to decrease virulence [2,4,12].
T20 3063-3252 Sentence denotes The potential negative fitness consequences of killing hosts rapidly (being highly virulent) can be counteracted by persisting in the environment until the arrival of new susceptible hosts.
T21 3253-3452 Sentence denotes Any presumptive selection on beneficence may be relaxed: parasites can detrimentally affect the health of hosts at no cost to transmission because most of their life cycle is spent outside of a host.
T22 3453-3594 Sentence denotes Previous studies support a positive correlation between free-living survival and mortality per infection (a common proxy for virulence) [13].
T23 3595-3750 Sentence denotes Alternatively, the “tradeoff” hypothesis suggests that there is some intermediate level of parasite virulence [3,6,14] that is optimal for a given setting.
T24 3751-3871 Sentence denotes In this scenario, too high a virulence kills the host and parasite and too low a virulence leads to failure to transmit.
T25 3872-4094 Sentence denotes Applying this hypothesis specifically to free-living survival would suggest that selection for increased free-living survival should come at the expense of virulence (producing a pathogen that is less harmful to the host).
T26 4095-4237 Sentence denotes Mechanistically, as a consequence of increased adaptation to a nonhost environment, a virus may be less fit to replicate inside a host [9,15].
T27 4238-4384 Sentence denotes For example, a more robust viral capsid may help to survive harsh environmental conditions but may make it more difficult to package RNA/DNA [15].
T28 4385-4572 Sentence denotes More generally, the tradeoff hypothesis can be framed in the context of a life-history tradeoff: investment in certain parts of the life cycle often comes at the expense of others [2,16].
T29 4573-4720 Sentence denotes Theoretical studies have explored varying evolutionary relationships between heightened virulence and extreme pathogen longevity [4,5,12,17,18,19].
T30 4721-4841 Sentence denotes One critical component of these studies revolves around whether virulence evolves independently of free-living survival.
T31 4842-5192 Sentence denotes For example, some models have argued [4] that pathogen virulence is independent of survival under a set of conditions: when the host–pathogen system is at an equilibrium (evolutionary and ecological), if host density fluctuates around an equilibrium, or if turnover of the infected host population is fast relative to the pathogen in the environment.
T32 5193-5442 Sentence denotes However, if the host–pathogen system is at disequilibrium and if the dynamics of propagules in the environment are fast compared to the dynamics of infected hosts, then virulence is, as hypothesized, an increasing function of propagule survival [4].
T33 5443-5709 Sentence denotes Kamo and Boots [17] examined this hypothesis by incorporating a spatial structure in the environment using a cellular, automata model and found that, if virulence evolution is independent of transmission, then long-lived infective stages select for higher virulence.
T34 5710-5942 Sentence denotes However, if there is a tradeoff between virulence and transmission, there is no evidence for the Curse of the Pharaoh hypothesis, and in fact, higher virulence may be selected for by shorter rather than long-lived infectious stages.
T35 5943-6056 Sentence denotes Further, the evolution of high virulence does not have to occur solely through a transmission–virulence tradeoff.
T36 6057-6242 Sentence denotes Day [18] demonstrated how pathogens can evolve high virulence and even select for traits to kill the host (e.g., toxins) if pathogen transmission and reproductive success are decoupled.
T37 6243-6327 Sentence denotes These studies emphasized the context-dependence of virulence–survival relationships.
T38 6328-6522 Sentence denotes Understanding where in the relationship between virulence and survival a given pathogen population exists may allow one to understand how virus evolution will manifest at the level of epidemics.
T39 6523-6719 Sentence denotes In this study, we examine the epidemic consequences of different virulence–survival relationships—Positive and negative correlation—In a viral disease with an environmental transmission component.
T40 6720-7051 Sentence denotes In order to measure how pathogen survival influences disease dynamics, we included an environmental compartment in our model, which represents contaminated environments that act as a reservoir for persisting pathogens, causing disease spread when they come in contact with susceptible individuals (infection via “fomites”) [20,21].
T41 7052-7217 Sentence denotes We find that the identity of the virulence–free-living survival relationship (e.g., positive vs. negative) has distinct implications for how an epidemic will unfold.
T42 7218-7353 Sentence denotes Some, but not all, features of an outbreak are dramatically influenced by the nature of the underlying virulence–survival relationship.
T43 7354-7512 Sentence denotes This indicates that signatures for evolution (adaptive or other) in a pathogen population will manifest more conspicuously in certain features of an outbreak.
T44 7513-7699 Sentence denotes We reflect on these findings in light of their theoretical implications on the evolution and ecology of infectious disease and for their potential utility in public health interventions.
T45 7701-7703 Sentence denotes 2.
T46 7704-7725 Sentence denotes Materials and Methods
T47 7727-7731 Sentence denotes 2.1.
T48 7732-7764 Sentence denotes Model Motivation and Application
T49 7765-8060 Sentence denotes The mathematical model explored in this study is adapted from a recent one developed to investigate environmental transmission of SARS-CoV-2 during the early-stage outbreak dynamics of coronavirus disease 2019 (COVID-19), with parameter values based on fits to actual country outbreak data [22].
T50 8061-8163 Sentence denotes In this study, we utilize this model to examine questions about the evolution of free-living survival.
T51 8164-8408 Sentence denotes While the phenomenon we examine is a very relevant one that manifests in the real world, we want to emphasize that none of the methods or results in this study are intended to be applied to the current COVID-19 pandemic (as of September, 2020).
T52 8409-8549 Sentence denotes This study is an attempt at responsible theoretical biology, with data-informed models and inferences that are germane to the natural world.
T53 8550-8702 Sentence denotes However, neither do we support the extrapolation of these findings to any particular aspect of COVID-19 nor should they inform a policy or intervention.
T54 8703-8796 Sentence denotes The model applies to a number of scenarios that include outbreaks in a naïve host population.
T55 8797-9024 Sentence denotes This describes situations such as the evolution of novel viral lineages, viral spillover events, or host shifts, where a virus with a preexisting relationship between virulence and survival emerges in a population of new hosts.
T56 9025-9284 Sentence denotes Another such scenario where this model applies is one where a virus has already emerged but evolves in a subpopulation in the novel hosts before a migration event of some kind introduces the evolved virus population to a fully susceptible population of hosts.
T57 9286-9290 Sentence denotes 2.2.
T58 9291-9308 Sentence denotes Model Description
T59 9309-9409 Sentence denotes The model is implemented via a set of ordinary differential equations, defined by Equations (1)–(6).
T60 9410-9608 Sentence denotes It implements viral free-living survival via the “Waterborne Abiotic or other Indirect Transmission (WAIT)” modelling framework, coupling individuals and the pathogen within the environment [23,24].
T61 9609-9852 Sentence denotes Within the model, the βw term allows for individuals to become infected via viral pathogen deposited in the environment and terms 𝜎A and 𝜎I allow asymptomatic and symptomatic individuals to deposit pathogens into the environment, respectively.
T62 9853-10215 Sentence denotes Adapted from the more traditional SEIR (susceptible-exposed-infected-recovered) model, the SEAIR-W (susceptible-exposed-asymptomatic-infected-recovered-WAIT) model interrogates the consequences of the two hypotheses outlined above while representing the dynamics of a very relevant disease system (SARS-CoV-2) that includes an asymptomatic infectious population.
T63 10216-10373 Sentence denotes While the importance of asymptomatic transmission was debated early in the pandemic, many studies have affirmed its role in the spread of disease [25,26,27].
T64 10374-10630 Sentence denotes Though environmental transmission of SARS-CoV-2 remains a controversial topic, it is plausible that asymptomatic individuals may spread disease through frequent contact with the environment, thus increasing the proportion of virus that is free-living [28].
T65 10631-10796 Sentence denotes We acknowledge that mathematical models of epidemics can be limited by “identifiability,” which can obfuscate the relative importance of some routes of transmission.
T66 10797-11081 Sentence denotes In models that have both indirect and direct routes of transmission, it can be very difficult to conclude that one route is predominant [29,30,31]. (1) dSdt=μN−S−βAA+βIIN+βWWS (2) dEdt=βAA+βIIN+βWWS−ε+μE (3) dAdt=εE−ω+μA (4) dIdt=1−pωA−v+μII (5) dRdt=pωA+vI−μR (6) dWdt=σAA+σIIN1−W−kW
T67 11082-11139 Sentence denotes Figure 1 depicts the compartmental diagram for the model.
T68 11140-11247 Sentence denotes The direction of the arrows corresponds to the flow of the individuals and the pathogen through the system.
T69 11248-11436 Sentence denotes Note that individuals can move directly from the asymptomatically infected compartment to the recovered compartment (bypassing the symptomatic compartment) via what we call a “mild track”.
T70 11437-11498 Sentence denotes The dashed arrows represent WAIT coupling to the environment.
T71 11499-11599 Sentence denotes The model is inspired by one developed to interrogate environmental transmission of SARS-CoV-2 [22].
T72 11601-11605 Sentence denotes 2.3.
T73 11606-11630 Sentence denotes Simulations of Outbreaks
T74 11631-11753 Sentence denotes The system was numerically integrated using the “odeint” solver in the Scipy 1.4—Python scientific computation suite [32].
T75 11754-11840 Sentence denotes The simulations track the populations for each of the compartments listed in Figure 1.
T76 11841-11958 Sentence denotes Each model run occurred over 250 days, which amounts to over 8 months of the epidemic or 5× the peak of the outbreak.
T77 11959-12091 Sentence denotes This length of time is consistent with the antecedent SARS-CoV-2 model [22], long enough for the dynamics of the system to manifest.
T78 12092-12210 Sentence denotes Note however that, for this study, we are especially interested in the early window of an outbreak: the first 30 days.
T79 12211-12409 Sentence denotes We focus on this window because this is the time frame that best captures the underlying physics of an epidemic, as 30 days is often before populations are able to adjust their individual behaviors.
T80 12410-12536 Sentence denotes The code constructed for the analysis in this study is publicly available on github: https://github.com/OgPlexus/Pharaohlocks.
T81 12538-12542 Sentence denotes 2.4.
T82 12543-12586 Sentence denotes Population Definitions and Parameter Values
T83 12587-12731 Sentence denotes Table 1 outlines the definitions of each population and provides the initial population values used for all simulations conducted in this study.
T84 12732-12789 Sentence denotes The nominal parameter values used are defined in Table 2.
T85 12790-12937 Sentence denotes The initial values are drawn from the aforementioned COVID-19 outbreak study, derived from empirical findings and country-level outbreak data [22].
T86 12939-12943 Sentence denotes 2.5.
T87 12944-12964 Sentence denotes Virulence Definition
T88 12965-13035 Sentence denotes In this study, we define virulence as the capacity to cause a disease.
T89 13036-13222 Sentence denotes In order to measure it, we utilize a set of parameters that uniformly increase the rate or probability of causing symptomatic disease or the severity of those symptoms (including death).
T90 13223-13523 Sentence denotes Our definition is more comprehensive than many other models of parasite virulence (e.g., [4,13]), which tend to focus on a single aspect of the natural history of disease associated with harm to a host (e.g., the fitness consequences of an infection on the host population or the case fatality rate).
T91 13524-13775 Sentence denotes Instead of having to justify a definition built around a single term (e.g., the term associated with fatality), we took a collective approach to defining virulence through all terms that foment the viral-induced onset of symptomatic disease and death.
T92 13776-13943 Sentence denotes This definition allows for the reality of pleiotropic effects in viral pathogens, where adaptations can have multiple effects on the natural history of disease [2,33].
T93 13944-14049 Sentence denotes Our definition of virulence emphasizes terms that influence host wellness and/or are symptoms of disease.
T94 14050-14224 Sentence denotes The iteration of virulence used in this study also undermines the potential for overly weighting only one or a small number of parameters under a large umbrella of virulence.
T95 14225-14532 Sentence denotes Because so many varying definitions exist for virulence, we have also performed calculations according to a different definition of virulence, one that exclusively considers terms that have a detrimental direct effect on the host and neither of the terms that reflect symptoms of severe disease (𝜎a and 𝜎I).
T96 14533-14596 Sentence denotes These calculations can be found in the Supplementary Materials.
T97 14597-15595 Sentence denotes The collection of parameters that we use to define virulence are as follows: the infected population death rate (𝜇I), the incubation period of SARS-CoV-2 (𝜂), the rate of transfer from asymptomatic to symptomatic (1/⍵), the infected population recovery rate (ν), the percent of individuals that move from the asymptomatic to the recovered compartment without showing symptoms (the “mild” recovery track, p), the contact rate of people with people × the transmission probability of people to people by an asymptomatic individual (βA), the contact rate of people with people × the transmission probability of people to people by an asymptomatically infected person (βI), the contact rate of people with the environment × the probability of shedding by an asymptomatic individual to the environmental (𝜎A), the contact rate of people with the environment × the probability of symptomatically infected individuals shedding in the environment (𝜎I), and the average number of days before infection (1/ε).
T98 15596-15730 Sentence denotes Table 3 outlines the direction in which each of the virulence-associated parameters are modulated as virulence decreases or increases.
T99 15731-15846 Sentence denotes An up arrow (↑) indicates the parameter increases (by an equivalent percent) when the percent virulence is changed.
T100 15847-15973 Sentence denotes A down arrow (↓) indicates the parameter decreases (by an equivalent percent) when the percent change in virulence is applied.
T101 15974-16109 Sentence denotes Changes in virulence are then defined, in this study, as an equivalent uniform (percent) change in each of the parameters listed above.
T102 16110-16220 Sentence denotes For the purposes of our study, we modify virulence by changing all parameters associated with virulence by 5%.
T103 16221-16354 Sentence denotes One could also disambiguate virulence into changes in individual subcomponents; however, that is not the focus of this current study.
T104 16356-16360 Sentence denotes 2.6.
T105 16361-16380 Sentence denotes Survival Definition
T106 16381-16574 Sentence denotes Survival is defined as the set of parameters that, when uniformly modulated, increases the pathogen’s probability of surviving the outside environment and successfully infecting a new host [2].
T107 16575-16777 Sentence denotes In our model, this includes both the waning virus rate in the environment (k) and the contact rate of an individual with the environment × the transmission probability of the environment to people (βw).
T108 16778-16916 Sentence denotes Table 4 outlines the direction (increasing or decreasing) in which these parameters are modulated when survival is decreased or increased.
T109 16917-17048 Sentence denotes Within both models, a (percent) change in survival is defined as an equivalent uniform (percent) change in the survival parameters.
T110 17049-17505 Sentence denotes Throughout this study, the impact of changes in virulence and survival (and the relationship between these traits) are assessed with respect to the following four epidemic metrics: the number of infected individuals (asymptomatic and symptomatic) at the maximum (when the outbreak is at its most severe), the rate at which the peak infected population is reached (tmax−1), the total infected population after 30 days, and the basic reproductive ratio (R0).
T111 17506-17691 Sentence denotes Importantly, among these signatures, the basic reproductive ratio is the most frequently used in epidemiology and benefits from familiarity and mathematical formalism (see Section 2.7).
T112 17692-17799 Sentence denotes The other signatures are determined through simulations of an epidemic for a given set of parameter values.
T113 17800-18001 Sentence denotes Nonetheless, this study’s inclusion of multiple features of the epidemic allows us to examine how variation in virus life-history traits may influence different aspects of an epidemic in peculiar ways.
T114 18003-18007 Sentence denotes 2.7.
T115 18008-18032 Sentence denotes Basic Reproductive Ratio
T116 18033-18150 Sentence denotes Equations (7)–(9) give the analytic expression of the basic reproductive ratio (R0) for the model used in this study.
T117 18151-18215 Sentence denotes This expression for R0 can be deconstructed into two components.
T118 18216-18407 Sentence denotes Equation (8) only contains parameters associated with person to person transmission (Rp), while Equation (9) solely contains parameters associated with transmission from the environment (Re).
T119 18408-18511 Sentence denotes In the Supplementary Materials, we provide additional information on these terms and their derivations.
T120 18512-18716 Sentence denotes Applying the parameters values in Table 2, the numerical value of the basic reproductive ratio is given as R0 ~ 2.82. (7) R0=RpRp2+4Re22 (8) Rp=εβAμI+v+βI1−pωμ+εμ+ωμI+v (9) Re2=εβWσAμI+v+σI1−pωkμ+εμ+ωμI+v
T121 18718-18720 Sentence denotes 3.
T122 18721-18728 Sentence denotes Results
T123 18730-18734 Sentence denotes 3.1.
T124 18735-18761 Sentence denotes Model Sensitivity Analysis
T125 18762-18871 Sentence denotes Figure 2 depicts a tornado plot that communicates the sensitivity of the model to permutations in parameters.
T126 18872-19059 Sentence denotes Across features, the model is most sensitive to parameters that are considered virulence-associated (Table 3) and is relatively less sensitive to survival-associated parameters (Table 4).
T127 19060-19164 Sentence denotes Similar to other features, R0 (Figure 2D) of the model is most sensitive to the parameters ⍵, βA, and ν.
T128 19165-19296 Sentence denotes The sensitivity of R0 to changes in ⍵ reflects the importance of the rate of conversion to the symptomatic state on model dynamics.
T129 19297-19496 Sentence denotes In addition, βA has a very important influence on the model, consistent with other findings for COVID-19 that have emphasized the importance of asymptomatic transmission in disease spread [25,26,27].
T130 19498-19502 Sentence denotes 3.2.
T131 19503-19540 Sentence denotes Illustrative Dynamics of Model System
T132 19541-19759 Sentence denotes Based on the parameter values in Table 2, Figure 3A demonstrates the base dynamics of the model playing out over the first 100 days while Figure 3B shows the dynamics within the environment over the course of 250 days.
T133 19760-19835 Sentence denotes In these dynamics, the population begins to be fixed for susceptible hosts.
T134 19836-19962 Sentence denotes The disease dynamics manifest in the shapes of the curves corresponding to exposed, asymptomatic, and symptomatic individuals.
T135 19963-20045 Sentence denotes Note the long tail of the curve corresponding to contamination by the environment.
T136 20046-20141 Sentence denotes The environment remains infectious even after the infected populations have declined in number.
T137 20142-20232 Sentence denotes The length and shape of this tail are influenced by the free-living survival of the virus.
T138 20234-20238 Sentence denotes 3.3.
T139 20239-20298 Sentence denotes The Epidemic Consequences of Varying Virulence and Survival
T140 20299-20415 Sentence denotes In the next analysis, we examine the epidemic consequences of varying traits associated with survival and virulence.
T141 20416-20668 Sentence denotes One can consider this as a scenario where we compare the endpoints of evolution of different virus populations (corresponding to combinations of values of survival and virulence) and calculating how these evolved populations manifest in epidemic terms.
T142 20669-20959 Sentence denotes In Figure 4, we observe how dynamics of the outbreak are influenced across a space of combinations of traits altering virulence (see Table 3 for a list of virulence-associated parameters) and survival (see Table 4 for a list of survival-associated parameters), changed by ±5% (10% overall).
T143 20960-21135 Sentence denotes In Figure 4D, we demonstrate how changes in virulence and free-living survival traits influence R0, with variation in virulence-related traits having the largest effect on R0.
T144 21136-21257 Sentence denotes Of note is how the range in R0 values varies widely across virulence–survival values, from nearly 2.0 to 3.7 (Figure 4D).
T145 21259-21263 Sentence denotes 3.4.
T146 21264-21339 Sentence denotes Implications of Virulence–Survival Relationships at Their Relative Extremes
T147 21340-21579 Sentence denotes Having observed how outbreak dynamics are influenced by variation in traits that alter virulence–survival phenotypes, we then examined how each outbreak metric is influenced by the extreme (±5%) values of the trait combinations considered.
T148 21580-21739 Sentence denotes Specifically, we assess how a change in pathogen survival affects outbreak dynamics, based on two expected relationships between survival and virulence traits.
T149 21741-21745 Sentence denotes 3.5.
T150 21746-21797 Sentence denotes Positive Correlation Between Survival and Virulence
T151 21798-21917 Sentence denotes In a positive correlation scenario, high values for survival would be associated with high values for virulence [4,13].
T152 21918-22079 Sentence denotes Because the correlations we observe are often not exactly linear, we utilize quadrants to express a trend, allowing for some variance around the expected “line”.
T153 22080-22220 Sentence denotes In Figure 5, the positive correlation scenario can be represented by combinations of virulence and survival residing in quadrants I and III.
T154 22221-22399 Sentence denotes If host–pathogen evolution proceeds according to a positive correlation scenario, all outbreak metrics would show an increase in severity as both survival and virulence increase.
T155 22400-22804 Sentence denotes Across the range of variation in virulence and survival traits considered (5% above and below the nominal value), the peak number of infected individuals increases by approximately 35%, the rate at which the peak is reached increases by approximately 16%, the total number of infected individuals after 30 days increases by approximately 98%, and R0 increases by approximately 94% (Figure 6 and Table 5).
T156 22806-22810 Sentence denotes 3.6.
T157 22811-22862 Sentence denotes Negative Correlation Between Survival and Virulence
T158 22863-23027 Sentence denotes In a negative correlation scenario, high values for survival would be associated with low values for virulence [2,9,15] and a low peak in total infected population.
T159 23028-23168 Sentence denotes Pathogens with a life history that exhibits negative virulence–survival associations would likely appear in quadrants II and IV in Figure 5.
T160 23169-23247 Sentence denotes Under negative correlation, outbreak severity decreases as survival increases.
T161 23248-23575 Sentence denotes Across the measured range of variation in virulence–survival traits, the peak number of infected individuals decreases by approximately 23%, the rate at which the epidemic peak is reached decreases by 0.15%, the total number of infected individuals decreases by 3%, and R0 decreases by approximately 84% (Figure 6 and Table 6).
T162 23576-23766 Sentence denotes Across all metrics considered, the effects of increased viral survival on outbreak dynamics is more extreme under the positive correlation than the negative correlation scenarios (Figure 6).
T163 23768-23772 Sentence denotes 3.7.
T164 23773-23843 Sentence denotes Dynamics of Epidemics at Extreme Values for Virus Free-Living Survival
T165 23844-24029 Sentence denotes In Figure 7, we observe the disease dynamics at extreme values for survival and the dynamics corresponding to the fraction of the environment that is contaminated with infectious virus.
T166 24030-24265 Sentence denotes Consistent with the data represented in Figure 6, we observe that minimum and maximum simulations differ more substantially for extreme survival scenarios in the positive correlation scenario than for the negative correlation scenario.
T167 24266-24431 Sentence denotes The feature of different outbreaks that varies most ostensibly between the correlation scenarios is the time needed to reach the peak number of infected individuals.
T168 24432-24607 Sentence denotes In positive correlation simulations, one can observe that the low virulence, low survival scenario (Figure 7A,B) takes longer to reach the peak number of infected individuals.
T169 24608-24812 Sentence denotes Most notably, however, the low virulence, low survival setting has a far smaller peak of environmental contamination and shorter tail relative to its high virulence, high survival counterpart (Figure 7D).
T170 24813-24972 Sentence denotes Similarly, intriguing findings exist in the comparison between the simulation sets corresponding to extremes in the negative correlation setting (Figure 7E–H).
T171 24973-25200 Sentence denotes Especially notable is the difference in the length of the tail of the environmental contamination for the high virulence, low survival combination (Figure 7F) vs. the low virulence, low survival combination variant (Figure 7H).
T172 25201-25411 Sentence denotes The explanation is that, in this model, higher virulence influences (among many other things) the rate at which the virus is shed into the environment from either the asymptomatic (𝜎A) or symptomatic (𝜎I) host.
T173 25412-25607 Sentence denotes We observe how the high virulence, low survival simulation (Figure 7E) features a symptomatic peak that is larger in size and is prolonged relative to the lower virulence counterpart (Figure 7G).
T174 25608-25807 Sentence denotes This relatively large symptomatic population sheds infectious virus into the environment for a longer period of time, contributing to the long tail of contaminated environments observed in Figure 5F.
T175 25809-25811 Sentence denotes 4.
T176 25812-25822 Sentence denotes Discussion
T177 25823-25935 Sentence denotes The virulence–survival relationship drives the consequences of virus evolution on the trajectory of an outbreak.
T178 25936-26146 Sentence denotes In this study, we examined how different virulence–survival relationships may dictate different features of outbreaks at the endpoints of evolution (according to the positive or negative correlation scenarios).
T179 26147-26459 Sentence denotes When the parameter space for virulence and survival is mapped, we find that certain outbreak metrics are more sensitive to change in free-living survival and virulence than others and that the nature of this sensitivity differs depending on whether survival and virulence are positively or negatively correlated.
T180 26460-26786 Sentence denotes For the positive correlation scenario, when free-living survival varies between 5% below and above the nominal value, we observed a dramatic change in the total number of infected individuals in the first 30 days (98% increase from minimum survival to maximum survival; Table 5), and R0 nearly doubles (94% increase; Table 5).
T181 26787-27035 Sentence denotes These two traits are, of course, connected: the theoretical construction of the R0 metric specifically applies to settings where a pathogen spreads in a population of susceptible hosts [34,35], an early window that is captured in the first 30 days.
T182 27036-27311 Sentence denotes When survival and virulence are negatively correlated, different outbreak dynamics emerge: while the R0 difference between minimum and maximum survival is significant (approximately 84% decrease), the total number of infected individuals only changes by roughly 3% (Table 6).
T183 27312-27530 Sentence denotes This large difference between R0 at higher and lower survival values also does not translate to a difference in the total number of infected individuals in the first 30 days of an infection (the early outbreak window).
T184 27531-27768 Sentence denotes In a scenario where survival and virulence are negatively correlated, a highly virulent and less virulent virus population can have similar signatures on a population with respect to the number of infected individuals in the first month.
T185 27769-28033 Sentence denotes Thus, simply measuring the number of infected individuals in the first month of an outbreak is unlikely to reveal whether a pathogen population has undergone adaptive evolution or has evolved in a manner that meaningfully influences the natural history of disease.
T186 28034-28385 Sentence denotes Notably, for scenarios where survival and virulence are both positively and negatively correlated, the time that it takes for an epidemic to reach its maximum number of infected individuals changes little across extreme values of survival (12% in the positive correlation scenario; 0.15% in the negative correlation scenario; see Table 5 and Table 6).
T187 28386-28533 Sentence denotes That is, the time that it takes for an epidemic to reach its peak (however high) is not especially sensitive to evolution in virulence or survival.
T188 28535-28619 Sentence denotes Practical Implications for the Understanding of Outbreaks Caused by Emerging Viruses
T189 28620-28888 Sentence denotes That different features of an outbreak are differentially influenced by the endpoints of viral life-history evolution highlights how epidemiology should continue to consider principles in the evolution and ecology of infectious disease in its analyses and predictions.
T190 28889-29221 Sentence denotes As not all features of an epidemic are going to be equally reliable signatures of virus evolution, we should carefully consider the data on how the dynamics of an epidemic change when making inferences about whether a pathogen population is essentially different from prior iterations (e.g., prior outbreaks of the same virus type).
T191 29222-29499 Sentence denotes The results of this study suggest that carefully constructed, mechanistically sound models of epidemics are important, both for capturing the dynamics of an outbreak and for abetting our efforts to understand how evolution of survival and virulence influences disease dynamics.
T192 29500-29657 Sentence denotes For example, the potential for adaptive evolution of SARS-CoV-2 has emerged as a possible explanation for different COVID-19 dynamics in different countries.
T193 29658-29799 Sentence denotes We suggest that such interpretations should be considered with caution and that they require very specific types of evidence to support them.
T194 29800-29972 Sentence denotes As of 1 July 2020, any conclusion that widespread SARS-CoV-2 evolution is an explanation for variation in disease patterns across settings (space and/or time) is premature.
T195 29973-30111 Sentence denotes The practical process of interpreting the evolutionary consequences of signals of virus evolution should encompass several discrete steps.
T196 30112-30199 Sentence denotes Firstly, we should determine whether molecular signatures exist for adaptive evolution.
T197 30200-30334 Sentence denotes Adaptive evolution would manifest in observable differences in genotype and phenotype and, perhaps, in the natural history of disease.
T198 30335-30453 Sentence denotes Secondly, we should aim to attain knowledge of the underlying mechanistic relationship between survival and virulence.
T199 30454-30737 Sentence denotes This knowledge is not necessarily easy to attain (it requires extensive laboratory studies) but would allow added biological insight: we may be able to extrapolate how changes in some traits (e.g., those that compose survival) influence others (e.g., those that influence virulence).
T200 30738-30987 Sentence denotes More generally, our findings suggest that the ability to detect the consequences of virus evolution would depend on which feature of an outbreak an epidemiologist measures: from our analysis, R0 is most impacted by changes in virulence and survival.
T201 30988-31174 Sentence denotes In addition, the total number of infected individuals in the early window and the size of the infected “peak” would each be impacted most readily by changes in virulence–survival traits.
T202 31175-31338 Sentence denotes The rate at which the epidemic peak was reached, on the other hand, showed relatively little change as survival increased or between the two correlation scenarios.
T203 31339-31410 Sentence denotes Consequently, it would not serve as a useful proxy for virus evolution.
T204 31411-31753 Sentence denotes While the stochastic, sometimes entropic nature of epidemics renders them very challenging to predict [36], we suggest that canons such as life-history theory and the evolution of virulence provide useful lenses that can aid in our ability to interpret how life-history changes in virus populations will manifest at the epidemiological scale.
T205 31754-32089 Sentence denotes We propose that, in an age of accumulating genomic and phenotypic data in many pathogen–host systems, we continue to responsibly apply or modify existing theory in order to collate said data into an organized picture for how different components of the host–parasite interaction influence the shape of viral outbreaks of various kinds.
T206 32091-32106 Sentence denotes Acknowledgments
T207 32107-32230 Sentence denotes The authors would like to thank members of the OGPlexus for helpful discussions and input on all aspects of the manuscript.
T208 32231-32309 Sentence denotes In particular, we thank M.M.D. and A.L.M. for especially helpful interactions.
T209 32311-32334 Sentence denotes Supplementary Materials
T210 32335-32417 Sentence denotes The following are available online at https://www.mdpi.com/1999-4915/12/9/1055/s1.
T211 32418-32427 Sentence denotes Table S1.
T212 32428-32467 Sentence denotes Fixed parameters, and their references.
T213 32468-32477 Sentence denotes Table S2.
T214 32478-32580 Sentence denotes Alternative virulence definition containing only items that directly affect host well-being (fitness).
T215 32581-32591 Sentence denotes Figure S1.
T216 32592-32625 Sentence denotes Alternative virulence definition:
T217 32626-32715 Sentence denotes The impact of varying virus virulence and survival assessed on four key epidemic metrics.
T218 32716-32726 Sentence denotes Figure S2.
T219 32727-32760 Sentence denotes Alternative virulence definition:
T220 32761-32941 Sentence denotes The percent change in SEAIR-W outbreak metrics as survival increases from −5% to +5% for different virulence-survival relationships (positive correlation and negative correlation).
T221 32942-32952 Sentence denotes Figure S3.
T222 32953-32986 Sentence denotes Alternative virulence definition:
T223 32987-33106 Sentence denotes Virus outbreak dynamics for the extreme values of virulence and free-living survival considered for the two hypotheses.
T224 33107-33116 Sentence denotes Table S3.
T225 33117-33150 Sentence denotes Alternative virulence definition:
T226 33151-33257 Sentence denotes Comparing epidemic metrics under low survival/low virulence versus high survival/high virulence scenarios.
T227 33258-33267 Sentence denotes Table S4.
T228 33268-33301 Sentence denotes Alternative virulence definition:
T229 33302-33450 Sentence denotes Comparing epidemic metrics under low survival/low virulence versus high survival/high virulence scenarios (as in the negative correlation scenario).
T230 33451-33461 Sentence denotes Figure S4.
T231 33462-33584 Sentence denotes Side by side comparison of the main text virulence definition (A1 → D1) and alternative definition of virulence (A2 → D2).
T232 33585-33595 Sentence denotes Figure S5.
T233 33596-33713 Sentence denotes Side by side comparison of the main text virulence definition (left) and alternative definition of virulence (right).
T234 33714-33724 Sentence denotes Figure S6.
T235 33725-33838 Sentence denotes Side by side comparison of the main text definition (A1 → H1) and supplemental definition of virulence (A2 → H2).
T236 33839-33875 Sentence denotes Click here for additional data file.
T237 33877-33897 Sentence denotes Author Contributions
T238 33898-34425 Sentence denotes Conceptualization, L.M.G., W.C.T. and C.B.O.; methodology, V.A.M. and C.B.O.; software, V.A.M.; validation, V.A.M. and C.B.O.; formal analysis, L.M.G., V.A.M., W.C.T. and C.B.O.; investigation, L.M.G., V.A.M., W.C.T. and C.B.O.; resources, C.B.O.; data curation, L.M.G and V.A.M.; writing—Original draft preparation, L.M.G., V.A.M., W.C.T. and C.B.O.; writing—Review and editing, L.M.G., V.A.M., W.C.T. and C.B.O.; visualization, V.A.M.; supervision, C.B.O. and W.C.T.; project administration, C.B.O.; funding acquisition, N/A.
T239 34426-34502 Sentence denotes All authors have read and agreed to the published version of the manuscript.
T240 34504-34511 Sentence denotes Funding
T241 34512-34555 Sentence denotes This research received no external funding.
T242 34557-34578 Sentence denotes Conflicts of Interest
T243 34579-34623 Sentence denotes The authors declare no conflict of interest.
T244 34625-34935 Sentence denotes Figure 1 Compartmental diagram of the SEAIR-W (susceptible-exposed-asymptomatic-infected-recovered) version of a-WAIT (Waterborne Abiotic or other Indirect Transmission)) model: this is based on a previously developed mathematical model used to interrogate environmental transmission of SARS-CoV-2 (see [22]).
T245 34936-35282 Sentence denotes Figure 2 Tornado plot showing the sensitivity of epidemic properties to individual parameter changes: (A) the number of infected individuals (asymptomatic and symptomatic) at the epidemic peak; (B) the rate at which the epidemic peak is reached, tmax−1; (C) the total infected population after 30 days; and (D) the basic reproductive ratio (R0).
T246 35283-35412 Sentence denotes Filled bars indicate the value of the epidemic feature when the associated parameter is increased by 5.0% from its nominal value.
T247 35413-35507 Sentence denotes White bars indicate the value of a feature when the associated parameter is decreased by 5.0%.
T248 35508-35686 Sentence denotes Blue coloring with checkered patterning indicates a parameter associated with survival, and orange coloring with lined patterning indicates a parameter associated with virulence.
T249 35687-35901 Sentence denotes Figure 3 Sample dynamics for the model system: (A) the dynamics for all host compartments within the model and (B) the fraction of environmental reservoirs in a setting that are contaminated with infectious virus.
T250 35902-36384 Sentence denotes Figure 4 Heatmap describing the impact of varying virus virulence and survival trait values assessed across four key epidemic metrics: these heatmaps express the change in (A) the number of infected individuals (asymptomatic and symptomatic) at the epidemic peak; (B) the rate at which the epidemic peak is reached, tmax−1; (C) the total infected population after 30 days; and (D) the basic reproductive ratio (R0) when virulence and survival are modulated by ±5% within the model.
T251 36385-36425 Sentence denotes Contour lines are available for clarity.
T252 36426-36726 Sentence denotes Figure 5 The expected effect of increasing survival on virulence for the two correlation models considered: here, we present a schematic of how the different hypotheses for the relationship between virulence and survival manifest on a map with a structure similar to the heat maps shown in Figure 4.
T253 36727-37010 Sentence denotes The directions of the arrows depict how increasing survival would affect virulence under the two hypotheses: the blue arrow indicates the flow of an increasing positive correlation dynamic, while the direction of the orange arrow indicates an increasing negative correlation dynamic.
T254 37011-37201 Sentence denotes Figure 6 The percent change in SEAIR-W outbreak metrics as survival increases from −5% to +5% for different virulence–survival relationships (positive correlation and negative correlation).
T255 37202-37561 Sentence denotes For each metric analyzed, we present the percent difference between the minimum and maximum survival values given the two hypotheses tested: (i) positive correlation between survival and virulence (comparing low virulence/low survival to high virulence/high survival) and (ii) negative correlation (high virulence/low survival to high survival/low virulence).
T256 37562-37724 Sentence denotes The bars here correspond to the values (percent) in the third columns of Table 5 and Table 6, which denote the differences between the minimum and maximum values.
T257 37725-37994 Sentence denotes Figure 7 Virus outbreak dynamics for the extreme values of virulence and free-living survival considered for the two different relationships (positive or negative) between virulence and survival traits: these plots are similar to the illustrative dynamics in Figure 1.
T258 37995-38105 Sentence denotes Here, we observe the dynamics of disease corresponding to the extreme values presented in Table 5 and Table 6.
T259 38106-38367 Sentence denotes Subfigures (A,C,E,G) depict disease dynamics, and (B,D,F,H) depict the dynamics of contaminated environments. (A–D) correspond to the parameter values considered for the positive correlation scenario, while (E–H) correspond to the negative correlation scenario.
T260 38368-38576 Sentence denotes Table 1 Definitions and initial values for the populations represented by each compartment: the values here are the averages of the model values across all countries developed in a prior COVID-19 study [22].
T261 38577-38611 Sentence denotes Symbols Value Units Definitions
T262 38612-38660 Sentence denotes S0 57.05 × 106 people Susceptible individuals
T263 38661-38699 Sentence denotes E0 66.50 people Exposed individuals
T264 38700-38743 Sentence denotes A0 13.30 people Asymptomatic individuals
T265 38744-38786 Sentence denotes I0 13.30 people Symptomatic individuals
T266 38787-38825 Sentence denotes Rec0 0 people Recovered individuals
T267 38826-38878 Sentence denotes W0 1% unitless % of viral pathogen in environment
T268 38879-39068 Sentence denotes Table 2 Definitions for the nominal parameter values used in this study: parameter values were developed from empirical findings and country-level data, as discussed in another study [22].
T269 39069-39104 Sentence denotes Symbols Values Units Definitions
T270 39105-39207 Sentence denotes 𝜇 1/(80.3 × 365) 1/day Natural death rate (reciprocal of the upper bound of average human lifespan)
T271 39208-39297 Sentence denotes 𝜇I 0.00159 1/day Infected death rate (natural death rate + disease-induced death rate)
T272 39298-39352 Sentence denotes 𝜂 = (⍵ − ε−1) 5.5 days SARS-CoV-2 incubation period
T273 39353-39412 Sentence denotes 1/⍵ 𝜂 − ε−1 days Expected time in the asymptomatic state
T274 39413-39470 Sentence denotes ν 0.0305 1/day Recovery rate (average of 3 to 6 weeks)
T275 39471-39540 Sentence denotes p 95.6% percent Percent that moves along the “mild” recovery track
T276 39541-39674 Sentence denotes k 0.649 1/day Waning virus rate in the environment (using the average of all material values, wood, steal, cardboard, and plastic)
T277 39675-39786 Sentence denotes βa 0.550 1/day Contact rate of people with people × transmission probability of people to people by A-person
T278 39787-39898 Sentence denotes βI 0.491 1/day Contact rate of people with people × transmission probability of people to people by I-person
T279 39899-40008 Sentence denotes βW 0.031 1/day Contact rate of person with environment × transmission probability of environment to people
T280 40009-40119 Sentence denotes 𝜎a 3.404 1/day Contact rate of person with environment × probability of shedding by A-people to environment
T281 40120-40232 Sentence denotes 𝜎I 13.492 1/day Contact rate of person with environment) × probability of shedding by I-people to environment
T282 40233-40295 Sentence denotes 1/ε 2.478 days Average number of days before infectiousness
T283 40296-40456 Sentence denotes Table 3 Virulence parameters: this is a list of uniformly modulated parameters and the direction in which they change when virulence is increased or decreased.
T284 40457-40646 Sentence denotes When virulence changes, an up arrow (↑) indicates the parameter is increased (by an equivalent percent) and a down arrow (↓) indicates the parameter is decreased (by an equivalent percent).
T285 40647-40708 Sentence denotes Symbols Definition Virulence Increased Virulence Decreased
T286 40709-40788 Sentence denotes 𝜇I Infected death rate (natural death rate + disease induced death rate) ↑ ↓
T287 40789-40838 Sentence denotes 𝜂 = (⍵ − ε−1) SARS-CoV-2 incubation period ↓ ↑
T288 40839-40889 Sentence denotes 1/⍵ Expected time in the asymptomatic state ↑ ↓
T289 40890-40938 Sentence denotes ν Recovery rate (average of 3 to 6 weeks) ↓ ↑
T290 40939-40998 Sentence denotes p Percent that moves along the “mild” recovery track ↓ ↑
T291 40999-41102 Sentence denotes βA Contact rate of people with people × transmission probability of people to people by A-person ↑ ↓
T292 41103-41206 Sentence denotes βI Contact rate of people with people × transmission probability of people to people by I-person ↑ ↓
T293 41207-41311 Sentence denotes 𝜎A Contact rate of person with environment) × (probability of shedding by A-people to environment ↑ ↓
T294 41312-41414 Sentence denotes 𝜎I Contact rate of person with environment × probability of shedding by I-people to environment ↑ ↓
T295 41415-41466 Sentence denotes 1/ε Average number of days before infectious ↓ ↑
T296 41467-41634 Sentence denotes Table 4 Survival parameters: this is a list of parameters that are uniformly modulated and the direction in which they change when survival is increased or decreased.
T297 41635-41764 Sentence denotes An up arrow (↑) indicates the parameter is increased by some percent when the equivalent (percent) change in survival is applied.
T298 41765-41895 Sentence denotes A down arrow (↓) indicates the parameter is decreased by some percent when the equivalent (percent) change in survival is applied.
T299 41896-41955 Sentence denotes Symbols Definition Survival Increased Survival Decreased
T300 41956-42077 Sentence denotes k Waning virus rate in environment (using the average of all material values, wood, steal, cardboard, and plastic) ↓ ↑
T301 42078-42179 Sentence denotes βW Contact rate of person with environment × transmission probability of environment to people ↑ ↓
T302 42180-42368 Sentence denotes Table 5 Positive correlation scenario: comparing epidemic metrics under low survival/low virulence versus high survival/high virulence scenarios (as in the positive correlation scenario).
T303 42369-42552 Sentence denotes For each metric analyzed, these are the heatmap values for the bottom left (at “coordinates” (Vir, Sur) → (−5%, −5%)) and top right (at “coordinates” (Vir, Sur) → (+5%, +5%)) corners.
T304 42553-42678 Sentence denotes Epidemic Metric min Virulence, min Survival max Virulence, max Survival % Difference between min Survival and max Survival
T305 42679-42740 Sentence denotes Peak total infected (people) 5.68 × 106 7.64 × 106 +34.51%
T306 42741-42791 Sentence denotes tmax−1 (days−1) 1.99 × 10−2 2.23 × 10−2 +12.06%
T307 42792-42853 Sentence denotes Total after 30 days (people) 8.18 × 107 1.62 × 108 +98.04%
T308 42854-42904 Sentence denotes Basic reproductive ratio (R0) 1.95 3.78 +93.84%
T309 42905-43093 Sentence denotes Table 6 Negative correlation scenario: comparing epidemic metrics under low survival/low virulence versus high survival/high virulence scenarios (as in the negative correlation scenario).
T310 43094-43284 Sentence denotes For each metric analyzed, these are the global heatmap values for the top left (at “coordinates” (Vir, Sur) → (+5%, −5%)) and bottom right corners (at “coordinates” (Vir, Sur) → (−5%, +5%)).
T311 43285-43410 Sentence denotes Epidemic Metric max Virulence, min Survival min Virulence, max Survival % Difference between min Survival and max Survival
T312 43411-43472 Sentence denotes Peak total infected (people) 7.39 × 106 5.99 × 106 −23.47%
T313 43473-43522 Sentence denotes tmax−1 (days−1) 2.10 × 10−2 2.23 × 10−2 −0.15%
T314 43523-43592 Sentence denotes Total infected after 30 days (people) 1.16 × 108 1.13 × 108 −2.68%
T315 43593-43643 Sentence denotes Basic reproductive ratio (R0) 3.67 1.99 −84.39%