DOCSLIB.ORG

Evolution of Acute Infections and the Invasion-Persistence Trade-Off

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Evolution of Acute Infections and the Invasion-Persistence Trade-Off vol. 173, no. 4 the american naturalist april 2009 Evolution of Acute Infections and the Invasion-Persistence Trade-Off Aaron A. King,1,2,* Sourya Shrestha,3 Eric T. Harvill,4 and Ottar N. Bjørnstad2,5 1. Departments of Ecology and Evolutionary Biology and Mathematics, University of Michigan, Ann Arbor, Michigan 48109; 2. Fogarty International Center, National Institutes of Health, Bethesda, Maryland 20892; 3. Applied and Interdisciplinary Mathematics Program, University of Michigan, Ann Arbor, Michigan 48109; 4. Department of Veterinary Sciences, Penn State University, University Park, Pennsylvania 16803; 5. Departments of Entomology and Biology, Penn State University, University Park, Pennsylvania 16803 Submitted April 7, 2008; Accepted September 16, 2008; Electronically published February 20, 2009 for biosecurity. Understanding the conditions that favor abstract: We seek to understand the conditions favoring the evo- the evolution toward acute and highly contagious path- lution of acute, highly transmissible infections. Most work on the life-history evolution of pathogens has focused on the transmission- ogens is therefore of obvious interest. A related question virulence trade-off. Here we focus on a distinct trade-off that op- concerns the conditions that allow continued circulation erates, even among avirulent pathogens, between a pathogen’s speed and persistence of such strains. Understanding these issues of invasion and its ability to persist in a finite host population. Other is tantamount to understanding the evolutionary forces authors have shown how this invasion-persistence trade-off can lead shaping the life histories of pathogens. to intermediate pathogen attack rates but have done so only by Life-history theory has proven to be of great value for imposing trade-offs between the pathogen’s transmissibility and the duration of the infectious period. Here we delve deeper, by linking explaining and predicting optimal patterns of virulence in a model of within-host pathogen dynamics—in which pathogen life- pathogens (Antia et al. 1994; Lenski and May 1994; Frank history parameters figure directly—to an epidemiological model at 1996). For example, the classic trade-off theory predicts the population level. We find that a key determinant of the evolu- that a virulent pathogen may kill its host so fast, or stim- tionary trajectory is the shape of the dose-response curve that relates ulate such a strong immune response, that it may have within-host pathogen load to between-host transmission. In partic- little time to transmit to a secondary host (May and An- ular, under the usual assumption of proportionality we find that derson 1983). A more commensalistic pathogen, by con- pathogens tend to evolve to the edge of their own extinction. Under more realistic assumptions, a critical host population size exists, trast, may have so low a within-host multiplication rate above which highly acute pathogens are buffered from extinction. that it fails to shed sufficiently many propagules to en- Our study is motivated by the emergence of acuteness in two human gender infection in recipient hosts. This trade-off can lead pathogens, Bordetella pertussis and Bordetella parapertussis, which in- to an intermediate optimal host-exploitation rate with as- dependently evolved from an ancestor, Bordetella bronchiseptica, char- sociated intermediate infectious period and degree of acterized by chronic (nonacute) infection of wildlife. In contrast to acuteness. In this model, evolution is assumed to favor life the plethora of models that predict evolution of more aggressive pathogens in larger or denser populations, the invasion-persistence histories that maximize the basic reproductive ratio, R0, trade-off also operates for frequency-dependent pathogens. under the trade-off between the transmission rate and the infectious period. This theory has garnered important em- Keywords: acute infection, trade-off, evolution of infectious disease, pirical support (Fenner 1983; Messenger et al. 1999). How- pathogen evolution, dose response, Bordetella. ever, as pointed out by Antia et al. (1994), Frank (1996), and Gilchrist and Sasaki (2002), it is one thing to postulate a particular transmission-virulence trade-off and deduce Introduction the corresponding optimal life-history traits, but it is quite Rapidly transmitting pathogens that cause acute disease another to deduce the trade-off from its basis in within- are among the most important public health concerns host dynamics and the biology of transmission. Moreover, worldwide because of their high burden of mortality and the transmission-virulence trade-off cannot explain dif- morbidity, their violent outbreaks, and their implication ferences in infectious period among equally virulent pathogens. * Corresponding author; e-mail: [email protected]. For pathogens that replicate within hosts, transmit be- Am. Nat. 2009. Vol. 173, pp. 446–455. ᭧ 2009 by The University of Chicago. tween them, and spread among local host populations 0003-0147/2009/17304-50363$15.00. All rights reserved. within metapopulations, selection may happen and trade- DOI: 10.1086/597217 offs may occur at several different levels (Keeling 2000; Evolution of Acute Infections 447 Figure 1: A, Within-host pathogen dynamics for three different r values. Also shown are the corresponding nonseasonal epidemic curves for the linear-transmission model (B), delayed-transmission model (C), and saturating-transmission model (D). Parameters a, d, and k are set to the values shown in table 1;g p 10Ϫ4 and␧ p 0 . In general, increasing acuteness eventually leads to elevated risk of stochastic extinction. Gilchrist and Sasaki 2002; Boots et al. 2004; van Balle- an intermediate acuteness. Here, we remove the restriction gooijen and Boerlijst 2004; Gilchrist and Coombs 2006). of equal R0 and replace the oversimple SIR framework with Arising at the level of the host population, the “invasion- a more mechanistic model of within-host pathogen dy- persistence” trade-off, described by Grenfell (2001), me- namics. In effect, we parameterize pathogen fitness in diates a balance between a strain’s infectious period and terms more directly related to pathogen life history. This its instantaneous rate of transmission. Over the short term, allows us to predict the direction of pathogen life-history an acute strain with short infectious period and high trans- evolution as a function of host population structure and mission rate has the evolutionary advantage in that it will the coupling between pathogen load and transmission po- spread more rapidly through a population than a strain tential (the dose-response curve) without the need for ar- with a longer infectious period and lower instantaneous tificial restrictions on parameters. transmission rate (Grenfell 2001). However, epidemics of Keeling (2000) examined the mathematical underpin- the more transmissible strain will exhibit more violent nings of the invasion-persistence trade-off in infinite meta- fluctuations and suffer greater risk of extinction—reflected populations. He showed that, in competition between a in a higher critical community size (Bartlett 1956; Keeling highly transmissible but extinction-prone strain and a and Grenfell 1997)—than those of their less transmissible strain that is less prone to extinction but is also less trans- equivalents. Thus, short-term invasion advantage comes missible, evolution may favor either strain, depending on at the cost of diminished intermediate-term persistence. within-patch relative competitive ability, patch-level rela- Grenfell (2001), using a simple susceptible-infectious- tive extinction rate, and degree of stochasticity (itself re- recovered (SIR) formalism and under the artificial restric- lated to patch size). Here, we examine the dependence of tion that competing strains shared an identical basic re- these parameters on more basic parameters that govern productive ratio (R0), showed that evolution would favor pathogen life history and the coupling of within-host path- 448 The American Naturalist Table 1: Model parameters Model, parameter Symbol Value Within-host model: Parasite growth rate r 10–130 Kill rate of the immune response k 3.5 Baseline production rate of immune response a 1 Death rate of immune response d .5 Immune response recruitment rate g .5–1.5 # 10Ϫ4 Transmission models: Ϫ3 Transmissibility factor, linear model q1 10 # Ϫ3 Transmissibility factor, delayed model q2 1.5 10 3 Transmissibility factor, saturating model q3 10 Delayed-transmission coefficient s 25 Delay constant a∗ .1 Saturation constant P∗ 5 # 105 Between-host model: Host mortality rate m .02 Seasonality amplitude ␧ 0–1 ogen dynamics to between-host transmission. With respect is followed sometimes by longer-lasting mild symptoms to the latter, the almost invariable practice in the literature and eventually by complete systemic clearance. According has been to assume that instantaneous transmission rate to the World Health Organization, these two bacteria is simply proportional to within-host pathogen load. Here caused 140 million cases of whooping cough in 2002. We we show that even small deviations from this assumption ask why acute infections are favored in some hosts whereas can have profound consequences on the ability of the op- more commensal infections are favored in others. What timal life-history strategy to persist. In particular, when evolutionary advantage can these acute strains possess that transmission depends nonlinearly on pathogen load, we compensates for the
Load more

Recommended publications
  • Some Simple Rules for Estimating Reproduction Numbers in the Presence of Reservoir Exposure Or Imported Cases
    Some simple rules for estimating reproduction numbers in the presence of reservoir exposure or imported cases Angus McLure1*, Kathryn Glass1 1 Research School of Population Health, Australian National University, 62 Mills Rd, Acton, 0200, ACT, Australia * Corresponding author: [email protected] 1 Abstract The basic reproduction number () is a threshold parameter for disease extinction or survival in isolated populations. However no human population is fully isolated from other human or animal populations. We use compartmental models to derive simple rules for the basic reproduction number for populations with local person‐to‐person transmission and exposure from some other source: either a reservoir exposure or imported cases. We introduce the idea of a reservoir‐driven or importation‐driven disease: diseases that would become extinct in the population of interest without reservoir exposure or imported cases (since 1, but nevertheless may be sufficiently transmissible that many or most infections are acquired from humans in that population. We show that in the simplest case, 1 if and only if the proportion of infections acquired from the external source exceeds the disease prevalence and explore how population heterogeneity and the interactions of multiple strains affect this rule. We apply these rules in two cases studies of Clostridium difficile infection and colonisation: C. difficile in the hospital setting accounting for imported cases, and C. difficile in the general human population accounting for exposure to animal reservoirs. We demonstrate that even the hospital‐adapted, highly‐transmissible NAP1/RT027 strain of C. difficile had a reproduction number <1 in a landmark study of hospitalised patients and therefore was sustained by colonised and infected admissions to the study hospital.
    [Show full text]
  • Seventy-Five Years of Estimating the Force of Infection from Current Status
    Epidemiol. Infect. (2010), 138, 802–812. f Cambridge University Press 2009 doi:10.1017/S0950268809990781 Seventy-five years of estimating the force of infection from current status data N. HENS 1,2*, M. AERTS 1,C.FAES1,Z.SHKEDY1, O. LEJEUNE2, P. VAN DAMME2 AND P. BEUTELS2 1 Interuniversity Institute of Biostatistics and Statistical Bioinformatics, Hasselt University, Diepenbeek, Belgium 2 Centre for Health Economics Research & Modelling Infectious Diseases; Centre for the Evaluation of Vaccination, Vaccine and Infectious Disease Institute, University of Antwerp, Antwerp, Belgium (Accepted 18 August 2009; first published online 21 September 2009) SUMMARY The force of infection, describing the rate at which a susceptible person acquires an infection, is a key parameter in models estimating the infectious disease burden, and the effectiveness and cost-effectiveness of infectious disease prevention. Since Muench formulated the first catalytic model to estimate the force of infection from current status data in 1934, exactly 75 years ago, several authors addressed the estimation of this parameter by more advanced statistical methods, while applying these to seroprevalence and reported incidence/case notification data. In this paper we present an historical overview, discussing the relevance of Muench’s work, and we explain the wide array of newer methods with illustrations on pre-vaccination serological survey data of two airborne infections: rubella and parvovirus B19. We also provide guidance on deciding which method(s) to apply to estimate the
    [Show full text]
  • Population Behavioural Dynamics Can Mediate the Persistence
    medRxiv preprint doi: https://doi.org/10.1101/2021.05.03.21256551; this version posted May 5, 2021. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license . 1 1 Population behavioural dynamics can mediate the 2 persistence of emerging infectious diseases 1;∗ 1 1 2 3 Kathyrn R Fair , Vadim A Karatayev , Madhur Anand , Chris T Bauch 4 1 School of Environmental Sciences, University of Guelph, Guelph, ON, Canada, N1G 2W1 5 2 Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada, N2L 6 3G1 7 *[email protected] 8 Abstract 9 The critical community size (CCS) is the minimum closed population size in which a 10 pathogen can persist indefinitely. Below this threshold, stochastic extinction eventu- 11 ally causes pathogen extinction. Here we use a simulation model to explore behaviour- 12 mediated persistence: a novel mechanism by which the population response to the pathogen 13 determines the CCS. We model severe coronavirus 2 (SARS-CoV-2) transmission and 14 non-pharmaceutical interventions (NPIs) in a population where both individuals and gov- 15 ernment authorities restrict transmission more strongly when SARS-CoV-2 case numbers 16 are higher. This results in a coupled human-environment feedback between disease dy- 17 namics and population behaviour. In a parameter regime corresponding to a moderate 18 population response, this feedback allows SARS-CoV-2 to avoid extinction in the trough 19 of pandemic waves.
    [Show full text]
  • Multiscale Mobility Networks and the Spatial Spreading of Infectious Diseases
    Multiscale mobility networks and the spatial spreading of infectious diseases Duygu Balcana,b, Vittoria Colizzac, Bruno Gonc¸alvesa,b, Hao Hud, Jose´ J. Ramascob, and Alessandro Vespignania,b,c,1 aCenter for Complex Networks and Systems Research, School of Informatics and Computing, Indiana University, Bloomington, IN 47408; bPervasive Technology Institute, Indiana University, Bloomington, IN 47404; cComputational Epidemiology Laboratory, Institute for Scientific Interchange Foundation, 10133 Torino, Italy; and dDepartment of Physics, Indiana University, Bloomington, IN 47406 Edited by H. Eugene Stanley, Boston University, Boston, MA, and approved October 13, 2009 (received for review June 19, 2009) Among the realistic ingredients to be considered in the computational two questions stand out: (i) Is there a most relevant mobility scale modeling of infectious diseases, human mobility represents a crucial in the definition of the global epidemic pattern? and (ii) At which challenge both on the theoretical side and in view of the limited level of resolution of the epidemic behavior does a given mobility availability of empirical data. To study the interplay between short- scale become relevant, and to what extent? scale commuting flows and long-range airline traffic in shaping the To begin addressing these questions, we use high-resolution spatiotemporal pattern of a global epidemic we (i) analyze mobility worldwide population data that allow for the definition of sub- data from 29 countries around the world and find a gravity model populations according to a Voronoi decomposition of the world able to provide a global description of commuting patterns up to 300 surface centered on the locations of International Air Transport kms and (ii) integrate in a worldwide-structured metapopulation Association (IATA)-indexed airports (www.iata.org).
    [Show full text]
  • Population Behavioural Dynamics Can Mediate the Persistence of Emerging Infectious Diseases
    1 Supplementary information - Population behavioural dynamics can mediate the persistence of emerging infectious diseases Kathyrn R Fair1;∗, Vadim A Karatayev1, Madhur Anand1, Chris T Bauch2 1 School of Environmental Sciences, University of Guelph, Guelph, ON, Canada, N1G 2W1 2 Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada, N2L 3G1 *[email protected] 2 Supplementary methods Within the model, individuals states are updated based on the following events: 1. Exposure: fS; ·} individuals are exposed to SARS-CoV-2 with probability λ(t), shifting to fE; ·}. 2. Onset of infectious period: fE; ·} individuals become pre-symptomatic and infectious with probability (1 − π)α, shifting to fP; ·}. Alternatively, they become asymptomatic and infectious (with probability πα), shifting to fA; ·}. 3. Onset of symptoms: fP; ·} individuals become symptomatic with probability σ, shifting to fI; ·}. 4. Testing: fI;Ug individuals are tested with probability τI shifting to fI;Kg. 5. Removal: fI; ·} and fA; ·} individuals cease to be infectious with probability ρ, shifting to fR; ·}. With probability m = 0:0066 [1], individuals transitioning from the symptomatic and infec- tious state (fI; ·}) to the removed (i.e. no longer infectious) state are assigned as COVID-19 deaths. Individuals who have died due to COVID-19 do not factor into subsequent birth and non-COVID-19 death calculations. At the onset of infectiousness, newly infected individuals have a probability s = 0:2 of being assigned as super-spreaders [2]. We differentiate between super-spreaders and non-super-spreaders using subscripts (s and ns respectively), such that we have Ps, Pns, As, Ans, Is, Ins. Super-spreaders have their probability of infecting others increased by a factor of (1 − s)=s.
    [Show full text]
  • Understanding the Spreading Power of All Nodes in a Network: a Continuous-Time Perspective
    i i “Lawyer-mainmanus” — 2014/6/12 — 9:39 — page 1 — #1 i i Understanding the spreading power of all nodes in a network: a continuous-time perspective Glenn Lawyer ∗ ∗Max Planck Institute for Informatics, Saarbr¨ucken, Germany Submitted to Proceedings of the National Academy of Sciences of the United States of America Centrality measures such as the degree, k-shell, or eigenvalue central- epidemic. When this ratio exceeds this critical range, the dy- ity can identify a network’s most influential nodes, but are rarely use- namics approach the SI system as a limiting case. fully accurate in quantifying the spreading power of the vast majority Several approaches to quantifying the spreading power of of nodes which are not highly influential. The spreading power of all all nodes have recently been proposed, including the accessibil- network nodes is better explained by considering, from a continuous- ity [16, 17], the dynamic influence [11], and the impact [7] (See time epidemiological perspective, the distribution of the force of in- fection each node generates. The resulting metric, the Expected supplementary Note S1). These extend earlier approaches to Force (ExF), accurately quantifies node spreading power under all measuring centrality by explicitly incorporating spreading dy- primary epidemiological models across a wide range of archetypi- namics, and have been shown to be both distinct from previous cal human contact networks. When node power is low, influence is centrality measures and more highly correlated with epidemic a function of neighbor degree. As power increases, a node’s own outcomes [7, 11, 18]. Yet they retain the common foundation degree becomes more important.
    [Show full text]
  • Epidemic Response to Physical Distancing Policies and Their Impact on the Outbreak Risk
    Epidemic response to physical distancing policies and their impact on the outbreak risk Fabio Vanni∗†‡ David Lambert§ ‡ Luigi Palatella¶ Abstract We introduce a theoretical framework that highlights the impact of physical distancing variables such as human mobility and physical proximity on the evolution of epidemics and, crucially, on the reproduction number. In particular, in response to the coronavirus disease (CoViD-19) pandemic, countries have introduced various levels of ’lockdown’ to reduce the number of new infections. Specifically we use a collisional approach to an infection-age struc- tured model described by a renewal equation for the time homogeneous evolution of epidemics. As a result, we show how various contributions of the lockdown policies, namely physical prox- imity and human mobility, reduce the impact of SARS-CoV-2 and mitigate the risk of disease resurgence. We check our theoretical framework using real-world data on physical distanc- ing with two different data repositories, obtaining consistent results. Finally, we propose an equation for the effective reproduction number which takes into account types of interac- tions among people, which may help policy makers to improve remote-working organizational structure. Keywords: Renewal equation, Epidemic Risk, Lockdown, Social Distancing, Mobility, Smart Work. arXiv:2007.14620v2 [physics.soc-ph] 31 Jul 2020 1 Introduction As the coronavirus disease (CoViD-19) epidemic worsens, understanding the effectiveness of public messaging and large-scale physical distancing interventions is critical in order to manage the acute ∗Sciences Po, OFCE , France †Institute of Economics, Sant’Anna School of Advanced Studies, Pisa, Italy ‡Department of Physics, University of North Texas, USA §Department of Mathematics, University of North Texas, USA ¶Liceo Scientifico Statale “C.
    [Show full text]
  • Reproduction Numbers for Infections with Free-Living Pathogens Growing in the Environment
    Journal of Biological Dynamics Vol. 6, No. 2, March 2012, 923–940 Reproduction numbers for infections with free-living pathogens growing in the environment Majid Bani-Yaghouba*, Raju Gautama, Zhisheng Shuaib, P. van den Driesscheb and Renata Ivaneka aDepartment of Veterinary Integrative Biosciences, College of Veterinary Medicine and Biomedical Sciences, Texas A&M University, College Station, TX 77843, USA; bDepartment of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 3R4 (Received 29 January 2012; final version received 6 May 2012) The basic reproduction number 0 for a compartmental disease model is often calculated by the next generation matrix (NGM) approach.R When the interactions within and between disease compartments are interpreted differently, the NGM approach may lead to different 0 expressions. This is demonstrated by considering a susceptible–infectious–recovered–susceptible modelR with free-living pathogen (FLP) growing in the environment.Although the environment could play different roles in the disease transmission process, leading to different 0 expressions, there is a unique type reproduction number when control R strategies are applied to the host population.All 0 expressions agree on the threshold value 1 and preserve their order of magnitude. However, using data forR salmonellosis and cholera, it is shown that the estimated 0 values are substantially different. This study highlights the utility and limitations of reproduction numbersR to accurately quantify the effects of control strategies for infections with FLPs growing in the environment. Keywords: SIRSP model; infection control; free-living pathogen; basic reproduction number; type reproduction number 1. Introduction The basic reproduction number, 0, is considered as one of the most practical tools that R Downloaded by [University of Central Florida] at 08:28 15 August 2012 mathematical thinking has brought to epidemic theory [26].
    [Show full text]
  • Modeling Infectious Disease Dynamics in the Complex Landscape of Global Health Hans Heesterbeek Et Al
    RESEARCH ◥ REVIEW SUMMARY linear systems in which infections evolve and spread and where key events can be governed by unpredictable pathogen biology or human EPIDEMIOLOGY behavior. In this Review, we start with an ex- amination of real-time outbreak response using the West African Ebola epidemic as an Modeling infectious disease dynamics example. Here, the challenges range from un- ◥ derreporting of cases and in the complex landscape of ON OUR WEB SITE deaths, and missing infor- Read the full article mation on the impact of at http://dx.doi. control measures to under- global health org/10.1126/ standing human responses. science.aaa4339 The possibility of future .................................................. Hans Heesterbeek,* Roy M. Anderson, Viggo Andreasen, Shweta Bansal, zoonoses tests our ability Daniela De Angelis, Chris Dye, Ken T. D. Eames, W. John Edmunds, to detect anomalous outbreaks and to esti- Simon D. W. Frost, Sebastian Funk, T. Deirdre Hollingsworth, Thomas House, mate human-to-human transmissibility against Valerie Isham, Petra Klepac, Justin Lessler, James O. Lloyd-Smith, C. Jessica E. Metcalf, a backdrop of ongoing zoonotic spillover while Denis Mollison, Lorenzo Pellis, Juliet R. C. Pulliam, Mick G. Roberts, also assessing the risk of more dangerous Cecile Viboud, Isaac Newton Institute IDD Collaboration strains evolving. Increased understanding of the dynamics of infections in food webs and BACKGROUND: Despitemanynotablesuc- lenges for prevention and control. Faced with ecosystems where host and nonhost species cesses in prevention and control, infectious this complexity, mathematical models offer interact is key. Simultaneous multispecies diseases remain an enormous threat to human valuable tools for understanding epidemio- infections are increasingly recognized as a and animal health.
    [Show full text]
  • Extinction Thresholds in Host–Parasite Dynamics
    Ann. Zool. Fennici 40: 115–130 ISSN 0003-455X Helsinki 30 April 2003 © Finnish Zoological and Botanical Publishing Board 2003 Extinction thresholds in host–parasite dynamics Anne Deredec & Franck Courchamp* Ecologie, Systématique & Evolution, UMR CNRS 8079, Université Paris-Sud XI, Bâtiment 362, F-91405 Orsay Cedex, France (*e-mail: [email protected]) Received 13 Jan. 2003, revised version received 5 Feb. 2003, accepted 22 Feb. 2003 Deredec, A. & Courchamp, F. 2003: Extinction thresholds in host–parasite dynamics. — Ann. Zool. Fennici 40: 115–130. In this paper, we review the main thresholds that can infl uence the population dynamics of host–parasite relationships. We start by considering the thresholds that have infl u- enced the conceptualisation of theoretical epidemiology. The most common threshold involving parasites is the host population invasion threshold, but persistence and infec- tion thresholds are also important. We recap how the existence of the invasion thresh- old is linked to the nature of the transmission term in theoretical studies. We examine some of the main thresholds that can affect host population dynamics including the Allee effect and then relate these to parasite thresholds, as a way to assess the dynamic consequences of the interplay between host and parasite thresholds on the fi nal out- come of the system. We propose that overlooking the existence of parasite and host thresholds can have important detrimental consequences in major domains of applied ecology, including in epidemiology, conservation biology and biological control. Introduction the infection would not spread and would dis- appear, and the few infected hosts would die, The interplay between parasite species and their leaving a remaining healthy and uninfected host hosts constitutes a biological process that is both population.
    [Show full text]
  • Global Convergence of COVID-19 Basic Reproduction Number and Estimation from Early-Time SIR Dynamics
    PLOS ONE RESEARCH ARTICLE Global convergence of COVID-19 basic reproduction number and estimation from early-time SIR dynamics 1,2 1☯ 3,4☯ 5☯ Gabriel G. KatulID *, Assaad MradID , Sara BonettiID , Gabriele ManoliID , Anthony 6☯ J. ParolariID 1 Nicholas School of the Environment, Duke University, Durham, NC, United States of America, 2 Department of Civil and Environmental Engineering, Duke University, Durham, NC, United States of America, a1111111111 3 Department of Environmental Systems Science, ETH ZuÈrich, ZuÈrich, Switzerland, 4 Bartlett School of a1111111111 Environment, Energy and Resources, University College London, London, United Kingdom, 5 Department of a1111111111 Civil, Environmental and Geomatic Engineering, University College London, London, United Kingdom, 6 Department of Civil, Construction, and Environmental Engineering, Marquette University, Milwaukee, a1111111111 Wisconsin, United States of America a1111111111 ☯ These authors contributed equally to this work. * [email protected] OPEN ACCESS Abstract Citation: Katul GG, Mrad A, Bonetti S, Manoli G, Parolari AJ (2020) Global convergence of COVID- The SIR (`susceptible-infectious-recovered') formulation is used to uncover the generic 19 basic reproduction number and estimation from spread mechanisms observed by COVID-19 dynamics globally, especially in the early early-time SIR dynamics. PLoS ONE 15(9): phases of infectious spread. During this early period, potential controls were not effectively e0239800. https://doi.org/10.1371/journal. pone.0239800 put in place or enforced in many countries. Hence, the early phases of COVID-19 spread in countries where controls were weak offer a unique perspective on the ensemble-behavior of Editor: Maria Vittoria Barbarossa, Frankfurt Institute for Advanced Studies, GERMANY COVID-19 basic reproduction number Ro inferred from SIR formulation.
    [Show full text]
  • Into to Epidemic Modeling
    INTRO TO EPIDEMIC MODELING Introduction to epidemic modeling is usually made through one of the first epidemic models proposed by Kermack and McKendrick in 1927, a model known as the SIR epidemic model When a disease spreads in a population it splits the population into nonintersecting classes. In one of the simplest scenarios there are 3 classes: • The class of individuals who are healthy but can contract the disease. These people are called susceptible individuals or susceptibles. The size of this class is usually denoted by S. • The class of individuals who have contracted the disease and are now sick with it, called infected individuals. In this model it is assumed that infected individuals are also infectious. The size of the class of infectious/infected individuals is denoted by I. • The class of individuals who have recovered and cannot contract the disease again are called removed/recovered individuals. The class of recovered individuals is usually denoted by R. The number of individuals in each of these classes changes with time, that is, S(t), I(t), and R(t). The total population size N is the sum of these three classes 푁 푡 = 푆 푡 + 퐼 푡 + 푅(푡) Assumptions: (1) Infected individuals are also infectious; (2) The total population size remains constant; (3) The population is closed (no immigration/emigration); (4) No births/deaths; (5)All recovered individuals have complete immunity Epidemiological models consist of systems of ODEs which describe the dynamics in each class. To derive the differential equations, we consider how the classes change in time. When a susceptible individual enters into a contact with an infectious individual, that susceptible individual becomes infected and moves from the susceptible class into the infected class.
    [Show full text]