{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T13:56:51Z","timestamp":1791986211273,"version":"4.4.0"},"reference-count":63,"publisher":"Elsevier BV","issue":"3","license":[{"start":{"date-parts":[[2017,8,1]],"date-time":"2017-08-01T00:00:00Z","timestamp":1501545600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2017,5,19]],"date-time":"2017-05-19T00:00:00Z","timestamp":1495152000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000038","name":"NSERC","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Infectious Disease Modelling"],"published-print":{"date-parts":[[2017,8]]},"DOI":"10.1016\/j.idm.2017.06.002","type":"journal-article","created":{"date-parts":[[2017,6,29]],"date-time":"2017-06-29T15:21:20Z","timestamp":1498749680000},"page":"288-303","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":413,"title":["Reproduction numbers of infectious disease models"],"prefix":"10.1016","volume":"2","author":[{"given":"Pauline","family":"van den Driessche","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.idm.2017.06.002_bib1","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/0025-5564(94)90025-6","article-title":"Some discrete-time SI, SIR, and SIS epidemic models","volume":"124","author":"Allen","year":"1994","journal-title":"Mathematical Biosciences"},{"key":"10.1016\/j.idm.2017.06.002_bib2","series-title":"An introduction to stochastic processes with applications to biology","author":"Allen","year":"2010"},{"issue":"10\u201311","key":"10.1016\/j.idm.2017.06.002_bib3","doi-asserted-by":"crossref","first-page":"1127","DOI":"10.1080\/10236190802332308","article-title":"The basic reproduction number in some discrete-time epidemic models","volume":"14","author":"Allen","year":"2008","journal-title":"Journal of Difference Equations and Applications"},{"key":"10.1016\/j.idm.2017.06.002_bib4","doi-asserted-by":"crossref","DOI":"10.1371\/currents.outbreaks.91afb5e0f279e7f29e7056095255b288","article-title":"Estimating the reproduction number of Ebola virus (EBOV) during the 2014 outbreak in West Africa","author":"Althaus","year":"2014","journal-title":"PLoS Currents Outbreaks"},{"key":"10.1016\/j.idm.2017.06.002_bib5","series-title":"Infectious diseases of humans: Dynamics and control","author":"Anderson","year":"1991"},{"issue":"1","key":"10.1016\/j.idm.2017.06.002_bib6","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1137\/S0036139902413829","article-title":"Global results for an epidemic model with vaccination that exhibits backward bifurcation","volume":"64","author":"Arino","year":"2003","journal-title":"SIAM Journal on Applied Mathematics"},{"issue":"5","key":"10.1016\/j.idm.2017.06.002_bib7","doi-asserted-by":"crossref","first-page":"741","DOI":"10.1007\/s00285-010-0354-8","article-title":"Genealogy with seasonality, the basic reproduction number, and the influenza pandemic","volume":"62","author":"Baca\u00ebr","year":"2011","journal-title":"Journal of Mathematical Biology"},{"key":"10.1016\/j.idm.2017.06.002_bib8","series-title":"Nonnegative matrices in the mathematical sciences","author":"Berman","year":"1994"},{"key":"10.1016\/j.idm.2017.06.002_bib9","doi-asserted-by":"crossref","first-page":"229","DOI":"10.2307\/1403510","article-title":"Sensitivity and uncertainty analysis for complex models of disease transmission: An HIV model, as an example","volume":"62","author":"Blower","year":"1994","journal-title":"International Statistical Review"},{"issue":"5","key":"10.1016\/j.idm.2017.06.002_bib10","doi-asserted-by":"crossref","first-page":"1107","DOI":"10.1016\/j.bulm.2005.01.002","article-title":"A\u00a0mathematical model for assessing control strategies against West Nile virus","volume":"67","author":"Bowman","year":"2005","journal-title":"Bulletin of Mathematical Biology"},{"issue":"2","key":"10.1016\/j.idm.2017.06.002_bib11","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1016\/j.jmaa.2004.05.045","article-title":"Backward bifurcations in simple vaccination models","volume":"298","author":"Brauer","year":"2004","journal-title":"Journal of Mathematical Analysis and Applications"},{"issue":"1","key":"10.1016\/j.idm.2017.06.002_bib12","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.idm.2016.08.001","article-title":"Some models for epidemics of vector-transmitted diseases","volume":"1","author":"Brauer","year":"2016","journal-title":"Infectious Disease Modelling"},{"key":"10.1016\/j.idm.2017.06.002_bib13","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.mbs.2017.03.003","article-title":"Optimal control of a malaria model with asymptomatic class and superinfection","volume":"288","author":"Cai","year":"2017","journal-title":"Mathematical Biosciences"},{"key":"10.1016\/j.idm.2017.06.002_bib14","series-title":"Mathematical approaches for emerging and reemerging infectious diseases: An introduction. Vol. IMA 125","first-page":"229","article-title":"On the computation of \u211b0 and its role in global stability","author":"Castillo-Ch\u00e1vez","year":"2002"},{"issue":"2","key":"10.1016\/j.idm.2017.06.002_bib15","doi-asserted-by":"crossref","first-page":"361","DOI":"10.3934\/mbe.2004.1.361","article-title":"Dynamical models of tuberculosis and their applications","volume":"1","author":"Castillo-Ch\u00e1vez","year":"2004","journal-title":"Mathematical Biosciences and Engineering"},{"issue":"44","key":"10.1016\/j.idm.2017.06.002_bib16","doi-asserted-by":"crossref","first-page":"6747","DOI":"10.1016\/j.vaccine.2006.05.055","article-title":"Estimation of the reproductive number of the Spanish flu epidemic in Geneva, Switzerland","volume":"24","author":"Chowell","year":"2006","journal-title":"Vaccine"},{"key":"10.1016\/j.idm.2017.06.002_bib17","series-title":"Mathematical and statistical estimation approaches in epidemiology","first-page":"1","article-title":"The basic reproduction number of infectious diseases: Computation and estimation using compartmental epidemic models","author":"Chowell","year":"2009"},{"key":"10.1016\/j.idm.2017.06.002_bib18","doi-asserted-by":"crossref","DOI":"10.1371\/currents.outbreaks.f14b2217c902f453d9320a43a35b9583","article-title":"Using phenomenological models to characterize transmissibility and forecast patterns and final burden of Zika epidemics","author":"Chowell","year":"2016","journal-title":"PLOS Currents Outbreaks"},{"key":"10.1016\/j.idm.2017.06.002_bib19","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1016\/j.plrev.2016.07.005","article-title":"Mathematical models to characterize early epidemic growth: A review","volume":"18","author":"Chowell","year":"2016","journal-title":"Physics of Life Reviews"},{"issue":"1","key":"10.1016\/j.idm.2017.06.002_bib20","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.idm.2016.07.004","article-title":"Is it growing exponentially fast?\u2013impact of assuming exponential growth for characterizing and forecasting epidemics with initial near-exponential growth dynamics","volume":"1","author":"Chowell","year":"2016","journal-title":"Infectious Disease Modelling"},{"issue":"123","key":"10.1016\/j.idm.2017.06.002_bib21","doi-asserted-by":"crossref","first-page":"20160659","DOI":"10.1098\/rsif.2016.0659","article-title":"Characterizing the reproduction number of epidemics with early subexponential growth dynamics","volume":"13","author":"Chowell","year":"2016","journal-title":"Journal of the Royal Society Interface"},{"key":"10.1016\/j.idm.2017.06.002_bib22","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/j.jtbi.2016.06.017","article-title":"The many guises of R0 (a didactic note)","volume":"404","author":"Cushing","year":"2016","journal-title":"Journal of Theoretical Biology"},{"issue":"1","key":"10.1016\/j.idm.2017.06.002_bib38","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1086\/588060","article-title":"On net reproductive rate and the timing of reproductive output","volume":"172","author":"de-Camino-Beck","year":"2008","journal-title":"The American Naturalist"},{"issue":"4","key":"10.1016\/j.idm.2017.06.002_bib39","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1007\/s00285-008-0240-9","article-title":"A\u00a0graph-theoretic method for the basic reproduction number in continuous time epidemiological models","volume":"59","author":"de-Camino-Beck","year":"2009","journal-title":"Journal of Mathematical Biology"},{"key":"10.1016\/j.idm.2017.06.002_bib23","series-title":"Mathematical tools for understanding infectious disease dynamics","author":"Diekmann","year":"2012"},{"issue":"4","key":"10.1016\/j.idm.2017.06.002_bib24","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1007\/BF00178324","article-title":"On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations","volume":"28","author":"Diekmann","year":"1990","journal-title":"Journal of Mathematical Biology"},{"key":"10.1016\/j.idm.2017.06.002_bib25","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/S0025-5564(02)00108-6","article-title":"Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission","volume":"180","author":"van den Driessche","year":"2002","journal-title":"Mathematical Biosciences"},{"key":"10.1016\/j.idm.2017.06.002_bib26","series-title":"Mathematical epidemiology","first-page":"159","article-title":"Further notes on the basic reproduction number","author":"van den Driessche","year":"2008"},{"key":"10.1016\/j.idm.2017.06.002_bib27","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.jtbi.2012.12.021","article-title":"Identifiability and estimation of multiple transmission pathways in cholera and waterborne disease","volume":"324","author":"Eisenberg","year":"2013","journal-title":"Journal of Theoretical Biology"},{"issue":"1","key":"10.1016\/j.idm.2017.06.002_bib28","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/j.mbs.2012.10.004","article-title":"Anthrax epizootic and migration: Persistence or extinction","volume":"241","author":"Friedman","year":"2013","journal-title":"Mathematical Biosciences"},{"key":"10.1016\/j.idm.2017.06.002_bib29","doi-asserted-by":"crossref","first-page":"28070","DOI":"10.1038\/srep28070","article-title":"Prevention and control of Zika as a mosquito-borne and sexually transmitted disease: A mathematical modeling analysis","volume":"6","author":"Gao","year":"2016","journal-title":"Scientific Reports"},{"issue":"1554","key":"10.1016\/j.idm.2017.06.002_bib30","doi-asserted-by":"crossref","first-page":"2223","DOI":"10.1098\/rspb.2004.2800","article-title":"Modelling strategies for controlling SARS outbreaks","volume":"271","author":"Gumel","year":"2004","journal-title":"Proceedings of the Royal Society of London B: Biological Sciences"},{"issue":"1","key":"10.1016\/j.idm.2017.06.002_bib31","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/0025-5564(94)00066-9","article-title":"A\u00a0core group model for disease transmission","volume":"128","author":"Hadeler","year":"1995","journal-title":"Mathematical Biosciences"},{"issue":"1","key":"10.1016\/j.idm.2017.06.002_bib32","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.mbs.2004.10.013","article-title":"The type-reproduction number T in models for infectious disease control","volume":"206","author":"Heesterbeek","year":"2007","journal-title":"Mathematical Biosciences"},{"issue":"4","key":"10.1016\/j.idm.2017.06.002_bib33","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1098\/rsif.2005.0042","article-title":"Perspectives on the basic reproductive ratio","volume":"2","author":"Heffernan","year":"2005","journal-title":"Journal of the Royal Society Interface"},{"issue":"2","key":"10.1016\/j.idm.2017.06.002_bib34","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1007\/s00285-011-0463-z","article-title":"On a new perspective of the basic reproduction number in heterogeneous environments","volume":"65","author":"Inaba","year":"2012","journal-title":"Journal of Mathematical Biology"},{"issue":"3","key":"10.1016\/j.idm.2017.06.002_bib35","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1007\/s11538-008-9374-6","article-title":"Threshold conditions for West Nile virus outbreaks","volume":"71","author":"Jiang","year":"2009","journal-title":"Bulletin of Mathematical Biology"},{"key":"10.1016\/j.idm.2017.06.002_bib36","series-title":"Modeling infectious diseases in humans and animals","author":"Keeling","year":"2008"},{"issue":"2","key":"10.1016\/j.idm.2017.06.002_bib37","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/S0025-5564(00)00003-1","article-title":"A\u00a0simple vaccination model with multiple endemic states","volume":"164","author":"Kribs-Zaleta","year":"2000","journal-title":"Mathematical Biosciences"},{"key":"10.1016\/j.idm.2017.06.002_bib40","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1007\/s11538-005-9039-7","article-title":"A\u00a0comparison of continuous and discrete-time West Nile virus models","volume":"68","author":"Lewis","year":"2006","journal-title":"Bulletin of Mathematical Biology"},{"issue":"4","key":"10.1016\/j.idm.2017.06.002_bib41","doi-asserted-by":"crossref","first-page":"961","DOI":"10.1007\/s00285-014-0839-y","article-title":"Model for disease dynamics of a waterborne pathogen on a random network","volume":"71","author":"Li","year":"2015","journal-title":"Journal of Mathematical Biology"},{"issue":"7","key":"10.1016\/j.idm.2017.06.002_bib42","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1093\/aje\/kwh092","article-title":"Containing pandemic influenza with antiviral agents","volume":"159","author":"Longini","year":"2004","journal-title":"American Journal of Epidemiology"},{"issue":"1","key":"10.1016\/j.idm.2017.06.002_bib43","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1007\/s11538-013-9918-2","article-title":"Estimating initial epidemic growth rates","volume":"76","author":"Ma","year":"2014","journal-title":"Bulletin of Mathematical Biology"},{"key":"10.1016\/j.idm.2017.06.002_bib44","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1016\/j.jtbi.2014.04.033","article-title":"Comparing dengue and chikungunya emergence and endemic transmission in A. aegypti and A. albopictus","volume":"356","author":"Manore","year":"2014","journal-title":"Journal of Theoretical Biology"},{"key":"10.1016\/j.idm.2017.06.002_bib45","article-title":"Introduction to mathematical epidemiology","volume":"Vol. 61","author":"Martcheva","year":"2015"},{"issue":"3","key":"10.1016\/j.idm.2017.06.002_bib46","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/s00285-010-0337-9","article-title":"A\u00a0note on a paper by Erik Volz: SIR dynamics in random networks","volume":"62","author":"Miller","year":"2011","journal-title":"Journal of Mathematical Biology"},{"issue":"2","key":"10.1016\/j.idm.2017.06.002_bib47","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1137\/S003614450342480","article-title":"The structure and function of complex networks","volume":"45","author":"Newman","year":"2003","journal-title":"SIAM Review"},{"issue":"6","key":"10.1016\/j.idm.2017.06.002_bib48","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1289\/ehp.1307799","article-title":"Estimated effects of projected climate change on the basic reproductive number of the Lyme disease vector Ixodes scapularis","volume":"122","author":"Ogden","year":"2014","journal-title":"Environmental Health Perspectives"},{"issue":"1522","key":"10.1016\/j.idm.2017.06.002_bib49","doi-asserted-by":"crossref","first-page":"1359","DOI":"10.1098\/rspb.2003.2339","article-title":"A\u00a0new method for estimating the effort required to control an infectious disease","volume":"270","author":"Roberts","year":"2003","journal-title":"Proceedings of the Royal Society of London B: Biological Sciences"},{"issue":"1","key":"10.1016\/j.idm.2017.06.002_bib50","doi-asserted-by":"crossref","first-page":"754","DOI":"10.1186\/s12879-016-2076-z","article-title":"Estimation of Zika virus prevalence by appearance of microcephaly","volume":"16","author":"Saad-Roy","year":"2016","journal-title":"BMC Infectious Diseases"},{"issue":"2","key":"10.1016\/j.idm.2017.06.002_bib51","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/s11538-016-0238-1","article-title":"A\u00a0mathematical model of anthrax transmission in animal populations","volume":"79","author":"Saad-Roy","year":"2017","journal-title":"Bulletin of Mathematical Biology"},{"issue":"1","key":"10.1016\/j.idm.2017.06.002_bib52","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.idm.2016.08.002","article-title":"A\u00a0comparative analysis of three different methods for the estimation of the basic reproduction number of dengue","volume":"1","author":"Sanches","year":"2016","journal-title":"Infectious Disease Modelling"},{"issue":"5","key":"10.1016\/j.idm.2017.06.002_bib53","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.1007\/s00285-012-0579-9","article-title":"Extending the type reproduction number to infectious disease control targeting contacts between types","volume":"67","author":"Shuai","year":"2013","journal-title":"Journal of Mathematical Biology"},{"issue":"4","key":"10.1016\/j.idm.2017.06.002_bib54","doi-asserted-by":"crossref","first-page":"1513","DOI":"10.1137\/120876642","article-title":"Global stability of infectious disease models using Lyapunov functions","volume":"73","author":"Shuai","year":"2013","journal-title":"SIAM Journal on Applied Mathematics"},{"issue":"1","key":"10.1016\/j.idm.2017.06.002_bib55","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1137\/080732870","article-title":"Spectral bound and reproduction number for infinite-dimensional population structure and time heterogeneity","volume":"70","author":"Thieme","year":"2009","journal-title":"SIAM Journal on Applied Mathematics"},{"issue":"6","key":"10.1016\/j.idm.2017.06.002_bib56","doi-asserted-by":"crossref","first-page":"1506","DOI":"10.1007\/s11538-010-9507-6","article-title":"Multiple transmission pathways and disease dynamics in a waterborne pathogen model","volume":"72","author":"Tien","year":"2010","journal-title":"Bulletin of Mathematical Biology"},{"key":"10.1016\/j.idm.2017.06.002_bib57","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.epidem.2016.01.002","article-title":"A\u00a0generalized-growth model to characterize the early ascending phase of infectious disease outbreaks","volume":"15","author":"Viboud","year":"2016","journal-title":"Epidemics"},{"issue":"2","key":"10.1016\/j.idm.2017.06.002_bib58","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1137\/16M1087916","article-title":"Dynamics of a time-delayed Lyme disease model with seasonality","volume":"16","author":"Wang","year":"2017","journal-title":"SIAM Journal on Applied Dynamical Systems"},{"issue":"1","key":"10.1016\/j.idm.2017.06.002_bib59","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1186\/1476-072X-12-35","article-title":"Estimating the reproductive number in the presence of spatial heterogeneity of transmission patterns","volume":"12","author":"White","year":"2013","journal-title":"International Journal of Health Geographics"},{"key":"10.1016\/j.idm.2017.06.002_bib60","series-title":"Anthrax in humans and animals","author":"WHO","year":"2016"},{"key":"10.1016\/j.idm.2017.06.002_bib61","series-title":"Mathematical epidemiology","first-page":"365","article-title":"A\u00a0comparative analysis of models for West Nile virus","author":"Wonham","year":"2008"},{"key":"10.1016\/j.idm.2017.06.002_bib62","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1090\/dimacs\/075\/04","article-title":"Introduction to discrete-time epidemic models","volume":"75","author":"Yakubu","year":"2010","journal-title":"DIMACS Series in Discrete Mathematics and Theoretical Computer Science"},{"key":"10.1016\/j.idm.2017.06.002_bib63","series-title":"Dynamical systems in population biology","author":"Zhao","year":"2013"}],"container-title":["Infectious Disease Modelling"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S2468042717300209?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S2468042717300209?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,9,27]],"date-time":"2019-09-27T13:32:14Z","timestamp":1569591134000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S2468042717300209"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8]]},"references-count":63,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2017,8]]}},"alternative-id":["S2468042717300209"],"URL":"https:\/\/doi.org\/10.1016\/j.idm.2017.06.002","relation":{},"ISSN":["2468-0427"],"issn-type":[{"value":"2468-0427","type":"print"}],"subject":[],"published":{"date-parts":[[2017,8]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Reproduction numbers of infectious disease models","name":"articletitle","label":"Article Title"},{"value":"Infectious Disease Modelling","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.idm.2017.06.002","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"Crown Copyright \u00a9 2017 Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd.","name":"copyright","label":"Copyright"}]}}