{"title":"Uniform Asymptotic Approximations for the Phase Plane Trajectories of the SIR Model with Vital Dynamics","authors":"Todd L. Parsons, David J. D. Earn","doi":"10.1137/23m1576050","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1580-1608, August 2024. <br/> Abstract. We derive accurate, closed-form analytical approximations for the phase-plane trajectories of the standard susceptible-infectious-removed (SIR) epidemic model, including host births and deaths, giving a complete description of the transient dynamics. Our approximations for the SIR ordinary differential equations also allow us to provide convenient, accurate analytical approximations for the associated Poincaré map, and the minimum and maximum susceptible and infectious host densities in each epidemic wave. Our analysis involves matching asymptotic expansions across branch cuts of the Lambert [math] function.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"94 1","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1576050","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1580-1608, August 2024. Abstract. We derive accurate, closed-form analytical approximations for the phase-plane trajectories of the standard susceptible-infectious-removed (SIR) epidemic model, including host births and deaths, giving a complete description of the transient dynamics. Our approximations for the SIR ordinary differential equations also allow us to provide convenient, accurate analytical approximations for the associated Poincaré map, and the minimum and maximum susceptible and infectious host densities in each epidemic wave. Our analysis involves matching asymptotic expansions across branch cuts of the Lambert [math] function.
期刊介绍：
SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.
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