文章基本信息

标题：A Lyapunov–Schmidt method for detecting backward bifurcation in age-structured population models
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作者：Maia Martcheva ; Hisashi Inaba
期刊名称：Journal of Biological Dynamics
印刷版ISSN：1751-3758
电子版ISSN：1751-3766
出版年度：2020
卷号：14
期号：1
页码：543-565
DOI：10.1080/17513758.2020.1785024
出版社：Taylor & Francis
摘要：Backward bifurcation is an important property of infectious disease models. A centre manifold method has been developed by Castillo-Chavez and Song for detecting the presence of backward bifurcation and deriving a necessary and sufficient condition for its occurrence in Ordinary Differential Equations (ODE) models. In this paper, we extend this method to partial differential equation systems. First, we state a main theorem. Next we illustrate the application of the new method on a chronological age-structured Susceptible-Infected-Susceptible (SIS) model with density-dependent recovery rate, an age-since-infection structured HIV/AIDS model with standard incidence and an age-since-infection structured cholera model with vaccination.
关键词：Lyapunov–Schmidt theory; backward bifurcation; age-structured population model; epidemic model