具有年龄结构的 SIRI 传染病模型的分岔分析。

Bifurcation analysis of an age-structured SIRI epidemic model.

机构信息

Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, China.

Institute of Applied Mathematics, Army Engineering University, Shijiazhuang 050003, Hebei, China.

出版信息

Math Biosci Eng. 2020 Oct 21;17(6):7130-7150. doi: 10.3934/mbe.2020366.

DOI:10.3934/mbe.2020366

PMID:33378890

Abstract

In this paper, an SIRI epidemic model with age of infection and the proliferation of susceptible individuals with logistic growth is investigated. By using the theory of integral semigroup and Hopf bifurcation theory for semilinear equations with non-dense domain, it is shown that if the threshold parameter is greater than unity, sufficient condition is derived for the occurrence of the Hopf bifurcation. Numerical simulations are carried out to illustrate the theoretical results.

摘要

本文研究了具有感染年龄和逻辑增长易感染个体增殖的 SIRI 传染病模型。通过使用积分半群理论和非稠密域半线性方程的 Hopf 分支理论，证明了当阈值参数大于 1 时，存在发生 Hopf 分支的充分条件。通过数值模拟验证了理论结果。