具有时滞影响的SIRC传染病模型的Hopf分支分析

doi:10.6040/j.issn.1671-9352.0.2018.366

摘要/Abstract

摘要： 讨论了一个具有时滞影响的关于流感A的SIRC传染病模型。首先求得基本再生数R₀,研究了模型平衡点的存在性及稳定性;其次证明了时滞可以导致系统Hopf分支的产生;然后,利用中心流形定理和规范型理论讨论了分支方向和周期解的稳定性;最后给出了数值模拟。

关键词: SIRC传染病模型, 交叉感染, 时滞, Hopf分支, 周期解

Abstract: This article concerns a SIRC model for Influenza A with time delay. The basic reproduction number R₀ is calculated. For the model without delay, we demonstrate the conditions for global stability of equilibria. And we show that the delay can only change the stability of the endemic equilibrium and lead to the existence of Hopf bifurcation. By applying the center manifold theorem, normal form theory, we also derive some explicit formulae determining the bifurcation direction and the stability of the bifurcated periodic solutions. Finally, numerical simulation is given to support our results.

Key words: SIRC model, cross-immune, delay, Hopf-bifurcation, periodic solution

中图分类号:

O175.12

李乐乐,贾建文. 具有时滞影响的SIRC传染病模型的Hopf分支分析[J]. 《山东大学学报(理学版)》, 2019, 54(1): 116-126.

LI Le-le, JIA Jian-wen. Hopf bifurcation of a SIRC epidemic model with delay[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(1): 116-126.

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