张子振,缑超博,张振辉

• 1:安徽财经大学管理科学与工程学院

摘要(Abstract)：

以恢复个体临时免疫期时滞为分支参数,研究了一类具有阶段结构和非线性发生率的时滞SIRS传染病模型的局部Hopf分支.首先计算得到模型的有病毒平衡点,然后通过分析模型相应特征方程根的分布,得到模型有病毒平衡点局部渐近稳定和产生Hopf分支的时滞临界点τ_0.研究表明,当时滞的值低于临界点τ_0时,有病毒平衡点是局部渐近稳定的.而一旦时滞的值超越临界点,模型的有病毒平衡点将失去稳定性并在有病毒平衡点附近产生一簇分支周期解.最后,利用仿真示例对理论分析结果的正确性进行了验证.

关键词(KeyWords)： SIRS模型;阶段结构;时滞;Hopf分支

Abstract:

Keywords:

基金项目(Foundation): 2015年度安徽省高等学校省级自然科学研究项目(KJ2015A144)

作者(Author): 张子振,缑超博,张振辉

DOI: 10.16393/j.cnki.37-1436/z.2016.02.002

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