摘要
考虑到时滞效应及空间扩散的影响,建立了一个具有一般传染率的病毒感染仓室模型,分析了模型的动力学性态.定义了模型的基本再生数R0,讨论了平衡点的存在性,并通过构造Lyapunov函数分析了平衡点的稳定性.结果表明,当R0<1时,无病平衡点全局渐近稳定;当R0> 1时,无病平衡点不稳定且地方病平衡点在一定条件下全局渐近稳定.同时,以Beddington-DeAngelis感染率为例的数值模拟进一步验证和扩展了理论结果.
In this paper,we propose a virus compartmental model with general incidence function that incorporates diffusion and time delays.A detailed analysis of dynamic behaviors is conducted,including defining the basic reproductive number R0,discussing the existence of equilibria and proving the stability by constructing Lyapunov functional.The results show that if R0<1,then the infection-free equilibrium is globally asymptotically stable.Conversely,if R0>1,the infection-free equilibrium is unstable and the endemic equilibrium is globally asymptotically stable under certain conditions.Meanwhile,taking Beddington-DeAngelis incidence function as a typical example,numerical simulations are provided to illustrate the main theoretical results.
作者
安兆凤
张素霞
AN Zhao-feng;ZHANG Su-xia(School of Science,Xi'an University of Technology,Xi'an 710048,China)
出处
《数学的实践与认识》
北大核心
2020年第11期149-159,共11页
Mathematics in Practice and Theory
基金
国家自然科学基金(11801439)
陕西省自然科学研究项目(2019JM338)。
关键词
时滞病毒模型
空间效应
一般传染率
稳定性
delayed viral infection model
diffusion
general incidence function
stability
