具有非线性免疫反应的随机HIV模型的平稳分布
Stationary Distribution of a Stochastic HIV Model with Nonlinear Immune Response Function
张艳敏 1刘明鼎 1孙荣庭2
作者信息
摘要
针对一类具有靶细胞生长和非线性免疫反应的随机HIV模型,利用随机Lyapunov分析法以及Itô公式证明其存在唯一的遍历平稳分布,得到了存在平稳分布的充分条件.证明中构造了新颖的随机Lyapunov函数,得出了当关键阈值基本再生数RS0＞1和病毒繁殖数RS1＞1同时成立时,随机HIV模型存在唯一的遍历平稳分布的结论.遍历平稳分布的存在意味着所有个体都可以长期共存.
Abstract
In this paper,a sufficient condition for the existence of unique ergodic stationary distribution in a stochastic HIV model with target cell growth and nonlinear immune response is given.Stochastic Lyapunov analysis method and Ito formula are used to prove the stochastic HIV model.By constructing a novel combination of Lyapunov functions,it is proved that the stochastic HIV model has a unique ergodic stationary distribution when the critical thresholds basic reproduction number RS0＞1 and virus reproduction number RS1＞1 are established.The existence of an ergodic stationary distribution implies that all individuals can coexist in the long run.
关键词
随机HIV模型/非线性免疫应答/Lyapunov函数/平稳分布Key words
Stochastic HIV model/Uncertainty/Nonlinear immune response/Lyapunov function/Stationary distribution引用本文复制引用
基金项目
山东省本科高校改革研究资助项目(M2021150)
陕西省自然科学基础研究计划资助项目(2021JM-187)
出版年
2024
NETL
NSTL
万方数据