四川大学学报（自然科学版）2025，Vol.62Issue(4)：812-822,11.DOI:10.19907/j.0490-6756.240149
一个包含先天免疫因素的Markov切换传染病模型
A Markovian switching epidemic model with innate immunity
摘要
Abstract
Due to the characteristics of rapid mutation,high infectivity,fast transmission and morbidity con-cealment,there are great difficulties in the prevention of some infectious diseases.In order to prevent and con-trol the spread of infectious diseases effectively,mathematical models are basic tools to analyze the transmis-sion and dynamic properties of infectious diseases.Innate immunity of different individuals helps the exposed recover to the susceptible while the vaccination is beneficial for individuals to produce a certain amount of anti-bodies.In this paper,considering the important role of innate immunity and vaccination in the control of infec-tious diseases,a Markovian switching epidemic model is proposed,which takes the vaccination,Beddington-DeAngelis incidence rate and saturated innate immunity rate into accounts.The fitness of a unique global posi-tive solution is firstly proved by combining the stopping time theory and constructing appropriate Lyapunov functions.Further,by using the generalized It ô's formula and proper Lyapunov functions,the existence of er-godicity and stationary Markov process under the condition Rs0>1 is obtained.Meanwhile,the extinction of the exposed and the infected under the condition Re0<1 for the model is figured out.Finally,numerical simu-lations are carried out to verify the theoretic results.It is concluded that both the exposed and the infected tend to extinction faster as the environmental fluctuation,the vaccination rate or the innate immunity increases.关键词
随机传染病模型/先天免疫/疫苗接种/平稳Markov过程/绝灭Key words
Stochastic epidemic model/Innate immunity/Vaccination/Stationary Markov process/Extinc-tion分类
数理科学引用本文复制引用
陈丽君..一个包含先天免疫因素的Markov切换传染病模型[J].四川大学学报（自然科学版）,2025,62(4):812-822,11.基金项目
福建省中青年教师教育科研项目(JAT210662) （JAT210662）
福建农林大学金山学院青年教师科研基金项目(kx230301) （kx230301）
