一个包含先天免疫因素的Markov切换传染病模型OA北大核心

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.