Dynamic Analysis Of Population Model And Infectious Disease Model With Markov Switching

In the course of studying biological models,there have been a lot of conclusions about deterministic models.However,in the actual biological environment,the population is always affected by various random environmental factors.Therefore,the study of stochastic model has inestimable significance to explore the dynamic behavior of population model.In this paper,we discuss the dynamics of a class of stochastic Holling-Tanner predator-prey model and SIQS infectious disease model.In the course of studying biological models,there have been a lot of conclusions about deterministic models.However,in the actual biological environment,the population is always affected by various random environmental factors.Therefore,the study of stochastic model has inestimable significance to explore the dynamic behavior of population model.In this paper,we discuss the dynamics of a class of stochastic Holling-Tanner predator-prey model and SIQS infectious disease model.The main work is as follows:The first part gives the background,research status and basic knowledge of stochastic Holling-Tanner predator-prey model and SIQS infectious disease model.In the second part,a stochastic Holling-Tanner predator-prey model is presented under two-parameter perturbation and Markov switching environment,and its dynamic behavior is investigated.Firstly,the existence and uniqueness of the positive solution of the system is given.Secondly,some basic theories of stochastic differential equations and inequality techniques are used to prove the stochastic boundedness of the system and the existence of a unique traversal stationary distribution.Thirdly,the conditions of stationary distribution and extinction of random Holling-Tanner model traversal for two-parameter perturbations of the system are given.Finally,the effects of two-parameter disturbance and Markov switching on population dynamics are visually demonstrated by numerical simulation,and the theoretical results of this chapter are verified.In the third part,a stochastic SIQS infectious disease model with Markov switching is presented and its dynamic behavior is studied.Firstly,the existence and uniqueness of global positive solutions of stochastic SIQS epidemic model with Markov switching is proved.Secondly,sufficient conditions are given for the stochastic SIQS infectious disease model with Markov switching to have a unique traversal stationary distribution,and the ergodicity of the stochastic SIQS infectious disease model with constant parameters is obtained,and the probability density function of the system is obtained.Finally,the conclusions of this chapter are further verified by numerical simulation.