Dynamics Analysis Of Several Types Of Epidemic Models With Random Disturbance

In real life,any biological system is inevitably subject to some random disturbances.In addition,the occurrence,development and spread of various infectious diseases is an extremely complicated process,and there are a lot of real-world randomness.Therefore,when it comes to disease modeling,considering the effects of stochastic disturbances can more accurately reveal the laws of biological systems.we established and analyzed three types of infectious disease models in this paper.Chapter 2 studies a class of stochastic periodic SIVS epidemic model with proportional inoculation and time delay.This chapter shows that the system has a unique global positive solution by defining the stopping time,using the It?o formula,and establishing an appropriate Lyapunov function.In addition,it gives that the sufficient condition of the extinction and persistence of disease by defining the threshold expression of the system.Then this chapter proves the existence of a non-trivial positive periodic solution of the stochastic system.Finally,the results are verified by numerical simulation.Chapter 3 discusses a class of stochastic periodic SIRS epidemic model with temporary immunity.By using the stochastic differential equation comparison theorem,the boundedness of the system solution is proved.Then this cheaper proves the existence and uniqueness of global positive solution,persistence,extinction,and existence of a non-trivial positive periodic solution.Finally,the influence of random disturbance on system dynamics behavior is revealed by numerical simulation.Chapter 4 studies a class of cholera epidemic model with stochastic disturbance.Firstly,this chapter shows that the system has a unique global positive solution.Then,we discuss the asymptotic properties of the solutions of stochastic systems in the vicinity of the system disease-free equilibrium and the corresponding deterministic system endemic equilibrium.We mainly use the It?o formula and choose appropriate Lyapunov function to prove the relevant theorem.Finally,numerical simulations are present to illustrate our mathematical findings.