A Study Of Stochastic Infectious Disease Models With Ebola Virus

As an important branch of ecological mathematics,infectious disease dynamics reveals the epidemic law of disease,which can make people predict the trend of the disease.This paper focuses on the study of ebola virus,and we introduce a stochastic mathematical model,infectious diseases with Ebola virus are established and studied by applying the related theory of stochastic differential equation.The article is divided into five chapters:The preface is in chapter 1,we introduce the research background and main task of this article,as well as some important preliminaries.In Chapter 2,we establish a stochastic SIRD model by adding random disturbance to a deterministic SIRD model.Firstly,we know that this model has a unique global positive solution.Secondly,we establish the asymptotic relationship between the stochastic SIRD model and the corresponding deterministic model by choosing suitable Lyapunov function.Finally,the correctness of the analysis results is verified by numerical simulation.In Chapter 3,on the basis of the previous chapter,the stochastic SIRD model is futher studied and new theoretical results are obtained.Firstly,Khasminskii theorem are applied to prove the existence of stationary distribution for stochastic system,this shows that the disease is meaning persistence.Secondly,using stochastic Lyapunov function,Ito's formula and the strong law of large numbers to give the conditions of the disease extinction.Finally,numerical simulation results support our theoretical results.In Chapter 4,a stochastic SIRDP model of Ebola virus is established and discussed by adding the influence of environmental factors on disease transmission.Firstly,we know that this model has a unique global positive solution.Secondly,Khasminskii theorem are applied to prove the existence of stationary distribution for stochastic system,this shows that the disease is meaning persistence.Further,using stochastic Lyapunov function,Ito's formula and the strong law of large numbers to give the conditions of the disease extinction.At last,the mathematical conclusions are explained by numerical simulation.In chapter 5,the main work of this paper is summarized and the future research work is prospected.