Dynamical Analysis Of Stochastic Epidemic Model With Double Diseases

This paper considered the environment under the influence of random dynamic model of infectious diseases,and analyzes the existence and uniqueness of global solutions,and research disease persistence and extinction.This paper is divided into five chapters to study the stochastic dynamic model of different factors affected by the environment.The first chapter briefly introduces the background,present situation,basic definitions,theorems and structure of dynamics model of infectious diseases.Under the influence of the environment on mortality incidence Beddington-DeAngelis random SIS epidemic model in the second chapter.We mainly apply ITO formula and Lyapunov function to prove the existence of the stochastic system globally unique positive solution,determine the extinction of the stochastic system of two kinds of epidemic and in the sense of mean lasting threshold,and the white noise environment can be contributed to extinct.The mortality due to illness under the influence of the environment of a stochastic SIQS epidemic model with the Beddington-DeAngelis incidence and double diseases is proposed and analysed in the third chapter,we explored the threshold of the stochastic system and determined the conditions which lead to the extinction and permanence in mean of two infectious diseases,we also received that the two diseases will die out if the white noise disturbance is sufficiently larger.The fourth chapter,We discuss the mortality due to illness and infection rates are affected by the environment of a stochastic SIQS epidemic model with the Beddington-DeAngelis incidence and double diseases.At the same time,the conditions which lead to the extinction of two infectious diseases are determined by Ito formula.Moreover,by constructing suitable Lyapunov function,some sufficient conditions for the existence of an ergodic stationary distribution for the model are established.Finally,some numerical simulations are provided to illustrate the analytical results.The fifth chapter mainly reviews the main work of this paper and looks forward to the future.