The Asymptotic Behavior Of A Stochastic Eco-Epidemiology System

Eco-Epidemiology appears with establishment and rapid development of Malthus population model, Voltera predator model and Kermack-Mckendrick Epidemic Model. Eco-Epidemiology is an important branch which contains ecology and epi-demiology group. The Eco-Epidemiology system experiences internal and external random disturbance all the time, therefore, the research of the asymptotic behav-ior of stochastic Eco-Epidemiology system play an increasingly important role in theoretical ecology.In this paper, Firstly, we discuss the asymptotic behavior of stochastic SI sys-tem; Secondly, we study the dynamical behavior of a predator-prey model with dis-ease in the prey; Finally, we give the dynamics of the perturbed eco-epidemiological model with linear mass-action functional response by white noise and carry on nu-merical simulation.Above all, we show the existence and uniqueness of the globally nonnegative solution of the stochastic system by Lyapunov analysis method, which is the theoretical foundation of our research; Moreover, we are going to investigate the persistence and non-persistence, extinction or the stochastic, asymptotic be-havior of the systems under certain conditions, sometimes we obtain there exist stationary distributions and they are ergodic; What is more, we give the basic productive number Ro of the researched epidemic model,which can tell us when the disease is prevalent or when the disease will die out.In a word, we point out that the stochastic systems have properties similar to the corresponding deterministic systems if the white noise is small enough; while if the white noise is large enough, the stochastic systems have more different proper-ties. In real life, the large white noise can be considered as sudden natural disasters or outbreaks of infectious diseases etc.