Dynamical Behavior Of Stochastic Eco-Epidemiological Model Perturbed By White Noise

Eco-epidemiology combines population ecology and epidemiology to deal with diseases among the species in the environment,simulates predation relationships among the species and the spread of diseases within species,lays the foundation for better control and protection of species,and helps to protect species diversity.The eco-epidemiological system is subject to stochastic perturbation from inside and outside the system,so using stochastic differential equations to study the eco-epidemiological system helps to accurately describe actual system,which is also of great significance.The paper mainly investigates the dynamic behaviors of stochastic eco-epidemiological models perturbed by white noises.The results are divided into the following two parts:In the first part,we investigate the stochastic eco-epidemiological model of infected prey.Using the method of Lyapunov analysis,we prove the existence and uniqueness of the positive solution; We obtain sufficient conditions for the extinction of infected prey by classic stochastic inequalities such as Chebyshev’s inequality and Doob’s martingale inequality; Then,the Lyapunov functions satisfying the ergodicity theorem and the bounded region D are constructed to study the stationary distribution and ergodicity of the model by the stationary distribution theory of Khasminskii.Finally,the theoretical results are proved by numerical simulation.In the case of low noise intensity,stochastic model and corresponding deterministic model have similar properties.We study the stochastic eco-epidemiological model of the plankton with Holling type II functional response in the second part,and prove the existence and uniqueness of the global positive solution of the stochastic model by constructing appropriate Lyapunov function.Then,using the theory of stochastic differential equations,such as Strong law of large numbers,we study the persistence and extinction of the model.Moreover,the sufficient conditions for the positive recurrence of the model are obtained.Finally,numerical results of the deterministic eco-epidemiological model and the stochastic ecoepidemiological model are obtained,and the theoretical results are proved.