Asymptotic Behavior Of Stochastic Predator-prey Model And Epidemic Model With Regime Switching

There always exist stochastic perturbations in the real ecological and epidemicsystems. If we take environmental perturbations fully into account during modelingsystems, we can ge more accurately describe the systems, and precisely reveal theirvariation. In this paper, we mainly consider the parameters in ecological systems andepidemic models with stochastic perturbation, and study their dynamic behaviors.This paper is arranged as follows:Chapter1give the research background, development and significance ofecological system and epidemic model and the major work of this paper is introduced.Chapter2consider a stochastic ratio-dependent food-chain system. By thecomparison theorem of stochastic equations and Ito ’s formula, we show that thereis a unique positive solution to the system and the positive solution is stochasticallyultimately bounded. Then under some conditions, we conclude that the stochasticmodel is persistent in mean and extinction. In the end, we give some numericalsimulations to confirm our theoretical analysis.Chapter3consider a stochastic epidemic model under regime switching. For thestochastic epidemic model with information variable and saturated incidence rate, weshow that this model has a unique positive solution. We mainly study the asymptoticbehavior around the equilibriums of deterministic model in stochastic model. Forstochastic epidemic model under regime switching, by the generalized Ito ’s formulaand ergodicity of Markov, we show that the model is stochastically stable undercertain condition and the moment average in time of the model solution is bounded.We also give some numerical simulations to illustrate our findings.Chapter4summarizes the work of this paper.