The Dynamical Analysis Of Vector-borne Disease Model With Stochastic Perturbation

In recent years,the research on dynamically behaviour of biological mathematics with stochastic perturbation model has been widespread attention to domestic and inter-national scholars.Based on vector-borne diseases,this paper discusses the impact of two types of random disturbances on the outbreak and extinction of vector-borne diseases.Its main contents can be summarized as follows:1.In the first part,considering the effect of environmental white noise on the bio-logical population,a dynamic model of the transmission of Dengue virus with stochastic perturbation between mosquitoes and humans is introduced.We proved that the exis-tence and uniqueness of global positive solutions for this model.Further,by constructing some suitable Lyapunov functions,the asymptotic behaviors of the disease-free equilibri-um and the endemic equilibrium of the corresponding deterministic model are discussed,respectively.Theoretical results show that the oscillation behavior of stochastic model is closely related to white noise,that is,the white noise intensity will weaken with the drop of the oscillation and vice verse.Finally,the presented results are demonstrated by numerical simulations.2.Considering the impact of environmental white noise on vector borne disease transmission,a stochastic differential model describing the transmission of Dengue fever bet,ween mosquitoes and humans,in this paper,is proposed.By using Lyapunov methods and Ito's formula,we first prove the existence and uniqueness of a global positive solution for this model.Further,we obtain sufficient conditions for the extinction and persistence in the mean of this stochastic model by using the techniques of a series of stochastic inequalities.In addition,we also discuss the existence of a unique stationary distribution which leads to the stochastically persistence of this disease.Finally,we carry out,several numerical simulations to illustrate the main results of this contribution.3.A stochastic West Nile virus epidemic model under regime switching is pro-posed.We obtain some sufficient conditions for the extinction of this stochastic model by constructing appropriate Lyapunov function.Then,by a.pplying the relevant theo-ry of Markov conversion we prove the model has the ergodicity and unique stationary distribution.Finally,numerical simulations are carried out to illustrate our analytical results.