| Stochastic propagation model describes the dynamic behavior of population quantity in stochastic environment,and it is widely used in population dynamics,infectious diseases,news transmission and other fields.A stochastic mosquito population model and its dynamic behaviors under the influence of Wolbachia are investigated in this thesis.Then,a stochastic rumor propagation model under the influence of official media and the asymptotic behaviors are studied.The specific contents are as follows:The first chapter introduces the historical research of mosquito population and rumor propagation model,as well as the preliminary knowledge needed in this paper.In chapter 2,a stochastic model of mosquito population under the influence of wolbachia is established.Firstly,the existence and uniqueness of global positive solutions are proved.Secondly,the basic reproduction number R0 of this model is defined.It is proved that,when R0<1,the number of infected mosquitoes tends to become extinct.Then,a sufficient condition for stochastic persistence in mean of the model is given.Finally,The application of the theorem in this chapter is illustrated by numerical simulation.The third chapter establishes a stochastic rumor propagation model under the influence of official media and studies the asymptotic properties near the no-rumor equilibrium point and the positive equilibrium point.Firstly,the existence and uniqueness of positive solutions of the stochastic differential equation are proved.Then,a new basic reproduction number R'0 is defined.And it is proved that when R'0<1 and some conditions are satisfied,the solution of the system is asymptotically stable near the rumor free equilibrium point.When R'0>1 and some other requirements are met,the solution of the system is asymptotically stable near the positive rumor equilibrium point.The fourth chapter summarizes the research contents and conclusions of this paper,and puts forward the research prospects and considerations. |
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