Analysis Of Stability And Extinction Of Stochastic HIV Infection Model

Because of the more and more extensive circulation of people in today’s society,the social value presents the trend of diversity.It is very critical to understand the basic mechanism of the HIV infection and the progression of the HIV epidemic.More and more scholars devote themselves to the study of the spread of AIDS.In this paper,a stochastic model is introduced to investigate the process of disease transmission under the influence of noise environment and the extinction of disease in individuals.The Allee effect reflects the significant effect of overcrowding on population life.Furthermore,in this paper,we assume that the infection process of uninfected cells is affected by the Allee effect.Works of this thesis are as follows:Firstly,the moment asymptotic stability analysis of a class of stochastic HIV models is performed.We obtain the differential equations’ necessary and sufficient conditions for the asymptotic stability of the first order moment.By using the Ito formula,we obtain the necessary and sufficient conditions for the asymptotic stability of the two order moment of the differential equations of the system.Secondly,under the assumption of the HIV system with Allee effect,by using the Ito formula,Lyapunov function,Borel-Cantelli inequality and martingale inequality,martingale theorem of large numbers to further prove the existence and uniqueness of positive solutions of stochastic HIV model and the extinction of the diseases’ sufficient condition.And we proved the existence and uniqueness of the global positive solution in a stochastic HIV epidemic model with mixed bilinear incidence and divided into five groups.And further proved almost sure exponentially converges’ sufficient condition and almost surely converges’ sufficient condition.All of this provides reference for the control of theepidemic.Finally,the highlight of this paper is the innovation of the block-pulse function for solving nonlinear stochastic dynamical systems.The block-pulse function is widely used to solve the numerical solution of the integral equation.Onthis basis,it is introduced into the stochastic differential equation.