Research On Two Kinds Of Stochastic HIV Models With Nonlinear Incidence Rate

HIV/AIDS is an incurable infectious disease caused by HIV,HIV will attack the immune cells of the human body,reducing the body s immunity,resulting in a variety of infections,which is a serious threat to human's health.According to statistical data[1-6],there have been many scholars have made great efforts for the treatment of HIV/AIDS,and got some progress,but research on HIV/AIDS is still a long-term and urgent arduous task.Through the transmission of HIV/AIDS,HIV/AIDS can be set up a description of a deterministic model,which studies its dynamical behaviors,such as the existence and uniqueness of the solution,the stability of the equilibrium point and other theornes,then obtain the main factors leading to the spread of HIV/AIDS.Because the real world is full of randomness and contingency,stochastic models with stochastic factors will be more realistic.In this paper,based on the influence of stochastic factors in the environment,two stochastic HIV models with nonlinear incidence rate are established by adding stochastic perturbation into the deterministic model,and the conditions of disease extinction and persistence in the system are studied.This paper is divided into four parts,the first two parts are introduction and preliminaries,the third part sets a stochastic HIV/AIDS model with nonlinear incidence rate,then studies the local asymptotic stability of the deterministic model at the equilibrium points,and the conditions of disease extinction in stochastic HIV/AIDS model when the white noise disturbance is large enough and the white noise disturbance is not strong enough,and when the threshold R0*>1 of the stochastic model,the persistence of the infected population will be in the mean sense.The fourth part sets the stochastic HIV model with nonlinear incidence rate,then studies the global asymptotic stability of the deterministic model at the equilibrium points,and when basic reproduction number R10 satisfies R10<1,the disease-free equilibrium point E10 is globally asymptotically stable.Furthermore,the susceptible always be persistence in the mean sense with probability 1 also be proved.Finally,according to the conditions of extinction and persistence of disease,in order to prove the correctness of the conclusions of the above two kinds of models,appropriate parameters are selected for numerical simulation.