A Randomized HIV Model With Two Types Of Infected People

AIDS,also known as acquired immunodeficiency syndrome,is a great risk of infectious diseases caused by HIV virus(HIV).HIV virus can attack the body's immune system,which makes the human body lose immune function,thus easily infecting various diseases and causing a higher fatality rate.Many medical re-searchers around the world have made great efforts to find ways to treat AIDS,but so far there has been no effective way to cure AIDS.As far as China is concerned,AIDS epidemic situation is not optimistic,the epi-demic has been rising trend.Therefore,the study of AIDS is a long and arduous task,and it is urgent.Through the transmission of AIDS,AIDS can set up a description of a deterministic model,study dynamic behavior of the system such as the existence and uniqueness of the solution,the stability of equilibrium theory,so as to find out the main factors leading to the AIDS epidemic and control the AIDS epidemic.But the real life is full of randomness,and the model established by stochastic differential equation can reflect the actual situation more accurately.This paper is based on the theory of stochastic differential equation,according to the impact of AIDS related knowledge propaganda and education and other factors,the uncertainty of infectious disease model with random disturbance parameters,random HIV model with two types of infection,and to study the negative results of the global existence and uniqueness of non system,progressive and stability and the stability of the disease-free equilibrium.This paper is divided into three parts,the first two parts are introduction and preliminaries,the third part studies the stochastic HIV model with two kinds of infection.First,the global existence and uniqueness of the nonnegative solution of the stochastic HIV model are proved,and then the V function is defined to prove the solution is globally asymptotically stable.Getting the basic reproduction number R,when R<1,using the Ito formula to prove the system with probability 1 to the equilibrium state,which indicates that with the passage of time,ultimately dying.Then,the stability of the system in the disease-free equilibrium is discussed,and the almost sure exponential stability is obtained.Then the numerical simulation of the model is carried out.The result is consistent with the result of theorem 3.