Stochastic Stability Of Several Kinds Of Virus Models

In recent decades,the threat of hepatitis B virus(HBV)to the safety of human life is increasing.Therefore,in order to reduce the harm of infectious diseases to people and effectively control the prevalence of diseases,more and more scholars try to establish mathematical models to explore the transmission mechanism of hepatitis B virus.Because the interference of random factors generally exists in the transmission process of hepatitis B virus,the establishment and analysis of stochastic HBV models is more conducive to the prevention and control of infectious diseases.On the one hand,considering the proven role of exosomes and the inevitable randomization within-host,we establish a HBV model with cell-to-cell transmission and CTL immune response.It is proved that the basic reproduction number R0 can determine whether the disease is epidemic or not.Under certain assumptions,if R0?1,the solution of the random HBV model always fluctuates around the infection-free equilibrium of the corresponding ordinary differential equation(ODE)model,which indicates that the HBV will eventually disappear almost surely;if R0>1,under extra conditions,the solution of the random HBV model fluctuates around the positive equilibrium of the corresponding ODE model,which reveals that the stochastic persistence of the HBV with probability one.One of the most interesting findings is that the fluctuation amplitude of the random HBV model around each equilibrium of the corresponding ODE model is positively related to the intensity of the white noise,and the larger the noise intensity is,the more skewed the distribution of the solution of the random HBV model is.On the other hand,assuming that the infection rate is affected by white noise,we establish a stochastic HBV model with drug therapy and cellular immunity.The asymptotic behavior of global positive solution of stochastic HBV model near the disease-free equilibrium and positive equilibrium of the corresponding deterministic HBV model is studied.The results of numerical simulation show that the effect of inhibiting virus production is more significant than blocking new infection.But the combination of two treatment methods is the best way to reduce HBV infection and reduce the concentration of free virus.