Stability Analysis Of HIV/AIDS Models With Media Coverage Impact

Acquired immune deficiency syndrome,also known as HIV/AIDS,is a high-ly harmful infectious disease caused by human immunodeficiency virus.At present,HIV/AIDS is still prevalent in the world,and the number of newly infected people with human immunodeficiency virus is more than one million.If it is not handled properly,it will seriously affect the development of economy and society.Thus,accord-ing to the transmission characteristics and epidemic laws of HIV/AIDS,it is of theoretical and practical significance to establish a dynamic model of the disease transmission to prevent and control the spread of HIV/AIDS.The infection rate function plays a key role in the study of infectious disease models.At the same time,various groups will be affected by random factors,so adding random disturbance to the epidemic model can make the model more practical.This paper considers the HIV/AIDS model with nonlinear incidence and second-order random disturbance.Firstly,this paper constructs a stochastic differential equation model by introducing square perturbation into the equations of the deterministic system;then,using random process theory,it is obtained that under some conditions,a stationary distribution exists,which means that the disease persists;then,it is proved that under some conditions the disease tends to zero with probability one,that is,the disease will die out.Finally,the conclusions are verified by numerical simulation.Considering the impact of environmental fluctuation on the population,a ran-dom HIV/AIDS model of vulnerable people affected by media reports is discussed.By constructing Lyapunov function and using the martingale theory,the condition of disease extinction is obtained.That is,if（?）₀<1 and white noise intensity is small,the disease is almost surely to die out exponentially.If（?）₀>1 and under some conditions,the disease is persistent.Finally,the conclusions are verified by numerical simulation.