| HIV/AIDS is a highly harmful infectious disease,which is also known as ac-quired immune deficiency syndrome.The widespread epidemic of the disease has seriously affected the economic and social development of the country.Thus,estab-lishing a dynamic model of HIV/AIDS has theoretical and practical significance in preventing and controlling the spread of HIV/AIDS.In the transmission of HIV/AIDS,infection rate plays a key role,but in real life,it is often influenced by random factors.Firstly,considering the infection rate coefficient is affected by white noise,this paper establishes a stochastic HIV/AIDS model in which infected people are affected by intervention strategies and proves the existence and uniqueness of stochastic model's solutions;secondly,the paper obtains the conditions of disease extinction,this is,if R0s<1 and white noise intensity is small,or white noise intensity is large enough,the disease will be extinct with probability one;then,using Markov semigroups theory,to prove that when R0s>1 and under some conditions,the disease is persistent;finally,the conclusions are verified by numerical simulation.Considering that natural mortality is affected by random factors,a class of stochastic HIV/AIDS model with ratio-dependent infection rate function is estab-lished.Firstly,the boundedness and permanence of the solution of the stochastic model are proved;secondly,the paper analyzes the extinction of the disease,that is,if the threshold of stochastic model R0s<1,the disease is almost surely to die out exponentially,and the model has a unique disease-free stationary distribution;then,by using correlational theory of ergodicity,the paper obtains the conditions that the solution of stochastic model converges to the stationary distribution of endemic disease,that is,if R0s>1 and some conditions are satisfied,the stochastic model has a unique stationary distribution of endemic disease;finally,the theoretical results are verified by numerical simulation. |
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