Dynamic Analysis Of Stochastic HIV/AIDS Models With Nonlinear Incidence Rate

Acquired immune deficiency syndrome is the human body's immune deficien-cy caused by HIV infection.It can cause a series of opportunistic infections and death syndrome.At present,HIV/AIDS is still one of the most devastating dis-eases in the world,and it is a serious threat to human health.Establishing suitable mathematical models are helpful to analyze the dynamic behavior of diseases.They have theoretical and practical significance for the prevention and control of AIDS.In reality,population dynamics are inevitably affected by environmental noise.en-vironmental noise is more practical to consider this factor in the model.This paper mainly studies the dynamic behaviors of diseases under the influence of stochastic disturbance factors.For the stochastic HIV/AIDS model with bilinear incidence,the existence and uniqueness of its positive solution is first proved.Then,the paper studies the extinc-tion and persistence of the disease.When the white noise intensity is large enough,the disease will eventually disappear.When the intensity of white noise is small,if the threshold R₀^s<1 of the stochastic model,the disease will become extinct.If the threshold R₀^s>1 of the stochastic model,the disease will persist.Finally,numerical simulations are presented to illustrate our theoretical results.For the stochastic HIV/AIDS model with nonlinear incidence,the paper first finds the equilibrium and threshold of the deterministic model.Then it discusses threshold R₀^sdynamic behavior of stochastic model.If R₀^s>1,the distribution density of the model solution converges to a constant density in L¹.If the threshold R₀^s<1,the disease almost surely tends to extinction under the certain conditions.Finally,The correctness of the conclusion is verified by numerical simulation.