Dynamic Analysis Of HIV Virus Model Influenced By Random Noise

Epidemic dynamic analysis is an important part of mathematical models in biology,however the virus dynamics analysis is one of important infectious disease dynamics analysisthat has aroused people’s enough attention. Mainly on the basis of previous studies, thispaper was done some improvements for HIV model, and two types of HIV models have beenconstructed: one kind is an HIV model with saturated incidence, the other is of the impactof random noise model with saturated incidence. Using the theories of diferential equations,the dynamics properties of two kinds of models are analyzed.In chapter one, we introduces the historical background of this issue and the signif-cance of this research subject. And we analyze the present research in both domestic andinternational, and propose the structure of this article.In chapter two, an HIV model with the saturated incidence has been investigated. Byanalyzing the characteristic equations and using the method of Lyapunov function, we haddiscussed both the disease-free equilibrium E0and the endemic equilibrium E. By studying,we had obtained that when R0<1, the disease-free equilibrium is globally asymptoticallystable. When R0>1, the endemic equilibrium is locally asymptotically stable. Finally,numerical simulations are carried out to support our theoretical analysis.In chapter three, frstly HIV models with saturated incidence have been build whichhave the forms of diferent random noise. For the frst form, frst of all we prove the existenceand uniqueness of positive solutions for stochastic diferential equation, and then analyse theasymptotic behavior of the solution of the stochastic diferential equation. Then, the meanreverting process was studied, and under the certain conditions we obtain the expectationand variance. At last, we use the numerical simulation to verify the theoretical analysis. Forthe second form, using theories of the stochastic diferential equation, we prove that R0>1,the positive equilibrium point is stochastic stable. Finally, numerical simulations are givento illustrate the theoretical result.