Research On A Kind Of HIV Model Of Highly Active Anti-retroviral:Stability And Hopf Bifurcation

Viral dynamics is one of the effective ways for people to understand the mechanism of viral infection.The incidence and death rate showed an descending trend because of a highly active anti-retroviral therapy(HAART),which is a combination therapy that can keep the virus from replicating.In this thesis,based on the hottopic investigated background of HAART,the models with Logistic growth term and a general incidence rate were studied,respectively.The thesis first chapter has discussed research background,significance and listed some definitions and Lemmas used in the later.In biology,it is more realistic to assume that the population of the CD4+T cell has a logistic growth function.In the second chapter,the model with Logistic growth term has been investigated.Some dynamic behavior of the model have been analysed and discussed by using stability theory,persistence theory and Hopf branch theory.Furthermore,we are devoted to illustrating numerical simulation.The hypotheses can be satisfied by different types of the incidence rate including the mass action,the Holling type II function,the saturation incidence,Crowley-Martin incidence function.In the third chapter,at first,a HIV model with general Incidence rate is investigated.the basic regeneration number and the existence of equilibrium point are obtained.Furthermore,the condition of local asymptotic stability of equilibrium point is obtained by using Hurtwitz criterion.At last,the global asymptotic stability of equilibrium point is proved by constructing Lyapunov function and using LaSalle invariance principle.