Dynamical Analysis Of HIV Viral Infection Dynamic Models With Two Types Of Viruses

In this paper,three viral dynamic models with two types of viruses are proposed.We analyzed the dynamic behaviors and discussed the biological meanings of these models.There are five chapters.In the first chapter,the background of HIV virus,immunity system and basic content of related mathematical models are introduced.In the second chapter,an HIV viral dynamical model which includes two types of viruses and the non-linear force of infection is studied.The two types of viruses are wild and resistant. we get threshold values:Rs and Rr which are the basic reproductive numbers of wild virus and resistant virus respectively.The global asymptotical stabilities are obtained by the means of Lyapunov functions.It is shown that the disease-free equilibrium is globally asymptotically stable and the disease eventually disappears if Rs<1and Rr<1.Further,if Rs>1and Rs/Rr> dRs+βs/d+βs,the equilibrium incorporating only wild virus is globally asymptotically stable.IfRr>1and Rr/Rs>dRr+βr/d+βr,the equilibrium incorporating only resistant virus is globally asymptotically stable.If Rr/Rs<dRr+βr/d+βr and Rs/Rr<dRs+βs/d+βs,the equilibrium incorporating two types of viruses is globally asymptotically stable.In the third chapter,we consider the influence of mutation.We study an HIV viral dynami-cal model incorporating two types of viruses which are wild and resistant.Between the extinction and uniform persistence of the disease,we get threshold values:Rs and Rr which are the basic reproductive numbers of wild virus and resistant virus respectively.This Rs is little1est than the second chapter’s.It is shown that the disease-free equilibrium is globally asymptotically stable and the disease eventually disappears if Rs<1and Rr<1.Further,if Rs<1<Rr,wild virus is extinct and resistant virus is uniformly persistent.Moreover, if Rs>Rr and Rs>1,two types of viruses are uniformly persistent.In the fourth chapter, an HIV viral dynamical model which includes two types of viruses and two types of CTL immune responsees is studied.we get threshold values:Rs and Rr which are the basic reproductive numbers of wild virus and resistant virus respectively.This Rs is the same as the third chapter’s.We discuss the conditions of the steady states.It is shown that the disease-free equilibrium is globally asymptotically stable and the disease eventually disappears if Rs<1and Rr<1.Further,if Rs<1<Rr,wild virus is extinct and resistant virus is uniformly persistent.Moreover,if Rs>Rr and Rs>1+βrprμr/dcrmr,two types of viruses are uniformly persistent.In the last chapter, the contents of this paper are summarized.The develop aspects of the dynamic behaviors and the biological meanings of these models are discussed.