Dynamics Analysis Of Several HIV Infections Models With Impulse Treatment

The dissertation is divided into three parts,which consider the effects of immunotherapy,drug therapy and combination therapy on HIV dynamics respectively.We have had a more comprehensive understanding of the development of HIV through qualitative analysis and numeral simulation of viral dynamics,help to analyze the causes and key factors of HIV epidemic,and then sought the optimal treatment regimen for prevention and treatment of AIDS,which laid a theoretical foundation for clinical practice.Part ?:Based on the immune mechanism of interleukin-2(IL-2),we study the dynamic behavior of a class of HIV infection model with pulsed immunotherapy.Firstly,the non-negative and uniform boundedness of the solutions of the pulse immunotherapy model are analyzed by using the impulsive differential equation theory.Secondly,using the Floquet multiplier theory and the comparison theorem,we obtain the threshold condition which the local and global asymptotic stability of the infection-free periodic solution as well as uniformly persistence of virus.The correctness of the theoretical results is verified by numerical simulation.Part ?:Considering the antiviral effect of fusion enzyme inhibitor drugs(T-20),a class of HIV infection model with periodic drug therapy was studied.Using the qualitative theory of differential equation,the non-negative,existence and uniform boundedness of solutions of periodic drug therapy model are discussed.Qualitative analysis shows that the disease-free equilibrium state is globally asymptotically stable when R0(t)?1,whereas the virus persists.In addition,the critical drug dosage Dc.is defined,and the effective treatment strategy(D',?)for virus control is given.The threshold for dosage and dosing intervals were determined to ensure that the disease-free equilibrium remains stable.Moreover,the study found that intermittent therapy may be a failed treatment strategy,and the adherence of AIDS patients is the key to the success of antiviral therapy.Part ?:Considering the drug-drug interactions among IL-2,CD4+T cell and T-20,We develop a mathematical model that describes the virus-immune interaction and the effect on it of pulsed mixed therapy.By using the difference equation theory and Floquet multiplier theory,the stability condition for the infection-free periodic solution are provided with different frequencies of T-20 and CD4+T cell applications as well as IL-2.In addition,in order to study how to enhance the immune response and reduce the number of viral populations,we analyze many antiviral treatment regimens whether to perform IL-2,T-20 and CD4+T cell therapy.The study found that the use of IL-2 at high concentrations and high frequencies can both enhance the immune response and effectively control the virus.The periodic input of high concentrations of IL-2 and CD4+T cell resulted in small fluctuations in CD4+T cell counts and IL-2 concentrations,respectively,which reflect the immune mechanism of IL-2 and CD4+T cell interactions.Although mixed therapy can not eradicate the virus,the frequent use of IL-2 mixed treatment has less toxic side effects,can enhance the immune response and reduce the number of virus populations,laying a theoretical foundation for clinical trials.