The Studies Of HIV-1Virus Dynamic Models With Time Delays

By using mathematical modeling methods, Human Immunodeficiency Virus (HIV) dynamic models are investigated, which can reveal the variation rules of the scalar dis-tribution of the HIV-1virus particles and different types of host cells within the body during the process of the dynamic changes, depict the influence of each factor on the above-mentioned rules during the invasion of HIV-1virus particles in the body and the virus infection in the host cells. Moreover, the mechanism of HIV-1infection, the esti-mation of viral load, the conditions of virus survival and complete clearance are studied. Meanwhile, two constant delays are incorporated into the model, which describe (i) the time needed for infected cells to produce virions after viral entry and (ii) the time need-ed for the adaptive immune response to emerge to control viral replication. Therefore, it is an interesting question for us to study the effects of dynamic processes of the hys-teresis phenomena for HIV-1infection. This dissertation focuses on the global dynamic behaviors of some delayed HIV-1dynamic models with immune response and saturat-ed infection rate、delayed HIV-1virus dynamic models with multiple target cells and non-autonomous HIV-1virus infection dynamic models with time delays.Firstly, we study some delayed HIV-1dynamic models with immune response and saturated infection rate. By constructing Lyapunov functional and combining the LaSalle invariant principle, we prove that the global dynamic behavior of the system is complete-ly determined by the basic reproductive number and the immune reproductive number. Moreover, we find that the introduction of immune response can increase the counts of CD4-T-cells whereas reduce viral load, and the extension of time delays can effective-ly decrease the basic reproductive number and immune response reproductive number of system, thus reduce viral load and inhibit the proliferation of the virus.Secondly, we focus on investigating delayed HIV-1virus dynamic models with mul-tiple target cells. Utilizing the uniform persistence of dynamic system, the uniform persis-tence and the existence of positive equilibrium of the system are obtained. Then, by con-structing Lyapunov functional and combining LaSalle invariant principle, the global dy-namic behavior of the system is proved. Finally, the numerical simulation results on a de-layed HIV-1virus dynamic model with two target cells (CD4+T-cells and macrophages) illustrate our mathematical findings. In addition, when the delay increases, we find that the viral load contribution values of infected CD4-T-cells decrease, and the viral load contribution values of infected macrophages increase during the advanced stage of HIV infection.Thirdly, we analyze a non-autonomous HIV-1virus dynamic model with time de-lays. According to the basic theory of delay differential equation, we established the sufficient conditions of persistence and extinction utilizing explicit expression of system parameters. Using the vibration theory, we obtained the accurate estimations of the upper and lower bounds of the viral load. By the time-varying characteristics of drug treat-ment, we find that rational use of protease inhibitors and reverse transcriptase inhibitors can control viral replication and reduce viral load. Through the numerical simulations, parameters sensitivity testing on the critical condition of the uniform persistence of the system is obtained. The results also generalize the corresponding conclusions in existing autonomous HIV-1virus dynamic system.Finally, we introduce multiple stages of infection into the above model, and discuss the effects of time-varying environment and multistage infection on the dynamic behavior of the system, viral load and the counts of uninfected cells. Accurate estimates of viral load are established by using the upper and lower bounds of the time-varying coefficient of system. And the global dynamic behaviors of system which contains multi-stage infection are obtained. Furthermore, parameters sensitivity analysis on the critical condition of the uniform persistence of the system is obtained through numerical simulation. The results show that when the system parameters remain unchanged and the infection stage increases, the viral load of a non-autonomous delayed HIV-1viral infection model for infected cells with multi-infected-stages is relatively low.