Research On HIV Infection Models With Different Treatment Strategies

Drug therapy plays an important role in the prevention and control of the spread of infectious diseases.In this paper,we establish a dynamic model of HIV virus transmission which is based on thymus and proliferation through mitosis and drug therapy for T cells.By using the theory of differential equation to analyze the dynamics of HIV virus,we analyze the factors that affect the transmission of HIV virus,and provide the theoretical basis for the prevention and control of HIV virus.This paper will analyze it from the following aspects.First of all,a dynamic model of HIV virus transmission was established considering the effect of protease inhibitor?PIs?on T cells which are stimulated by two ways of thymus and mitosis.It is found that when the basic reproduction number R₀ is less than 1,there only exists the disease-free equilibrium which is locally asymptotically stable.When the basic reproduction number R₀ is greater than 1,there is a unique positive equilibrium.We give the condition of global asymptotical stable.By numerical simulation we verified the stability of equilibrium of the system and the effect of PIs on T cells.The results show that increasing the efficiency of PIs can control the spread of HIV virus.Secondly,we consider the dynamic model of HIV virus transmission and T cells are stimulated by two ways of thymus and mitosis with antiretroviral therapy?ART?.Through the analysis,we get the basic reproduction number R₀ and the critical threshold of drug therapy,and the relationship between them.When the basic reproduction number R₀ is less than 1,there is only the disease-free equilibrium which is globally asymptotically stable under certain conditions.When the basic reproduction number R₀ is greater than 1,there exists a unique positive equilibrium which is global asymptotically stable under certain conditions.We verified the stability of the equilibrium point of the system and the change of T cells and the virus treated with antiretroviral therapy by numerical simulation.The results show that the higher the effective rate of ART treatment,the higher the concentration of healthy T cells,and the lower the concentration of infected T cells and virus,which is beneficial to the control of HIV virus.Finally,we consider the dynamic model of HIV virus transmission the effect of immune reaction and antiretroviral therapy?ART?.According to the analysis,we can get the basic reproduction number R₀,and there always exists the disease free equilibrium.In addition,when R₀< 1,the disease-free equilibrium is global asymptotically stable under certain conditions;when R₀> 1,there exists a unique positive equilibrium which is locally asymptotically stable under certain conditions.Through numerical simulation we verified the stability of the equilibrium and found that the higher the probability that CTL cells were infected by immune cells,the probability of CD4+T infection was reduced.It improves the immunity of patients with HIV and effectively controls the spread of the disease.