Dynamic Modeling And Analysis Of HIV Infection Based On Experimental Phenomena

As the causative agent of AIDS,HIV impairs the immune system and continues to pose enormous global socio-economic and public health challenges.The course of HIV infection within a host is extremely complex and exhibits a variety of experimental phenomena.The reasonable explanation of experimental phenomena helps people to understand the pathogenesis of the disease,the dynamics of viral load and the key factors of experimental phenomena,which provide a reliable theoretical basis for the therapy program.This paper introduces the research questions for the different experimental phenomena,develops corresponding mathematical models,performs theoretical analysis by using the methods in virus dynamics,reveals the essential reasons for experimental phenomena,and gives some results that are difficult to obtain by experimental methods.The main research works of this dissertation are stated as follows:1.During the acute HIV infection,the plasma viral load decreases significantly in the absence of drug treatment.The reduction in viral load is closely related to CTL immune response and antibody immune response.The relationship between these immune responses and their effects on the dynamics of HIV infection are not fully understood.In this paper,a mathematical model with two immune responses is formulated to investigate the dynamics of HIV infection.In order to describe the virus infection process more realistically,the model incorporates two routes of infection and two intracellular delays.By constructing Lyapunov functionals,we show that the global dynamics of the model can be explicitly determined by five reproduction numbers.We also carry out the uncertainty and sensitivity analyses for five reproduction numbers.By analyzing the effect of immune parameter on dynamics and comparing four related HIV models,it is shown that there is competition between the two immune responses,and the immune response contributes to viral inhibition.2.Current antiretroviral therapy cannot eradicate the virus,and a low-level residual viremia persists in patients under suppressive treatment.How macrophages affect the viral load persistence at a low level and the dynamics of HIV infection remain unclear.In this paper,we develop an HIV model that includes the infection of CD4+ T cells and macrophages via cell-free virus infection and cell-to-cell viral transmission.We derive the basic reproduction number and obtain the local and global stability of the steady states.Sensitivity and viral dynamics simulations show that even when the infection of CD4+T cells is completely blocked by therapy,virus can still persist because of the infection of macrophages.Analysis of the sources of macrophage infection shows that cell-free virus infection leads to the majority of macrophage infection.3.In addition to the infection of macrophages,the low viral load persistence may also be related to cell-to-cell viral transmission.The number of virions transmitted between cells each time is determined by the activation status of infected cells.How the activation status of infected cells affects low viral load persistence and HIV dynamics under antiretroviral therapy remain unclear.In this paper,we develop a new mathematical model that structures the population of infected cells continuously according to their activation status.The basic reproduction number of the model is shown to determine the existence and stability of the equilibria.Numerical investigation shows that even when treatment can completely block cell-free virus infection,virus can still persist due to cell-to-cell transmission.Numerical simulations also give the sources of the latent reservoir.4.Multiple infection of target cells by HIV may lead to viral escape from host immune responses and drug resistance to antiretroviral therapy,bringing more challenges to the control of infection.Thus,it is very valuable to study the mechanisms underlying HIV multiple infection and their relative contributions.In this paper,we develop a general mathematical model that includes cell-to-cell transmission and sequential cell-free virus infection.Theoretical results show that the basic reproduction number can completely determine the global dynamics of the model.Fitting results show that multiple infection can be well explained only when the two modes of viral transmission are both included.Numerical simulation using the parameter estimates from data fitting shows that cell-tocell viral transmission is the main cause of cell's multiple infections.5.Drug resistance can hamper the success of antiviral therapy for virus infection,which is considered as an obstacle to viral elimination.Many mathematical models studying within-host drug resistance consider only two viral strains: wild-type and drugresistant strains.However,the level of drug resistance can be continuous.The effect of continuous resistance levels on the dynamics of HIV infection remains unclear.In this paper,we develop a within-host viral dynamic model that structures the virus population continuously on the basis of the level of drug resistance.We derive the basic reproduction number,which is shown to completely determine the global stability of the steady states.This model serves as a new continuous modeling framework to study the emergence and evolution of drug resistance during the therapy of virus infection.