Dynamics Of Within-host HIV Models With Two Transmission Modes

HIV can infect target cells via two routes:cell-free and cell-to-cell.These two transmission modes can facilitate viral production and the establishment of the latent HIV reservoir.This reservoir is considered as a major barrier to cure HIV infection.Although there is no cure for HIV infection,the current antiretroviral drugs are effective and can keep the viral load below the detection limit,largely preventing the spread of the infection.The purpose of this thesis is to study the stability of HIV infection dynamical models with the two transmission modes and to explore the optimal control strategy with antiviral therapy.Precisely,we propose and study two such models as follows.In Chapter 2,we develop an HIV infection model including these two infection routes and the age of infection.Firstly,we derive the expression of the basic repro-ductive number and show the existence,positivity and boundedness of solutions.We find that existence and local stability of steady states are completely determined by the basic reproduction number.Secondly,after obtaining the existence of a global compact attractor and uniform persistence of the system,we establish a threshold dynamics by the approach of Lyapunov functionals.When the basic reproduction number is less than one,the infection-free steady state is globally asymptotically stable.When the basic reproduction number is larger than one the infected steady state is globally asymptotically stable.Finally,we consider the optimal control problem and get necessary conditions that minimize the viral load and the cost of drug treatment.Moreover,numerical simulation are carried out for different drug treatment strategies.In Chapter 3,taking into about of mobility of virus particles and the clearance of CTL immune response to infected cells,we build a different HIV infection model with the two infection routes.Depending on the values of the basic reproduction number R₀and the basic CTL immune reproduction number R₁,the model can have at most three steady states.These three steady states are the infection-free steady state,which has no infection,the immune-free steady state,which doesn't have immune response,and the infected steady state,which has immune response,respectively.The locally asymptotically stable and the uniform persistence of system are proved.If R₀?1,the infection-free steady state is globally asymptotically stable.If R₁?1<R₀,the immune-free steady state is globally asymptotically stable.If R₁>1,then the infected steady state is globally asymptotically stable.These theoretical results are demonstrated with numerical simulations.