Dynamical Analysis Of HIV Infection Models With CTL Immune Response

Acquired Immune Deficiency Syndrome(AIDS)is a chronic infectious disease caused by HIV,has become a major public health problem.The process of HIV infection in a host is very complex.On the one hand,being infected with HIV leads to a decrease in the number of CD4~+T lymphocytes in the body and an increase in viral load,and impairs the immune system.On the other hand,cytotoxic T lymphocytes(CTLs)can cause lysis or apoptosis to the target cells and a reduction of viral load during the acute infection phase without drug therapy.Therefore,to investigate HIV infection models with CTL immune response is beneficial to reveal the infection mechanism of HIV and provide theoretical basis for the formulation of prevention and treatment programs.This paper mainly investigates the dynamics of HIV infection models with CTL immune response.In the first chapter,the background and significance of HIV infection,the current research situation and the main content of this paper are briefly introduced.In the second chapter,an HIV infection model with intracellular delay,saturated CTL immune response and immune impairment is developed.Firstly,the positivity and bound-edness of solutions of the model are proved.By calculations,the immunity-inactivated and immunity-activated reproduction ratios are derived.By analyzing the distribution of the roots of corresponding characteristic equations,the local stabilities of feasible equilibria are addressed.With the help of suitable Lyapunov functionals and La Salle’s invariance principle,the global asymptotical stability of each equilibria is analyzed.Furthermore,by using Latin Hypercube Sample and Partial Rank Correlation Coefficient,sensitivity analysis is carried out to illustrate the correlations between parameter values and reproduction ratios.Considering the activation of non-activated CTL precursor cells(CTLp)into CTL effec-tor cells(CTLe),which can specifically kill target cells,in the third chapter,an HIV infection model with CTLp and CTLe is established.The effects of drug-sensitive and drug-resistant strains,cell-to-cell and virus-to-cell transmission on HIV infection are also considered.The basic reproduction ratios for each strain are derived,and two thresholds are defined,and the conditions for existence of feasible equilibria are discussed.By Routh-Hurwitz Criterion,the stability of feasible equilibria is studied.Selecting the death rate of infected cells as a bifurcation parameter,its effect on the stability of two immunity-activated equilibria are analyzed.The critical value of the bifurcation parameter is calculated,at this time,the system undergoes Hopf bifurcation.More information about the limit cycles,such as the amplitude,phase and stability can be found by using normal form theory.In the forth chapter,the research content of this paper is summarized.In this paper,two kinds of dynamical model for HIV infection with CTL immune response are analyzed,the stabilities of equilibria are discussed,and the deficiencies in theoretical derivation and further research directions are pointed out.