Theory And Applications On The Dynamics Of Human Immunodeficiency Virus Infection And Therapy

Acquired immunodeficiency syndrome (AIDS) is one of the serious infectious diseases which threaten to the global human health. AIDS has become an important social and public health problem. Human immunodeficiency virus (HIV) mainly infects host’s CD4+T cells, causes gradual depletion of CD4+T cells counts and thus progressively compromises the host’s immune response to opportunistic infections. Drug combination treatments have become an important development direction for clinical anti-HIV infection treatment. They only control HIV producing in patient’s body, but cannot cure the HIV infection patients. Bone marrow transplantation has been an only way to cure HIV infection in so far.Clinical-based mathematical dynamic modeling has an important significance for the study of the (anti-) HIV infection (treatments). Reasonable (anti-) HIV infection (treatment) mathematical model can help to understand the mechanism and laws of virus infection, clearance and evolution, reveal some new features of HIV infection, evaluate new medical programs and make long term efficacy prediction. This thesis mainly studies the (anti-) HIV infection (treatment) dynamics mathematical modeling, stability analysis of infection-free equilibrium point and endemic infection equilibrium point, and numerical simulations based on clinical data. The main results and highlights of this thesis are listed as follows:(1) This thesis studies five HIV infection dynamics models proposed by Srivastava, Rong and Nowak et al. It has been pointed out that the basic reproductive numbers of the five models all depend upon the total number of CD4+T cells in vivo, which implies a paradox that individuals with more CD4+T cells will be more easily infected by HIV than individuals with less CD4+T cells. Using saturated infection rate formulates five modified HIV infection models. The basic reproductive numbers of the five modified models are independent of total number of CD4+T cells in vivo.(2) Based on the mechanism of HIV inducing the apoptosis of T cells, this thesis formulates a new death rate of CD4+T cells including HIV inducing the apoptosis of CD4+T cells, and uses this death rate when modifying the basic reproductive number of Nowak’s basic HIV infection model. When modifying the basic reproductive number of Nowak’s HIV infection model with immune response, this thesis also uses a constant produced rate of immune response. (3) This thesis sets up five group theorems. The five group theorems give the conditions that the infection-free equilibrium point is globally asymptotically stable (or locally stable) and the endemic infection equilibrium point is globally asymptotically stable (or locally stable) for the five modified HIV infection models, respectively.The theoretical results suggest the following.1) One HIV infection person with basic reproductive number less than one can recover automatically even if infected with a large amount of HIV; if an anti-HIV infection treatment makes a patient’s basic reproductive number be less than one, the patient will be cured eventually.2) One HIV infection person with basic reproductive number more than one will have endemic infection even if infected with only a few HIV; if an anti-HIV infection treatment cannot make a patient’s basic reproductive number be less than one, the patient’s HIV in vivo cannot be cleared up eventually.Based on the analysis above, this thesis proposes one postulate that most HIV infection individuals will clear up HIV in vivo automatically without any treatments. The fact has not been well recognized since AIDS has been discovered in1981.(4) This thesis uses five modified models to simulate clinical data.1) Based on the clinical data from HIV drug resistance database of Stanford University, using the first four modified models simulate the dynamics of several group patients’ anti-HIV infection treatment, explain the clinical data, and make long term efficacy prediction for these group patients. The prediction results show that only one group patients’ anti-HIV infection treatment was effect, and the other gourp patients’ anti-HIV infection treatment were all failed.2) This thesis gives a hypothesis about how the first cured HIV patient by bone marrow transplantation in the world (Berlin Patient) was cured:the C-C chemokine receptor type5(CCR5) Δ32/Δ32CD4+T cells, differentiate by bone marrow transplantation, enhanced cytotoxic T lymphocyte (CTL)’s ability of killing infected CD4+T cells which made Berlin Patient’s basic reproductive number be less than one, and thus HIV was cleared up eventually. Using the fifth modified model (with immune response) simulates the dynamics of Berlin Patient’s bone marrow transplantation to verify the hypothesis above.