Mathematical modeling and simulation of the progression of AIDS

Acquired Immunodeficiency Syndrome (AIDS) caused by Human Immunodeficiency Virus (HIV) is a pernicious disease acknowledged as a world health problem. One of the major issues in the study of AIDS is understanding the manifestation and the progression of the disease following the transmission of HIV. Unfortunately, the present state of biological knowledge does not yet give us a reliable means of evaluating these phenomena. A simulation approach is, therefore, extremely useful in predicting the various phases of the deteriorating physiological status of the patient. In the present study we have focused on the development of a mathematical model of the immune response to HIV and subsequently the dynamics of AIDS progression. The model is based on a set of ordinary differential equations solved using numerical analysis techniques. The model predicts the response of the T4 helper cells, cytotoxic and natural killer cells, macrophages and monocytes, and antibodies to the infection. Three cases are presented in this thesis. Each case has a different initial concentration of the virus. The rate of depletion of the immune cells is directly proportional to the increase in the initial concentration of the virus. These model-based investigations show that the theoretical results generated by the model are in close agreement with real life clinical observations of patients. A hypothetical detoxification unit is proposed for the treatment of AIDS. It is believed that this detox unit may not be able to cure the patient, but would at least increase the patient\u27s life. Simulation results of AIDS progression using this detox machine are plotted in this thesis. The detox unit is in the experimental stage of blood separation. The experimental procedures and results obtained from the detox machine up to this day are also presented in the following chapters. Further research in this field is in progress