A Study on some Aspects of Mathematical Modeling of HIV/AIDS Epidemics

Abstract

The thesis entitled “A Study On Some Aspects of Mathematical Modeling of IIIV/AIDS Epidemics” is being presented for the partial fulfillment of the requirements for the degree of Master of Philosophy in Applied Mathematics, American World University, California, USA. This thesis work has been Partitioned into five chapters. The lsl is an introductory chapter which consists of the general idea of mathematical modeling and its principal concepts. It has been discussed about conceptual framework, classifications, characteristics, methods, applications, and limitations o f mathematical modeling which are needed in the subsequent chapters. In the 2nd chapter, we have discussed the history of mathematical modeling of AIDS progression: limitations, expectations and future directions. In the 3rd chapter, we have discussed the effects of the Mathematical Modeling of Epidemics. We discussed about the concept of mass action, without removals and with removals of epidemic models and its solutions, results and discussion with sufficient figures. In the 4lh chapter, we have studied mathematical model for major mode of I IIV/AIDS transmission. We discussed here the routes of HIV/AIDS transmission i.e., mother to child transmission, heterosexual mode of transmission, the homosexuals population compartment and their mathematical models and solutions. In the 5'h chapter, we have studied the mathematical models for HIV and antiretroviral therapy. We discussed the effects of antiretroviral therapy in purpose of prevention. Mathematical formulation of the model equations on existence and stability of equilibrium states and results are presented. Analysis of implicitly and explicitly of antiretroviral drug in the HIV models with elaborate discussion with sufficient figures. The results and discussions as well as all necessary figures are depicted in every chapter