Concerns have spread across the globe on the emergence and introduction of infectious diseases. The application of mathematical models can be developed to estimate the size and speed of spread of an emerging epidemic, irrespective of the nature of the infectious agent or the size and spatial distribution of the affected population. Mathematical analysis can offer precision to complicated fields, such as biology. It has the potential to provide a powerful tool to demonstrate or assess the use or impact of a particular intervention before it is put into practice. These models aid in the development of policy options for containment and assist in the development of guidelines for effective population treatment programs. The chapter reviewed limitations of various mathematical models, the construction of cost-benefit models, and the application of simple deterministic models to study HIV pathogenesis, viral life and infected cell life expectancies, the rate of evolution of drug resistance, and the dynamics of the immune system when invaded by the virus. Tables and references