| Mathematical modeling of epidemiological and immunological processes helps in generating insights into the dynamics of disease processes as well as in the design of intervention strategies. This research can take place at different biological scales: at the level of an individual or a population. We study models of the Human Immunodeficiency Virus (HIV) at both the population and cellular scales.;First we examine a model for the spread of the Acquired Immunodeficiency Syndrome (AIDS) in a purely heterosexual population. We derive a set of governing differential equations which we then analyze both numerically and analytically.;Secondly we examine a model for the invasion of HIV in the human immune system. We examine, through the use of mathematics, a simple model presented by Alan S. Perelson, and rigorously establish some of the model's behavior seen in simulations. Then we extend that model to include a more complete immune system representation and again examine the equations for structure and dynamics.;We show that quite simple mathematical models, incorporating only conventional hypotheses, are capable of explaining many of the disease's peculiar features observed at both the population and cellular levels. |
