Deterministic Epidemic Models

Abstract

We begin by looking at a sequence of three increasingly complicated mathematical models for the development of an epidemic of a contagious disease. The first model is so simple as to be almost entirely unrealistic; however, its shortcomings suggest how it can be improved. The second model, which results from modifying the first model, is considerably better, but still leads to unacceptable results. The third model is likewise an outgrowth of the previous models. Although still imperfect, the third model manifests a property which was not built into the formulation explicitly, but which is in fact observable in an actual epidemic of a contagious disease.