The SIR model and the Foundations of Public Health

Abstract

We introduce and analyze a basic transmission model for a directly transmitted infectious disease. The model consists of a system of three coupled non-linear ordinary differential equations which does not possess an explicit formula solution. However, simple tools from calculus allow us to extract a great deal of information about the solutions. Along the way we illustrate how this simple model helps to lay a theoretical foundation for public health interventions and how several cornerstones of public health required such a model to illuminate.