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.