This chapter introduces the mathematical background to the theory of epidemics. It presents a simple model for an epidemic, and discusses the restrictions of such models. The chapter provides the importance of contact patterns and immunity for the shape of an epidemic – or endemic –. The regular recurrence of epidemics and the similar shapes of consecutive epidemics of a disease have for a long time tempted people with a mathematical inclination to make some kind of model. Models of diseases that spread person-to-person rely on the concept of reproduction rate which is the average number of people infected by one case. A simple model for a childhood disease consists of several differential equations, and it exhibits a few of the details characteristic of such a disease. The major problem with all infectious disease models is that the contact pattern in the population is often unknown, is complicated to model and may often change as a result of the epidemic.