# The Mathematics of Epidemiology

## Why you need to understand the math in order to understand how pathogens spread.

I’ve run across many people who discuss topics of epidemiology and public health, and yet have little to no understanding of the underlying mathematics that are required to model and understand how a pathogen spreads through a population.

Dynamical systems and differential equations, graph theory, and probability theory/stochastic processes, are at the heart of epidemiology. I would argue that the mathematical background is actually more important than the biological one.

The biology determines the basic parameters that are fed into the model, but the model itself, as well as the analysis of the model, is all about the math. In fact, we can use the exact same types of models, with just different parameters, to study the flow of information across a social network. The only thing that changes is the parameters and which model to use.

# Dynamical Systems and Differential Equations

Difference and differential equations are the basics required to understand even the simplest epidemiological model: the SIR — susceptible, infected, recovered — model. This model is a compartmental model, and results in the basic difference/differential…