Understanding the spread of infections in populations is crucial for predicting their behavior and counteracting epidemics. However, empirical observations across several outbreaks are usually hard to obtain and real world experiments are not viable. Therefore, mathematical models of epidemics are of central importance for studying the behavior of infections. Not only they allow for simulations, but also give rise to rigorous results about the impact of different parameters of an infection process.
Driven by an improved understanding of properties of real world networks, models which allow for structured populations became more popular within recent decades. To this end, a population is modeled by an undirected graph. Vertices of the graph represent individuals (people, computer in a network, ...) which, depending on the model in question, can have different states, such as susceptible, infected or recovered (immune). Further, edges in the graph serve as potential contacts between individuals, along which the infection can spread from an infected vertex to a susceptible neighbor.