ABSTRACT
In this chapter models of infectious disease transmission are introduced. The models contain randomness and specify the dependency of the infection events, which is a key characteristic of infectious disease data analysis. In the model the population is partitioned into susceptible (S), infectious (I), and recovered individuals (R), and considered is a continuous time version, which is well approximated by a deterministic set of differential equations, and a discrete generation type model known as the Reed-Frost or chain binomial model. Some key properties of the models are presented. A description is provided showing how these models can be extended by introducing birth and death to the host population, by adding more compartments to acknowledge a more complex infection cycle, and by introducing structure to the host population. Then an illustration is provided on how these models can be used to infer the values of key parameters from infectious disease data, and how this knowledge can be used to inform policy measures to control infectious diseases.
