Modeling epidemics on a regular tree graph

We will first provide a brief introduction to models of disease transmission on so-called contact networks, which can be represented by various structures from the mathematical field of graph theory. These models allow for exploration of stochastic effects and incorporation of more biological detail than the classical compartment-based ordinary differential equation models, which usually assume both homogeneity in the population and uniform mixing. In particular, we use an agent-based modelling platform to compare theoretical predictions from mathematical epidemiology to results obtained from simulations of disease transmission on a regular tree graph. We also demonstrate how this graph reveals connections between network structure and the spread of infectious diseases. Specifically, we discuss results for how certain properties of the tree graph, such as network diameter and density, alter the duration of an outbreak.