Mathematical Approaches to Infectious Disease Prediction and Control

Mathematics has long been an important tool for understanding and controlling the spread of infectious diseases. Here, we begin with an overview of compartmental models, the traditional approach to modeling infectious disease dynamics, and then introduce contact network epidemiology, a relatively new approach that applies bond percolation on random graphs to model the spread of infectious disease through heterogeneous populations. As we illustrate, these methods can be used to address public health challenges and have recently been coupled with powerful computational methods to optimize epidemic control strategies.