Contact network epidemiology: Bond percolation applied to infectious disease prediction and control

Mathematics has long been an important tool in infectious disease epidemiology. I will provide a brief overview of compartmental models, the dominant framework for modeling disease transmission, and then contact network epidemiology, a more powerful approach that applies bond percolation on random graphs to model the spread of infectious disease through heterogeneous populations. I will derive important epidemiological quantities using this approach and provide examples of its application to issues of public health.