Using statistics and mathematical modelling to understand infectious disease outbreaks: COVID-19 as an example
Christopher E. Overton, Helena B. Stage, Shazaad Ahmad, Jacob Curran-Sebastian, Paul Dark, Rajenki Das, Elizabeth Fearon, Timothy Felton, Martyn Fyles, Nick Gent, Ian Hall, Thomas House, Hugo Lewkowicz, Xiaoxi Pang, Lorenzo Pellis, Robert Sawko, Andrew Ustianowski, Bindu Vekaria, Luke Webb
Abstract
During an infectious disease outbreak, biases in the data and complexities of the underlying dynamics pose significant challenges in mathematically modelling the outbreak and designing policy. Motivated by the ongoing response to COVID-19, we provide a toolkit of statistical and mathematical models beyond the simple SIR-type differential equation models for analysing the early stages of an outbreak and assessing interventions. In particular, we focus on parameter estimation in the presence of known biases in the data, and the effect of non-pharmaceutical interventions in enclosed subpopulations, such as households and care homes. We illustrate these methods by applying them to the COVID-19 pandemic.