  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.
