Most theoretical results in mathematical epidemiology come from the analysis of models where parameters are assumed constant. This assumption is also often made when studying outbreaks in medium-sized populations (e.g. classrooms, schools, hospitals, care homes, prisons, etc.), as it facilitates analytical tractability. Constant-parameter models can be very useful as caricature of reality and to inform decisions, and they might even be appropriate in very small populations (e.g. households), but they lead to a bimodal final size distribution, where outbreaks either die out infecting only a few cases or take off and infect a large fraction of the population. This is rarely what happens in reality, where intermediate final sizes are generally observed, primarily because of a reactive response to a detected outbreak.

This project will focus on the development of analytical or semi-analytical theory for a relatively simple models that include a reactive response. This can be used for planning purposes, to generate scenarios based on the time and strength of the response or to explore the trade-off between how early and how strongly a control policy should be implemented, or to assess retrospectively the effectiveness of the control policies implemented. The latter application, in particular, is an estimation problem, and hence will hugely benefit from the building of any theoretical insight or the development of any fast, analytical result. Crucially, it is also a key question that stakeholder responsible for the outbreak response, in particular in vulnerable settings like care homes or prison, will want an answer to.

The research will be carried on under the supervision of prof. Lorenzo Pellis and within the Mathematical Epidemiology group in the Department of Mathematics at the University of Manchester. The group has long-standing collaborations with the UKHSA teams managing public health and social care in prisons, care homes and other vulnerable settings, which will help shaping the research directions and directly benefit from the research results.