Mathematical and Statistical Methods in Epidemiology

The highly successful COVID-19 vaccination program has, according to Public Health England, saved over 100 000 lives in the England alone. One contributing factor to this success has been the vaccination schedule, with older people and those with underlying conditions being vaccinated first, as has been shown in a number of recent papers.

Motivated by the clear importance of vaccination scheduling, this DPhil project seeks to create a mathematical framework for the optimal scheduling of vaccinations during an epidemic. This will make use of a variety of dynamical models for disease transmission in order to provide a novel examination of a number of factors that could influence the schedule, such as household size and previous exposure to the disease. In order to do this, it will be necessary to combine the classical SIR-type compartmental models (where a population is split into a small number of groups, which allow averaged quantities to be used in place of individual infection statuses), applicable when considering large populations, with more recent network models (where each person and their contacts are considered individually), which will give insight into the dynamics on an individual scale.

Another novel aspect of the project will be the development of a combined immunity-testing and vaccination strategy, where at least some groups of people are tested before being vaccinated. When vaccinating in a population that has already had significant exposure to a disease, particularly one that often causes undetected asymptomatic infections, such testing could help to significantly improve the effectiveness of vaccine distribution, particularly if supplies of vaccine are significantly restricted.

In order to approximate the optimal scheduling, a novel algorithm will need to be developed, as the problem will have a complicated, non-convex structure. Moreover, the large number of population groups will mean that any algorithm will need to be very efficient, as computation of the success of any strategy will be time-consuming. The final algorithm will draw on many existing approaches in the literature, such as greedy algorithms (which aim for short-term gains), and genetic algorithms (which combine good strategies in order to try to improve them). This algorithm will be turned into a computer program so that simulations can be carried out to illustrate its effectiveness and the overall results.

As the COVID-19 vaccination program will be in a very different phase once this project has been completed, the principal application will be to inform vaccination policies for future pandemics. Because of this, it will consider a number of scenarios in which the vaccination program is started (such as during the peak of a wave or during a strict lockdown) alongside a range of different assumptions about a Disease X and the effectiveness of the vaccine.

Thus, it will be applicable to a wide-range of future vaccination campaigns and will help those planning it to maximise their effectiveness.

This project falls within the mathematical sciences research area, as defined on EPSRC website .