Mathematical and statistical methods in epidemiology

Thesis

Epidemiology is underpinned by mathematical and statistical models which are used to answer key questions about the origin, spread, and control of diseases. With the rapidly increasing availability of data and computational resources, coupled with the vast number of deterministic and stochastic factors affecting the trajectory of epidemics, the complexity of these models continues to grow.

Many questions can be answered, at least in part, with these models by applying simple methods. For example, the variance of an epidemic under stochastic models can be estimated by running such a model many times. However, rigorous mathematical derivations allow these answers to be calculated more accurately, computed more efficiently, and, ultimately, understood in a deeper way.

This thesis seeks to provide mathematical insight into three key areas in epidemiology. First, the development of new methods for solving phylogenetic optimisation problems allows modern machine-learning and Bayesian techniques to be used to more accurately estimate the true evolutionary history of disease pathogens, as well as providing an explanation for the effectiveness of minimum evolution methods. Second, it considers the aleatoric uncertainty of epidemics, deriving explicit equations for the variance of an epidemic under a Crump-Mode-Jagers model. Finally, it considers the problem of optimal vaccination, deriving constraints and asymptotic limits on the optimal vaccination policy under a multi-group Susceptible-Infected-Recovered (SIR) model.

Authors: Penn, M

• DOI: 10.5287/ora-gog5xq147
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: phylogenetics; epidemiology; optimisation
• Subjects: Phylogeny; Epidemiology; Statistics