This project is motivated by the 2014 Ebola epidemic in West Africa. It investigates a sequence of mathematical models which can be used to predict the course of an epidemic.
This outbreak of Ebola Virus Disease was eleven times larger than all previous outbreaks of Ebola combined. As of 26th May 2016, there had been 28 652 suspected, probable and confirmed cases of Ebola Virus Disease and 11 325 deaths from the 2014 West African Ebola epidemic. Most of these occurred in the poverty-stricken countries of Guinea, Liberia and Sierra Leone. Lesser outbreaks occurred in the nearby African nations of Mali, Nigeria and Senegal. Only eight cases occurred outside Africa and of these cases, there was only a single fatality.
In this thesis, we examine a number of models that describe the progress of an epidemic through a community. Our focus is on compartment models, starting with the SIR (susceptible, infectious, recovered) model and progressing through a sequence of more complex models: SEIR (susceptible, exposed, infectious, recovered), SIRD (susceptible, infectious, recovered, dead) and SIRUD (susceptible, infectious, recovered, unburied dead and buried dead). In each model, a member of the population can be a member of one and only one compartment at any given time. These models are expressed mathematically as a system of ordinary differential equations which must be solved numerically.
In this project, it is only in the final model (SIRUD) that we consider the effect of infection from dead bodies. For Ebola virus disease, traditional funerals, where the still-infectious body is washed and touched by loved ones, act as `super-spreader events'. Therefore, understanding how dead but still infectious bodies change the system is important to understand the epidemic course of a disease like Ebola.
The increasing complexity of the models demonstrate how additional information can improve a prediction of an epidemic's progress, however, improving predictive quality must be weighed against the risk of overfitting. In the case of Ebola, the sheer volume of data from may offset the disadvantage of adding additional compartments and parameters. More complex models have been published for this epidemic than have been considered in this thesis.