Approximate Bayesian computation for a spatial susceptible-exposed-infectious-removed model

Abstract

In this mini-dissertation we utilize population mobility data and COVID-19 case data in a variety of formats, from a variety of sources, in order to formulate a model for the spatial spread of COVID-19. The study region for this mini-dissertation is the Western Cape province of South Africa. Appropriate spatial structures are formulated using both standard and novel approaches, and the effect of these different conceptualisations of spatial association are illustrated, compared and discussed.

The spatial spread of COVID-19 is modelled using a susceptible-exposed-infectious-removed (SEIR) model that describes the progression of the disease. The model is stochastic in nature in order to incorporate the inherent uncertainty present in pandemic parameters. The stochastic nature of the model allows for greater inferential capabilities than deterministic models. Pandemic characteristics such as the spatial autocorrelation of COVID-19 cases and the reproductive number of the disease are determined and discussed.

Model fitting and inference are achieved through the use of approximate Bayesian computation (ABC) techniques for likelihood-free inference. This computational framework extends naturally to stochastic pandemic models, since the potentially complex disease system results in computationally infeasible likelihood expressions. The use of artificial neural networks for the purpose of improving the computational efficiency of this computational framework is evaluated and discussed.