| Summary: | Simulating from and making inference for stochastic epidemic models are key strategies for understanding and controlling the spread of infectious diseases. Current methods for modelling infection rate functions are exclusively parametric. This often involves making strict assumptions about the way the disease spreads and choices which may lack any biological or epidemiological justification. To remove the need for making such assumptions, we develop a Bayesian nonparametric framework which allows us to learn how the disease spreads directly from the data.
In this thesis, we consider individual-level models where the infection rate between each pair of individuals depends on characteristics of their relationship. We begin by considering infectious diseases where the infection rate between any two individuals can be modelled by a function of a single characteristic, for example, the distance between them. We model this function nonparametrically by assigning a Gaussian Process prior distribution to it and then develop an efficient data augmentation Markov Chain Monte Carlo algorithm to infer this function, alongside the prior distribution hyperparameters and the times individuals were infected.
We develop this methodology further, first for multi-type outbreaks and then for outbreaks where the infection rate function depends on more than one characteristic. For multi-type outbreaks, where the infection rate between two individuals not only depends on the characteristics, but also the type of individual being infected, we develop a Multi-Output Gaussian Process method. This method allows us to compare how susceptible each type of individual is to infection. We extend our Gaussian Process method into several dimensions for modelling outbreaks where the infection rate between individuals can be modelled as a function of multiple continuous variables.
Finally, we demonstrate our results on two data sets, giving new insights and analysis. The first is an outbreak of Avian Influenza in the Netherlands in 2003, where over 30 million birds were culled. Using the posterior predictive distribution of our nonparametric model, we simulate outbreaks of Avian Influenza to assess various control measures. Alongside our nonparametric analysis, we are able to investigate which of the pre-emptively culled farms were infected. The second is an outbreak of Foot and Mouth Disease in Cumbria, UK. We are able to analyse the relationship between the infection rate of farms with different kind of livestock, showing that farms with both cattle and sheep were much more susceptible to the virus than farms with a single type of livestock.
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