Consistent and fast inference in compartmental models of epidemics using Poisson Approximate Likelihoods

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The quantification and characterisation of infectious disease dynamics are essential for informing official decision makers in their response to emerging epidemics; they are also crucial in understanding previous outbreaks to better prepare for the future. The most popular paradigm for modelling the spread of a disease through a population is that of compartmental models. The likelihood for such models is inaccessible in all but the simplest cases, therefore, in order to perform inference, one needs to make approximations. Over the past few decades, computational advances have led to the development of many sophisticated and expensive simulation algorithms for inference on stochastic compartmental models. The aims of this project are to propose a class of computationally cheap and simple alternatives to these methods which are justified by rigorous consistency theory and demonstrated to be practically useful on real world data examples.