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Probabilistic models for infectious disease dynamics are useful forunderstanding the mechanism underlying the spread of infection. When thelikelihood function for these models is expensive to evaluate, traditionallikelihood-based inference may be computationally intractable. Furthermore,traditional inference may lead to poor parameter estimates and the fitted modelmay not capture important biological characteristics of the observed data. Wepropose a novel approach for resolving these issues that is inspired by recentwork in emulation and calibration for complex computer models. Our motivatingexample is the gravity time series susceptible-infected-recovered (TSIR) model.Our approach focuses on the characteristics of the process that are ofscientific interest. We find a Gaussian process approximation to the gravitymodel using key summary statistics obtained from model simulations. Wedemonstrate via simulated examples that the new approach is computationallyexpedient, provides accurate parameter inference, and results in a good modelfit. We apply our method to analyze measles outbreaks in England and Wales intwo periods, the pre-vaccination period from 1944-1965 and the vaccinationperiod from 1966-1994. Based on our results, we are able to obtain importantscientific insights about the transmission of measles. In general, our methodis applicable to problems where traditional likelihood-based inference iscomputationally intractable or produces a poor model fit. It is also analternative to approximate Bayesian computation (ABC) when simulations from themodel are expensive.

Emulating a gravity model to infer the spatiotemporal dynamics of an infectious disease