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Despite the recent development of methods dealing with partially observedepidemic dynamics (unobserved model coordinates, discrete and noisy outbreakdata), limitations remain in practice, mainly related to the quantity ofaugmented data and calibration of numerous tuning parameters. In particular, ascoordinates of dynamic epidemic models are coupled, the presence of unobservedcoordinates leads to a statistically difficult problem. The aim is to proposean easy-to-use and general inference method that is able to tackle theseissues. First, using the properties of epidemics in large populations, atwo-layer model is constructed. Via a diffusion-based approach, a Gaussianapproximation of the epidemic density-dependent Markovian jump process isobtained, representing the state model. The observational model, consisting ofnoisy observations of certain model coordinates, is approximated by Gaussiandistributions. Then, an inference method based on an approximate likelihoodusing Kalman filtering recursion is developed to estimate parameters of boththe state and observational models. The performance of estimators of key modelparameters is assessed on simulated data of SIR epidemic dynamics for differentscenarios with respect to the population size and the number of observations.This performance is compared with that obtained using the well-known maximumiterated filtering method. Finally, the inference method is applied to a realdata set on an influenza outbreak in a British boarding school in 1978.

Inference for partially observed epidemic dynamics guided by Kalman filtering techniques