ABSTRACT
Dynamic epidemic models have proven valuable for public health decision makers as they provide useful insights into the understanding and prevention of infectious diseases. However, inference for these types of models can be difficult because the disease spread typically is only partially observed, for example, in form of reported incidences in given time periods. This chapter discusses how to perform likelihood-based inference for partially observed Markov epidemic models when it is relatively easy to generate samples from the Markov transmission model while the likelihood function is intractable. The first part of the chapter reviews the theoretical background of inference for partially observed Markov processes by iterated filtering. In the second part of the chapter the performance of the method and associated practical difficulties are illustrated in two examples. In the first example, a simulated outbreak dataset consisting of the number of newly reported cases aggregated by week is fitted to a partially observed Markov processes where the underlying disease transmission model is assumed to be a simple Markovian susceptible-infective-removed model. The second example illustrates possible model extensions such as seasonal forcing and over-dispersion in the transmission and observation model, which can be used, for example, when analyzing routinely collected rotavirus surveillance data. Both examples are implemented using the R-package pomp (King et al., 2016) and the code is made available online.
