  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 is typically only partially observed e.g.
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 (POMP) via iterated filtering. In the second part of
the chapter the performance of the method and associated practical difficulties
are illustrated on two examples. In the first example a simulated outbreak data
set consisting of the number of newly reported cases aggregated by week is
fitted to a POMP where the underlying disease transmission model is assumed to
be a simple Markovian SIR model. The second example illustrates possible model
extensions such as seasonal forcing and over-dispersion in both, the
transmission and observation model, which can be used, e.g., when analysing
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.
