  In this paper we first introduce the general stochastic epidemic model for
the spread of infectious diseases. Then we give methods for inferring model
parameters such as the basic reproduction number $R_0$ and vaccination coverage
$v_c$ assuming different types of data from an outbreak such as final outbreak
details and temporal data or observations from an ongoing outbreak. Both
individual heterogeneities and heterogeneous mixing are discussed. We also
provide an overview of statistical methods to perform parameter estimation for
stochastic epidemic models. In the last section we describe the problem of
early outbreak detection in infectious disease surveillance and statistical
models used for this purpose.
