Modelling and inference for epidemic models featuring non-linear infection pressure.

We consider a Susceptible-Infective-Removed (SIR) stochastic epidemic model in which the infection rate is of the form βN⁻¹X(t)Y(t)(α). It is demonstrated that both the threshold behaviour of this model and the behaviour of the corresponding deterministic model differ markedly from the standard SIR model (i.e. α=1). Methods of statistical inference for this model are described, given outbreak data, and the extent to which all three model parameters can be estimated is considered.