Large-sample analysis for a stochastic epidemic model and its parameter estimators

This paper considers the simplest stochastic model for the spread of an epidemic in a closed, homogeneously mixing population. Approximate methods are presented for calculating the probability distribution of the epidemic size (i.e. number of infected individuals). In fact, a functional central limit theorem and a large deviation principle for the epidemic size when the population increases are shown. These results enable us to both obtain a global approximation for the epidemic size and study asymptotic properties of other random variables depending on the complete history of the epidemic. As an application of our results, we derive two sequences of estimators for the contact rate and analyze their asymptotic behaviour.