Asymptotic Properties of Some Estimators for the Infection Rate in the General Stochastic Epidemic Model

This is the authors' abstract. We don't add key points for this paper.

SUMMARY Some estimators for the infection rate in the general stochastic epidemic model are presented. The first estimator follows the approach of maximum likelihood. However, this approach requires us to observe most if not all of the epidemic process. As an alternative, an estimator which uses less detailed data is derived from a suitable martingale. Both estimators are shown to be consistent only when a major outbreak of disease is observed. Minor out-breaks do not provide enough information on the infection rate. The asymptotic distributions of these estimators are also obtained. Asymptotic normality holds only for a major outbreak. Finally, the estimators are applied to data on a smallpox outbreak.