An inference procedure for a simple epidemic model: a martingale approach

摘要

This paper studies various estimators the infection rate of the simple stochastic epidemic model using the theory of counting processes, martingales, and stochastic integrals. A class of estimators for the infection rate have been obtained which includes the maximum likelihood estimator. Explicit expressions are given for these estimators which involve only simple computation. In the case of incomplete observation of the epidemic, estimators are available by choosing an appropriate weight function. Asymptotic results are given. Asymptotic efficiencies among these estimators are considered.