Statistical inference for a multitype epidemic model

Abstract

A continuous-time model which allows for k types of susceptible individuals is constructed to study the spread of an infectious disease. Estimation of parameters is considered for the purpose in determining the mechanism of spread and in assessing the potential of a major epidemic. The inference procedure makes use of martingale estimating equations and explicit expressions for the estimates are obtained. Some of the estimators do not require complete observation of the epidemic. Only information at the end of the epidemic is needed. Asymptotic properties of the estimators and efficiencies among the estimators are determined. Simulation studies were done to assess the performance of the proposed estimators. The inference procedures were applied to epidemics of respiratory disease on the Island of Tristan de Cunha in the South Atlantic.