Estimation for Discrete Time Branching Processes with Application to Epidemics

Abstract

Certain estimators for the mean of the offspring distribution of a Galton-Watson process are considered. The asymptotic behavior of each of these estimators is studied when the true underlying model is in fact a multitype branching process or a branching process with a random environment. It is revealed which of the estimators remain consistent indicators of whether or not the process is subcritical, under these alternative underlying models. It is then indicated how this robustness result might influence the choice of an estimator by considering the problem of estimating the level of immunity required in a community in order to prevent major epidemics. The application is illustrated using data from a human smallpox outbreak in Sao Paulo, Brazil.