Heterogeneity among susceptibles in epidemic models

When the infection rate associated with an epidemic appears to decline over time, one explanation is a constant level of infectiousness combined with heterogeneity among the susceptible population. In this paper we consider random effects models for such heterogeneity, particularly in discrete time. Maximum likelihood techniques are discussed as well as a more convenient approach based on martingale estimating equations. An application to data on a smallpox outbreak is considered.