A note on the estimation of the initial number of susceptible individuals in the general epidemic model

Traditional inference for epidemic models depends on knowledge of the initial number of susceptible individuals. However, this may be difficult to obtain in practice. In this short note we show that it is possible to use data from a major epidemic to estimate the number of individuals initially susceptible to a disease and an approximate asymptotic variance is derived. The results are confirmed in simulations of major epidemics. An application to a data set on smallpox is given.