Estimating the initial relative infection rate for a stochastic epidemic model.

Consider the problem of making inference about the initial relative infection rate of a stochastic epidemic model. A relatively complete analysis of infectious disease data is possible when it is assumed that the latent and infectious periods are non-random. Here two related martingale-based techniques are used to derive estimates and associated standard errors for the initial relative infection rate. The first technique requires complete information on the epidemic, the second only the total number of people who were infected and the population size. Explicit expressions for the estimates are obtained. The estimates of the parameter and its associated standard error are easily computed and compare well with results of other methods in an application to smallpox data. Asymptotic efficiency differences between the two martingale techniques are considered.