Estimation in epidemics with incomplete observations

The construction of estimating equations by martingale methods is generalized to yield estimators with explicit expressions for the parameters of the birth-and-death and the general epidemic processes when only partial observations are available. (For the birth-and-death process the death process is observed but the number of births is observed only at the end and for the general epidemic process only the removal process is observed.) For large populations, the use of the martingale central limit theorem yields asymptotic confidence regions for the parameters. Explicit expressions are derived for estimators of the variances of the large sample distributions. The range of validity and usefulness of the new estimators is determined by simulation.