Reconstructing susceptible and recruitment dynamics from measles epidemic data

Dynamical epidemic studies are often based on the reported number of cases. For various purposes it would be helpful to have information about the numbers of susceptibles, but these data are rarely available. We show that under general theoretical assumptions it is possible to reconstruct, up to linear scaling parameters, the dynamics of the susceptible class, as well as the rate of recruitment to the susceptible class, based only on case report data. We demonstrate that susceptible data reconstructed by our method improve the performance of forecasting models. Our estimate of susceptible class dynamics also can be used to estimate the age distribution of recruitment into the susceptible class, if the birth rate is known from independent data. Simulation experiments show that the reconstruction is robust to errors in the reporting scheme. This work was motivated by measles in large developed-world cities prior to immunization programs; our theoretical assumptions are empirically justified for measles but should also be applicable to some other diseases with permanent immunity.