Estimating the basic reproductive number in the general epidemic model with an unknown initial number of susceptible individuals

Abstract

In any epidemic, there may exist an unidentified subpopulation which might be naturally immune or isolated and who will not be involved in the transmission of the disease. Estimation of key parameters, for example, the basic reproductive number, without accounting for this possibility would underestimate the severity of the epidemics. Here, we propose a procedure to estimate the basic reproductive number (R 0) in an epidemic model with an unknown initial number of susceptibles. The infection process is usually not completely observed, but is reconstructed by a kernel-smoothing method under a counting process framework. Simulation is used to evaluate the performance of the estimators for major epidemics. We illustrate the procedure using the Abakaliki smallpox data. © 2008 Board of the Foundation of the Scandinavian Journal of Statistics.