Improved Estimation of the Initial Number of Susceptible Individuals in the General Stochastic Epidemic Model Using Penalized Likelihood

The initial size of a completely susceptible population in a group of individuals plays a key role in drawing inferences for epidemic models. However, this can be difficult to obtain in practice because, in any population, there might be individuals who may not transmit the disease during the epidemic. This short note describes how to improve the maximum likelihood estimators of the infection rate and the initial number of susceptible individuals and provides their approximate Hessian matrix for the general stochastic epidemic model by using the concept of the penalized likelihood function. The simulations of major epidemics show significant improvements in performance in averages and coverage ratios for the suggested estimator of the initial number in comparison to existing methods. We applied the proposed method to the Abakaliki smallpox data.