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The Scientific World Journal
Volume 2014, Article ID 241687, 6 pages
http://dx.doi.org/10.1155/2014/241687
Research Article

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

Department of Statistics, Yeungnam University, Gyeongsan, Gyeongbuk 712-749, Republic of Korea

Received 24 March 2014; Revised 26 August 2014; Accepted 27 August 2014; Published 11 September 2014

Academic Editor: Getachew Dagne

Copyright © 2014 Changhyuck Oh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.