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Journal of Probability and Statistics
Volume 2017 (2017), Article ID 9064821, 6 pages
Research Article

Stochastic Models for the Infectivity Function in an Infinite Population of Susceptible Individuals

Department of Statistics, Universidad Nacional de Colombia, Bogotá, Colombia

Correspondence should be addressed to Viswanathan Arunachalam

Received 11 July 2016; Revised 19 December 2016; Accepted 25 December 2016; Published 11 January 2017

Academic Editor: Chin-Shang Li

Copyright © 2017 Viswanathan Arunachalam and Liliana Blanco. 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.


Two stochastic models to study the course of the transient behaviour of the total infectivity present in an infinite population of susceptible individuals are developed. The conditional intensity function of the contagion comprises two components: one is due to the external sources only and the other is the contribution of each of the infected persons which is nonstationary in nature. The statistical characteristics of the number of infected individuals at any time are explicitly obtained. Estimation of the model parameters is also indicated.