International Journal of Stochastic Analysis
Volume 2012 (2012), Article ID 598701, 32 pages
Research Article

Stochastic Methodology for the Study of an Epidemic Decay Phase, Based on a Branching Model

1Université Paris-Est, LAMA (UMR 8050), UPEMLV, UPEC, CNRS, 94010 Créteil, France
2INRA, MIA (UR 341), 78352 Jouy-en-Josas, France

Received 16 July 2012; Revised 10 October 2012; Accepted 10 October 2012

Academic Editor: Charles J. Mode

Copyright © 2012 Sophie Pénisson and Christine Jacob. 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.


We present a stochastic methodology to study the decay phase of an epidemic. It is based on a general stochastic epidemic process with memory, suitable to model the spread in a large open population with births of any rare transmissible disease with a random incubation period and a Reed-Frost type infection. This model, which belongs to the class of multitype branching processes in discrete time, enables us to predict the incidences of cases and to derive the probability distributions of the extinction time and of the future epidemic size. We also study the epidemic evolution in the worst-case scenario of a very late extinction time, making use of the Q-process. We provide in addition an estimator of the key parameter of the epidemic model quantifying the infection and finally illustrate this methodology with the study of the Bovine Spongiform Encephalopathy epidemic in Great Britain after the 1988 feed ban law.