Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 530472, 13 pages
http://dx.doi.org/10.1155/2012/530472
Research Article

Analysing Social Epidemics by Delayed Stochastic Models

Francisco-José Santonja1 and Leonid Shaikhet2

1Department of Statistics and Operational Research, University of Valencia, Dr. Moliner 50, 46100 Burjassot, Spain
2Department of Higher Mathematics, Donestsk State University of Management, 163a Chelyuskintsev Street, 83015 Donetsk, Ukraine

Received 8 May 2012; Revised 23 May 2012; Accepted 23 May 2012

Academic Editor: Seenith Sivasundaram

Copyright © 2012 Francisco-José Santonja and Leonid Shaikhet. 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

We investigate the dynamics of a delayed stochastic mathematical model to understand the evolution of the alcohol consumption in Spain. Sufficient condition for stability in probability of the equilibrium point of the dynamic model with aftereffect and stochastic perturbations is obtained via Kolmanovskii and Shaikhet general method of Lyapunov functionals construction. We conclude that alcohol consumption in Spain will be constant (with stability) in time with around 36.47% of nonconsumers, 62.94% of nonrisk consumers, and 0.59% of risk consumers. This approach allows us to emphasize the possibilities of the dynamical models in order to study human behaviour.