About this Journal Submit a Manuscript Table of Contents
Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 829386, 15 pages
http://dx.doi.org/10.1155/2012/829386
Research Article

Global Stability for a Binge Drinking Model with Two Stages

Department of Applied Mathematics, Lanzhou University of Technology, Gansu, Lanzhou 730050, China

Received 18 July 2012; Revised 6 September 2012; Accepted 4 October 2012

Academic Editor: Seenith Sivasundaram

Copyright © 2012 Hai-Feng Huo and Na-Na Song. 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

A more realistic two-stage model for binge drinking problem is introduced, where the youths with alcohol problems are divided into those who admit the problem and those who do not admit it. We also consider the direct transfer from the class of susceptible individuals towards the class of admitting drinkers. Mathematical analyses establish that the global dynamics of the model are determined by the basic reproduction number, . The alcohol-free equilibrium is globally asymptotically stable, and the alcohol problems are eliminated from the population if . A unique alcohol-present equilibrium is globally asymptotically stable if . Numerical simulations are also conducted in the analytic results.