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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 954069, 18 pages
Research Article

Optimal Control Strategies in an Alcoholism Model

1College of Electrical and Information Engineering, Lanzhou University of Technology, Lanzhou, Gansu 730050, China
2Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China
3School of Electrical and Information Engineering, Anhui Industrial University, Maanshan, Anhui 243032, China

Received 10 December 2013; Accepted 9 January 2014; Published 2 March 2014

Academic Editor: Weiming Wang

Copyright © 2014 Xun-Yang Wang et al. 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.


This paper presents a deterministic SATQ-type mathematical model (including susceptible, alcoholism, treating, and quitting compartments) for the spread of alcoholism with two control strategies to gain insights into this increasingly concerned about health and social phenomenon. Some properties of the solutions to the model including positivity, existence and stability are analyzed. The optimal control strategies are derived by proposing an objective functional and using Pontryagin’s Maximum Principle. Numerical simulations are also conducted in the analytic results.