Journal of Applied Mathematics

The Role of Optimal Intervention Strategies on Controlling Excessive Alcohol Drinking and Its Adverse Health Effects

Steady Mushayabasa

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Abstract

We propose and analyze a mathematical model for alcohol drinking problem. The transmission process is modeled as a social “contact” process between “heavy” alcohol drinkers and “light” alcohol drinkers within an unchanging shared drinking environment. The basic reproductive number of the model is computed and the stability of the model steady states is investigated. Further, the model is fitted to data on alcohol drinking for Cape Town and Gauteng, South Africa. In addition, the basic model is extended to incorporate three time dependent intervention strategies. The control functions represent the efforts and policies aimed at weakening the intensity of social interactions between light and heavy drinkers and increase the fraction of treated individuals who permanently quit alcohol drinking. Optimal control results suggest that effective control of high-risk alcohol drinking can be achieved if more resources and efforts are devoted on weakening the intensity of social interactions between light and heavy drinkers.

Article information

Source
J. Appl. Math., Volume 2015 (2015), Article ID 238784, 11 pages.

Dates
First available in Project Euclid: 17 August 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1439816414

Digital Object Identifier
doi:10.1155/2015/238784

Mathematical Reviews number (MathSciNet)
MR3370963

Citation

Mushayabasa, Steady. The Role of Optimal Intervention Strategies on Controlling Excessive Alcohol Drinking and Its Adverse Health Effects. J. Appl. Math. 2015 (2015), Article ID 238784, 11 pages. doi:10.1155/2015/238784. https://projecteuclid.org/euclid.jam/1439816414


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