Contextual Interventions for Controlling Alcohol Drinking

Abstract

The dynamics of an alcohol drinking population are subject to environment-specific control programs. The stochastic model is developed that includes populations of light, moderate, and heavy drinkers, interacting in two contrasting risk-level drinking environments. For colleges with serious drinking problems, the times to disappearance of serious drinkers show that environment-dependent control programs have lasting efficacy when they are implemented according to the risk level of the environments and not by simply focusing on heavy drinking.

Keywords:

• disappearance time
• prevention and interventions
• quasi-stationary state
• social environments
• social influences

ACKNOWLEDGMENTS

The authors would like to thank Dr. Carlos Castillo-Chavez for providing support for carrying out this research and Dr. Paul Gruenwald for assisting with obtaining some data and information on existing alcohol control programs. The authors would especially like to thank Dr. Noël Bonneuil and the anonymous reviewers for their helpful comments as well as Ms. Miriam Caraballo for her help on formatting and suggestions on editing this article. This work was partially supported by a 2008 Norman Hackerman Advanced Research Program grant, the National Science Foundation under Grant DMS-1020880, Mathematical and Theoretical Biology Institute (MTBI), and Statistical and Applied Mathematical Sciences Institute (SAMSI).

Notes

¹The average is taken over all individuals of the subpopulation of the environment (E ₁ or E ₂).

²It is taken over all the interventions existing in the particular environment.

³Equilibrium value is the value of a variable when the model system has stabilized. Equilibrium value is computed by simulating the system for sufficiently large time under the assumption that interventions are not being implemented in that population.

¹