Drinking as an Epidemic-A Simple Mathematical Model with Recovery and Relapse

This chapter discusses a simple mathematical model of drinking lapse. Problem drinking is modeled as an acquired state - the result of frequent or intense interactions among individuals in three drinking states within a specified drinking environment. The goal of the model is to identify mechanisms that facilitate or limit the conversion of a population of nondrinkers to one of drinkers within prespecified environments. The process of quantification helps to understand the role of social forces on the time evolution of drinking. The dynamics of the model support two distinct states. The nature of these distinct outcomes depends in general on the size of the initial proportion of drinkers, the overall average residence time in the drinking environment, and the intensity of the interactions between problem drinkers and the rest of the residents. Numerical simulations are used to illustrate the model results on drinking dynamics. It is found that the most general model can support two permanent prevalent states when treatment only has short-term effect and relapse rates are high.