Modeling Binge Drinking

Abstract

We develop a two-stage (four component) model for youths with serious drinking problems and their treatment. The youths with alcohol problems are split into two classes, namely those who admit to having a problem and those who do not. It is shown that the model possesses two steady states, one where people have no alcohol problems and one where there is an endemic state involving those with an alcohol problem. The stability of these states is analyzed and a threshold established such that each state will be stable depending on whether the incidence rate is above or below the threshold. The model is analyzed in the context of actual data.

Modelling alcohol problems: total recovery

“…The three subpopulations are similar to the classes defined in the work of Sanchez et al [36] (also see Benedict [3]) and Mulone and Straughan [30], however neither of these models allow for total recovery. Sanchez et al [36] found that the basic reproduction number alone is not always the key factor in controlling drinking in the population.…”

“…Following the method in Mulone and Straughan [30], we now introduce the variables s(t) = S(t)/N , a(t) = A(t)/N and r(t) = R(t)/N , which enables us to rewrite system (2.1)…”

“…This is achieved by allowing γ = 0, resulting in the model proposed by Mulone and Straughan [30]. We focus on how γ = 0 affects the basic reproduction number and the endemic equilibrium solution.…”

“…Behaviours which can result in adverse health effects have been represented, such as drinking [36,3,26,28,37,30], smoking [38], drug use [44,29], obesity [18,15] and eating disorders [14]. Even though the models for each social problem may appear mathematically similar at the onset, there are fundamental differences which must be catered for.…”

“…Sanchez et al [36] found that the basic reproduction number alone is not always the key factor in controlling drinking in the population. Mulone and Straughan [30] extended their model by splitting binge drinkers into those who admit that they have a problem and those that do not admit. Using data for the north east of England, they conclude that binge drinking is sustainable in the population.…”