Abstract
A more realistic two‐stage model for binge drinking problem is introduced, where the youths with alcohol problems are divided into those who admit the problem and those who do not admit it. We also consider the direct transfer from the class of susceptible individuals towards the class of admitting drinkers. Mathematical analyses establish that the global dynamics of the model are determined by the basic reproduction number, R0. The alcohol‐free equilibrium is globally asymptotically stable, and the alcohol problems are eliminated from the population if R0 < 1. A unique alcohol‐present equilibrium is globally asymptotically stable if R0 > 1. Numerical simulations are also conducted in the analytic results.
Highlights
Young people’s binge drinking problem is a major concern to public health
We consider the direct transfer from the class of susceptible individuals towards the class of admitting drinkers; we study the global dynamics of the model
We assume that β > γ due to the fact that they are more likely to be unaware of their condition. α is the rate at which represents those with the alcohol problems admitting to have these problems and transferring from class A1 to A2, π is that fraction of A2 who go into treatment, η is that fraction of R who relapse into admitting drinkers we adopt a linear relapse term rather than peer pressure since we argue that the relapse is primarily due to the person, p is the probability of a new drinker to admit having the problem
Summary
Young people’s binge drinking problem is a major concern to public health. Recently, US surveys indicate that approximately 90% of college students have consumed alcohol at least once 1 , and more than 40% of college students have engaged in binge drinking 2, 3. Mulone and Straughan investigate a model for binge drinking taking into account admitting and nonadmitting drinkers. A susceptible individual acquires alcohol problems through the direct contact with the admitting drinker or the nonadmitting drinker. We consider the direct transfer from the class of susceptible individuals towards the class of admitting drinkers; we study the global dynamics of the model. The reason to introduce this new direct transfer is that about one-third of the American population admit to drinking problems, 17.8% of the population admit to the binge drinking problem 16. This fact cannot be neglected in the binge drinking model.
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