This paper proposes the SISRS epidemic model to represent alcohol addiction among people. The spreading of alcohol addiction is controlled by creating awareness among the people and also by treating them to overcome it. Multiplex network is used to study the dynamics of addiction. Alcoholism spreads over the physical contact layer and follows the SISRS process whereas human awareness spreads over the virtual contact layer and follows the UAU process. Based on the Microscopic Markov Chain Approach competing dynamics of spreading of alcohol addiction and human awareness diffusion are studied. Necessary conditions for the existence of an alcohol-free population are found. An optimal control problem using a suitable cost index is formulated to reduce the alcohol addicts and the optimal control strategy using Pontryagin’s Minimum Principle is determined. Numerical results are developed to find the effect of various parameters and to analyze the effects of different control strategies. The results obtained from this model are closer to the data collected in the National Survey of Drug Use and Health (NSDUH) from 2002 to 2018.

中文翻译：

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通过多重网络的意识对酒精中毒的最佳控制

本文提出了 SISRS 流行模型来表示人们的酒精成瘾。酒精成瘾的蔓延是通过提高人们的意识和治疗他们克服它来控制的。多重网络用于研究成瘾的动态。酒精中毒在物理接触层上传播并遵循 SISRS 过程，而人类意识在虚拟接触层上传播并遵循 UAU 过程。基于微观马尔可夫链方法研究了酒精成瘾传播和人类意识扩散的竞争动态。发现了无酒精人群存在的必要条件。制定了一个使用合适的成本指数的最优控制问题，以减少酒精成瘾者，并确定了使用庞特里亚金最小原理的最优控制策略。开发了数值结果以发现各种参数的影响并分析不同控制策略的影响。从该模型获得的结果更接近于 2002 年至 2018 年全国药物使用与健康调查 (NSDUH) 中收集的数据。