Alfiniyah Cicik, Utami Tutik, Millah Nashrul, Gweryina Reuben Iortyer
Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya, 60115, Indonesia.
Department of Mathematics, Joseph Sarwuan Tarka University, Makurdi, PMB 2373, Nigeria.
MethodsX. 2025 Apr 14;14:103311. doi: 10.1016/j.mex.2025.103311. eCollection 2025 Jun.
Alcoholism affects individuals across all demographics and is a major global health challenge, contributing significantly to mortality rates. This study develops and analyzes a mathematical model of alcoholism, focusing on the dynamics of drinking behaviors within a population. The model identifies two equilibrium points: the non-endemic equilibrium and the endemic equilibrium, whose stability depends on the basic reproduction number . The non-endemic equilibrium is stable when , while the endemic equilibrium becomes stable when . Sensitivity analysis highlights the critical role of the contact rate between at-risk individuals and moderate drinkers, as well as the rate of alcohol cessation among moderate drinkers. The study incorporates control strategies, including educational campaigns and government policy measures, to reduce the spread of alcoholism. Numerical simulations demonstrate the effectiveness of a combined approach in significantly lowering alcoholism prevalence and its social and economic impacts. This study offers practical insights for designing evidence-based policies to address this issue. Some key features of the proposed method include:•Utilizing the next-generation matrix (NGM) approach to calculate .•Conducting equilibrium point analysis to examine the stability of the system.•Applying Pontryagin's maximum principle to determine optimal control policies.
酒精成瘾影响着所有人口统计学群体中的个体，是一项重大的全球健康挑战，对死亡率有显著影响。本研究建立并分析了一个酒精成瘾的数学模型，重点关注人群中饮酒行为的动态变化。该模型确定了两个平衡点：非流行平衡点和流行平衡点，其稳定性取决于基本再生数。当 时，非流行平衡点是稳定的，而当 时，流行平衡点变得稳定。敏感性分析突出了高危个体与适度饮酒者之间的接触率以及适度饮酒者戒酒率的关键作用。该研究纳入了控制策略，包括教育宣传活动和政府政策措施，以减少酒精成瘾的传播。数值模拟证明了综合方法在显著降低酒精成瘾患病率及其社会和经济影响方面的有效性。本研究为设计基于证据的政策来解决这一问题提供了实际见解。所提出方法的一些关键特征包括：
• 使用下一代矩阵（NGM）方法来计算 。
• 进行平衡点分析以检查系统的稳定性。
• 应用庞特里亚金极大值原理来确定最优控制策略。
