We consider in this research an age-structured alcoholism model. The global behavior of the model is investigated. It is proved that the system has a threshold dynamics in terms of the basic reproduction number (BRN), where we obtained that alcohol-free equilibrium (AFE) is globally asymptotically stable (GAS) in the case R0 ≤ 1, but for R0 > 1 we found that the system persists and the nontrivial equilibrium (EE) is GAS. Furthermore, the effects of the susceptible drinkers rate and the repulse rate of the recovers to alcoholics are investigated, which allow us to provide a proper strategy for reducing the spread of alcohol use in the studied populations. The obtained mathematical results are tested numerically next to its biological relevance.

中文翻译：

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年龄结构酗酒模型的全局阈值动态

我们在这项研究中考虑了一个年龄结构的酗酒模型。研究了模型的全局行为。证明了该系统在基本再生数（BRN）方面具有阈值动力学，我们得到无酒精平衡（AFE）在这种情况下是全局渐近稳定（GAS）的R0 ≤ 1， 但对于R0 > 1我们发现系统持续存在并且非平凡平衡（EE）是GAS。此外，研究了易感饮酒者率和对酗酒者的排斥率的影响，这使我们能够提供适当的策略来减少所研究人群中酒精使用的传播。获得的数学结果在其生物学相关性旁边进行了数值测试。