Alcoholism is a social phenomenon that affects all social classes and is a chronic disorder that causes the person to drink uncontrollably, which can bring a series of social problems. With this motivation, a delayed drinking model including five subclasses is proposed in this paper. By employing the method of characteristic eigenvalue and taking the temporary immunity delay for alcoholics under treatment as a bifurcation parameter, a threshold value of the time delay for the local stability of drinking-present equilibrium and the existence of Hopf bifurcation are found. Then the length of delay has been estimated to preserve stability using the Nyquist criterion. Moreover, optimal strategies to lower down the number of drinkers are proposed. Numerical simulations are presented to examine the correctness of the obtained results and the effects of some parameters on dynamics of the drinking model.

酗酒是一种社会现象，影响到所有社会阶层，是一种慢性疾病，会导致人无法控制地饮酒，从而带来一系列社会问题。在这种动机下，本文提出了包括五个子类的延迟饮酒模型。通过特征特征值法，以待治疗酒精中毒的暂时免疫延迟作为分叉参数，求出饮水平衡局部稳定的时间延迟阈值和Hopf分叉的存在。然后，使用奈奎斯特准则估计了延迟的长度以保持稳定性。此外，提出了减少饮酒者数量的最佳策略。