Ma Shuang Hong, Huo Hai Feng
College of Electrical and Information Engineering, Lanzhou University of Technology, Lanzhou, 730050, P. R. China.
Institute of Applied Mathematics, Lanzhou University of Technology, Lanzhou, 730050, P. R.China.
Math Biosci Eng. 2019 Feb 27;16(3):1683-1708. doi: 10.3934/mbe.2019080.
A new multi-group alcoholism model with public health education and alcoholism age is considered. The basic reproduction number ₀ is defined and mathematical analyses show that dynamics of model are determined by the basic reproduction number. The alcohol-free equilibrium ₀ of the model is globally asymptotically stable if ₀≤1 while the alcohol-present equilibrium of the model exists uniquely and is globally asymptotically stable if R₀>1. The Lyapunov functionals for the globally asymptotically stable of the multi-group model are constructed by using the theory of non-negative matrices and a graph-theoretic approach. Meanwhile, the combined effects of the public health education and the alcoholism age on alcoholism dynamics are displayed. Our main results show that strengthening public health education and decreasing the age of the alcoholism are very helpful for the control of alcoholism.
考虑一种包含公共卫生教育和酗酒年龄的新型多群体酗酒模型。定义了基本再生数(R_0)，数学分析表明模型的动态由基本再生数决定。如果(R_0\leq1)，模型的无酒精平衡点(E_0)是全局渐近稳定的；而如果(R_0>1)，模型的有酒精平衡点(E^*)唯一存在且是全局渐近稳定的。利用非负矩阵理论和图论方法构造了多群体模型全局渐近稳定的李雅普诺夫泛函。同时，展示了公共卫生教育和酗酒年龄对酗酒动态的综合影响。我们的主要结果表明，加强公共卫生教育和降低酗酒年龄对控制酗酒非常有帮助。
