Memarbashi Reza, Sorouri Elahe
Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran.
Eur Phys J Plus. 2020;135(1):54. doi: 10.1140/epjp/s13360-019-00064-5. Epub 2020 Jan 13.
In each community, there is a lot of information about the disadvantages and risks of drug use and its negative effects on health, work, honor, and other living funds of people. A group of individuals, who can be called responsive individuals, will be safe from the risk of drug abuse, by receiving and understanding such information. In this paper, by proposing mathematical models, we investigate the effect of the distribution of this kind of information on the transformation of susceptible individuals into responsive individuals as well as their effect in preventing the occurrence of substance abuse epidemics. In these models, we take into account the fact that the spirit of responsiveness of these individuals can be decayed with time, and these people can become susceptible people, and eventually to addicts. We analyze the dynamical properties of the models, such as local and global stability of equilibrium points and the occurrence of backward bifurcation. The results of this study show that the higher the rate of conversion of susceptible individuals to those responsive, the prevention of drug epidemy is easier.
在每个社区，都有大量关于吸毒的弊端和风险及其对人们健康、工作、名誉和其他生活方面的负面影响的信息。有一群人，可以称之为有反应能力的人，通过接收和理解这些信息，将免受药物滥用的风险。在本文中，通过提出数学模型，我们研究了这类信息的传播对易感个体向有反应能力个体转变的影响，以及它们在预防药物滥用流行方面的作用。在这些模型中，我们考虑到这些人的反应精神可能会随着时间而衰退，这些人可能会变回易感人群，并最终成为瘾君子。我们分析了模型的动力学性质，如平衡点的局部和全局稳定性以及反向分岔的出现。这项研究的结果表明，易感个体向有反应能力个体的转化率越高，预防药物流行就越容易。
