Eur. Phys. J. Plus (2020) 135: 54
https://doi.org/10.1140/epjp/s13360-019-00064-5

Regular Article

Modeling the effect of information transmission on the drug dynamic

Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran

^* e-mail: r_memarbashi@semnan.ac.ir

Received: 26 April 2019
Accepted: 19 October 2019
Published online: 13 January 2020

Abstract

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.