The role of media coverage in the dynamics of the spread of drug addiction

Abstract

A mathematical epidemiological model is developed to investigate the influences of media and assess its efficacy in reducing and declining drug use among new users, whether as a direct or indirect beneficial influence. A nonlinear differential equations system serves as the foundation for this model. Numerical simulations and mathematical analytic techniques are used to study the dynamic behavior of the suggested model. Under certain restrictions, the local and global stability of the equilibrium points is analytically asymptotically stable. Additionally, the model exhibits a forward bifurcation, which was examined using central manifold theory, demonstrating notable advancements in the fight against drug use in society resulting from media influence. To validate these analytical results, numerical simulations were carried out using MATLAB version R2021a code. The findings show which parameters should be improved and which should be targeted.