How do relapses among recovering people affect the spread of drugs in the presence of media coverage

The spread of drugs continues to pose a significant threat to societies. Given the widespread reach of various media outlets and technological advancements, media-based awareness campaigns can contribute to curbing drug abuse and preventing relapse following recovery. This paper suggests and analyzes a mathematical model of drug addiction that incorporates the positive role of media in raising public awareness and addresses the issue of relapse after recovery. The study examines the properties of the solutions and the model's dynamics. Furthermore, it investigates solution characteristics by analyzing the local and global stability of all possible equilibrium points and discussing bifurcation behavior. Numerical simulations were also conducted to validate the analytical results and assess the impact of varying key parameters. It was noted that media awareness and relapse are inversely proportional in controlling the spread of drugs, as increasing media awareness or reducing relapse leads to controlling the spread of drugs and lessening the harm and prevalence of substance abuse in populations, while decreasing media awareness or increasing relapse leads to a lack of control and drug prevalence in society. It is obtained that the occurrence of backward bifurcation under relapse even when ℛ 0 < 1.