How do relapses among recovering people affect the spread of drugs in the presence of media coverage
- 1epartment of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
Abstract
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 ℛ0 < 1.
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BibTeX
@article{hmood2026relapses,
title = {{How do relapses among recovering people affect the spread of drugs in the presence of media coverage}},
author = {Melad Jameel Hmood and Raid Kamel Naji},
journal = {Frontiers in Applied Mathematics and Statistics},
year = {2026},
month = oct,
doi = {10.3389/fams.2026.1976377},
url = {https://doi.org/10.3389/fams.2026.1976377},
note = {CC BY},
}
RIS
TY - JOUR
TI - How do relapses among recovering people affect the spread of drugs in the presence of media coverage
AU - Melad Jameel Hmood
AU - Raid Kamel Naji
PY - 2026
DA - 2026/10/26
JO - Frontiers in Applied Mathematics and Statistics
DO - 10.3389/fams.2026.1976377
UR - https://doi.org/10.3389/fams.2026.1976377
AB - 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 ℛ0 < 1.
SN - 2297-4687
ER -