Mathematical Modeling of Tobacco and Marijuana Coabuse and the Influence of Educational Campaigns

Cecilia Mbithe Wambua, Caroline Kanyiri and Hellen Waititu

Journal of Applied Mathematics, 2026, vol. 2026, 1-15

Abstract: Substance misuse is a serious threat to people's health and the socioeconomic stability of countries all over the world. Tobacco and marijuana are among the most abused drugs. The joint misuse of the two substances has made the drug problem in the community worse. In this study, a mathematical model was developed to explain the dynamics of the coabuse of marijuana and tobacco, as well as the impact of an educational campaign. In this research, the population is divided into seven compartments: the susceptible population (S), light smokers (L), heavy tobacco smokers (T), marijuana smokers (M), both tobacco and marijuana smokers (B), individuals undergoing rehabilitation (R), and the quitting population (Q). In addition, the study incorporated an educational campaign to determine its implications on those addicted to tobacco and marijuana use. In the study, the presence of equilibrium points, the endemic equilibrium, and the drug-free equilibrium of coabuse were analyzed. The next-generation matrix method was used to determine the basic reproduction number. The model was numerically simulated using Maple, which employs the Runge–Kutta fourth-order method for interpretation and qualitative analysis. From the numerical analysis of the coabuse model, the results showed that educational campaigns influence addicted individuals to go for treatment. This suggests that there is a need to intensify and improve the available educational campaigns to help reduce the menace in society.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:4942011

DOI: 10.1155/jama/4942011

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