Mathematical model for the dynamics of alcohol-marijuana co-abuse

Abstract

A mathematical model for the dynamics of alcohol-marijuana coabuse is presented in this work. In the past years legalization of recreational marijuana in several states in the United States has added a new layer to alcohol addiction. Much research has been done for alcohol addiction or drug abuse independently, but few include the incidence of marijuana use for alcohol users. A compartmental epidemiological model is used, and results such as the existence and boundedness of solutions, the basic reproduction number using the next-generation method, the disease-free equilibrium, and an analytical expression for the endemic equilibrium are included. Numerical simulations with parameters obtained from data in the United States are performed for different compartments of the population as well as the reproduction number for the alcohol and marijuana sub-models. The model can be adapted for different regions worldwide using appropriate data. This work contributes to understanding the dynamics of the co-abuse of addictive substances. Even though alcohol and marijuana are both legal, they can be of great harm to the brain of the individual when combined, having tremendous consequences for society as a whole. Creating awareness of a public health concern with facts based on scientific research is the ultimate goal of this work.

Keywords

• Alcohol-marijuana
• co-abuse
• epidemics
• endemic equilibrium

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