Mathematical Analysis of Substance Abuse and its Effect

Abstract

In this paper, a model for substance abuse was formulated. A compartmentalization approach was adopted to develop the model, and five nonlinear equations were developed based on the number of compartments. The model was analyzed qualitatively and quantitatively. The Invariant region, positivity, equilibrium points (substance-free and substance-present), basic reproduction number R0, the sensitivity analysis, and the model’s local and global asymptotic stability were obtained. Numerical simulations were conducted to see the changes in the population dynamics of different classes in the sub-population. The results authenticated that the recovery rate of moderate substance users and the recovery rate of rehabilitation/treatment of individuals are indications that they help reduce the number of substance abuse individuals. Also, the recruitment and contact rates impact the population of substance abuse.