Modeling the soft drug epidemic: Extinction, persistence and sensitivity analysis

Abstract

National Survey on Drug Use and Health indicates that Alcohol, Tobacco, and Marijuana are the most commonly abused drugs in the US. Poly-substance use of these drugs is increasingly more common. These substances are widespread among adolescents and young adults and are primarily labeled as soft drugs. Based on the principles of mathematical epidemiology, a model for the use of soft drug epidemic is formulated. An explicit formula for the basic reproduction number R0is derived. We established the dynamical behavior of the soft drug epidemic model using appropriate choices of Lyapunov functions. It is shown that the soft drug-free equilibrium is locally and globally asymptotically stable for R01. Sensitivity analysis with some numerical simulations are performed to illustrate the results.

Keywords

• Soft drugs
• Epidemic model
• Extinction
• Permanence
• Sensitivity analysis