FRACTIONAL-ORDER MODEL OF THE DRUG USER TRANSMISSION

Drug abuse poses significant challenges to public health and socio-economic stability worldwide. Narcotics, which are psychotropic compounds, are typically used for treating specific medical conditions. Currently, many individuals abuse drugs outside of the function of treatment. This misuse leads to central nervous system disorders, resulting in significant mental and behavioral health issues. In this article, we discuss a fractional-order mathematical model for the transmission of drug users with fractional-order α∈ (0,1]. We employ fractional-order differential equations using the Caputo derivative approach to model the transmission dynamics. We analyze the local stability of drug-free and endemic equilibrium points and calculate the basic reproduction number (ℛ₀). Our analysis indicates that the drug-free equilibrium is locally asymptotically stable when ℛ₀ < 1, while the endemic equilibrium is stable when ℛ₀ > 1. We implement a numerical scheme to simulate the fractional-order model, illustrating the theoretical findings.