Mathematical Analysis of the Concomitance of Illicit Drug Use and Banditry in a Population

Abstract One of the majors global health and social problem facing the world today is the use of illicit drug and the act banditry. The two problems have resulted into lost of precious lives, properties and even a devastating effects on the economy of some countries where such acts were been practiced. Of interest in this work is to study the global stability of illicit drug use spread dynamics with banditry compartment using a dynamical system theory approach. Illicit drug use and banditry reproduction number was evaluated analytically, which measures the potential spread of the illicit drug use and banditry in the population. The system exhibits supercritical bifurcation property, telling us that local stability of an illicit drug and banditry-present equilibrium exist and it is unique. In addition, the illicit drug and banditry-free and illicit drug and banditry-present equilibria were shown to be global asymptotically stable, this was achieved by construction of suitable Lyapunov functions. Sensitivity analysis was carried out to know the impact of each parameter on the dynamical spread of illicit drug use and banditry in a population. Numerical simulations were used to validate the obtained quantitative results, and examine the effects of some key parameters on the system. It was discovered that, to reduce the burden of banditry in the population, stringent control measures must be put in place to reduce the use of illicit drug in a population. Suggested control measures to use in curtail the menace of the illicit drug use and banditry were recommends.