Applied Mathematics & Information Sciences

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Among the major global health and social problems facing the world today is the use of illicit drugs and the act of banditry. The two problems have resulted in the loss of precious lives and possessions and even devastating effects on the economy of some countries where such acts were being practised. Of interest in this work is to study the global stability of illicit drug use spread dynamics with banditry compartments using a dynamical system theory approach. Illicit drug use and banditry reproduction number, which measures the potential spread of illicit drug use and banditry in the population, is evaluated analytically. The system exhibits supercritical bifurcation property, telling us that the local stability of an illicit drug and banditry-present equilibrium exists and is unique. In addition, the illicit drug and banditry-free and illicit drug and banditry-present equilibria are shown to be globally asymptotically stable; this was achieved by constructing suitable Lyapunov functions. Sensitivity analysis is carried out to know the impact of each parameter on the dynamic spread of illicit drug use and banditry in a population. Numerical simulations validate the quantitative results and examine the effects of some key parameters on the system. It has been discovered that to reduce the burden of banditry in the population, stringent control measures must be implemented to reduce the use of illicit drugs. Control measures are recommended to use in curtailing the menace of illicit drug use and banditry.

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