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Global asymptotic dynamics of a nonlinear illicit drug use system

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Abstract

In this paper, a nonlinear mathematical model of illicit drug use in a population is studied using dynamical system theory. The work is largely concerned with the analysis of asymptotic behaviour of solutions to a six-dimensional system of differential equations modeling the influence of illicit drug use in the population. The model is mathematically well-posed based on positivity and boundedness of solutions. A key threshold which measures the potential spread of the illicit drug use in the population is derived analytically. The model is shown to exhibit forward bifurcation property, implying the existence, uniqueness and local stability of an illicit drug-present equilibrium. Furthermore, the global asymptotic dynamics of the model around the illicit drug-free and drug-present equilibria are extensively investigated using appropriate Lyapunov functions. Numerical simulations are carried out to complement the obtained theoretical results, and to examine the effects of some parameters, such as influence rate, rehabilitation rates of drug users and relapse rate, on the dynamical spread of illicit drug use in the population. Measures to guide against the menace of the illicit drug use are suggested.

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Acknowledgements

The authors thank the editor and anonymous reviewers whose valuable and insightful comments have helped to improve the original manuscript.

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Authors and Affiliations

  1. Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso, Nigeria

    John O. Akanni, Samson Olaniyi & Folake O. Akinpelu

  2. Department of Mathematics, University of Lagos, Lagos, Nigeria

    Folake O. Akinpelu

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  1. John O. Akanni
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  2. Samson Olaniyi
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  3. Folake O. Akinpelu
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Correspondence to Samson Olaniyi.

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Akanni, J.O., Olaniyi, S. & Akinpelu, F.O. Global asymptotic dynamics of a nonlinear illicit drug use system. J. Appl. Math. Comput. 66, 39–60 (2021). https://doi.org/10.1007/s12190-020-01423-7

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  • DOI: https://doi.org/10.1007/s12190-020-01423-7

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