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Global Dynamics of a Social Hierarchy-Stratified Malaria Model: Insight from Fractional Calculus

Author

Listed:
  • Sulaimon F. Abimbade

    (Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso 212102, Nigeria)

  • Furaha M. Chuma

    (Department of Physics, Mathematics and Informatics, Dar es Salaam University College of Education, Dar es Salaam 2329, Tanzania)

  • Sunday O. Sangoniyi

    (Department of Mathematics and Computing Science Education, Emmanuel Alayande University of Education, Oyo 211172, Nigeria)

  • Ramoshweu S. Lebelo

    (Department of Education, Vaal University of Technology, Vanderbijilpark 1911, South Africa)

  • Kazeem O. Okosun

    (Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA)

  • Samson Olaniyi

    (Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso 212102, Nigeria)

Abstract

In this study, a mathematical model for the transmission dynamics of malaria among different socioeconomic groups in the human population interacting with a susceptible-infectious vector population is presented and analysed using a fractional-order derivative of the Caputo type. The total human population is stratified into two distinguished classes of lower and higher income individuals, with each class further subdivided into susceptible, infectious, and recovered populations. The socio hierachy-structured fractional-order malaria model is analyzed through the application of different dynamical system tools. The theory of positivity and boundedness based on the generalized mean value theorem is employed to investigate the basic properties of solutions of the model, while the Banach fixed point theory approach is used to prove the existence and uniqueness of the solution. Furthermore, unlike the existing related studies, comprehensive global asymptotic dynamics of the fractional-order malaria model around both disease-free and endemic equilibria are explored by generalizing the usual classical methods for establishing global asymptotic stability of the steady states. The asymptotic behavior of the trajectories of the system are graphically illustrated at different values of the fractional (noninteger) order.

Suggested Citation

  • Sulaimon F. Abimbade & Furaha M. Chuma & Sunday O. Sangoniyi & Ramoshweu S. Lebelo & Kazeem O. Okosun & Samson Olaniyi, 2024. "Global Dynamics of a Social Hierarchy-Stratified Malaria Model: Insight from Fractional Calculus," Mathematics, MDPI, vol. 12(10), pages 1-19, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1593-:d:1397874
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    References listed on IDEAS

    as
    1. Temesgen Duressa Keno & Lemesa Bedjisa Dano & Gamachu Adugna Ganati & Kenan Yildirim, 2022. "Optimal Control and Cost-Effectiveness Strategies of Malaria Transmission with Impact of Climate Variability," Journal of Mathematics, Hindawi, vol. 2022, pages 1-20, June.
    2. Samson Olaniyi & Sulaimon F. Abimbade & Olusegun A. Ajala & Furaha M. Chuma, 2024. "Efficiency and economic analysis of intervention strategies for recurrent malaria transmission," Quality & Quantity: International Journal of Methodology, Springer, vol. 58(1), pages 627-645, February.
    3. Ndii, Meksianis Z. & Adi, Yudi Ari, 2021. "Understanding the effects of individual awareness and vector controls on malaria transmission dynamics using multiple optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    4. Boukhouima, Adnane & Hattaf, Khalid & Lotfi, El Mehdi & Mahrouf, Marouane & Torres, Delfim F.M. & Yousfi, Noura, 2020. "Lyapunov functions for fractional-order systems in biology: Methods and applications," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
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