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Modelling epidemiological dynamics with pseudo-recovery via fractional-order derivative operator and optimal control measures

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  • Samson Olaniyi
  • Furaha M Chuma
  • Ramoshweu S Lebelo
  • Richard C Ogbonna
  • Sulaimon F Abimbade

Abstract

In this study, a new deterministic mathematical model based on fractional-order derivative operator that describes the pseudo-recovery dynamics of an epidemiological process is developed. Fractional-order derivative of Caputo type is used to examine the effect of memory in the spread process of infectious diseases with pseudo-recovery. The well-posedness of the model is qualitatively investigated through Banach fixed point theory technique. The spread of the disease in the population is measured by analysing the basic reproduction of the model with respect to its parameters through the sensitivity analysis. Consequently, the analysis is extended to the fractional optimal control model where time-dependent preventive strategy and treatment measure are characterized by Pontryagin’s maximum principle. The resulting Caputo fractional-order optimality system is simulated to understand how both preventive and treatment controls affect the pseudo-recovery dynamics of infectious diseases in the presence of memory. Graphical illustrations are shown to corroborate the qualitative results, and to demonstrate the importance of memory effects in infectious disease modelling. It is shown that time-dependent preventive strategy and treatment measure in the presence of memory engenders significant reduction in the spread of the disease when compared with memoryless situation.

Suggested Citation

  • Samson Olaniyi & Furaha M Chuma & Ramoshweu S Lebelo & Richard C Ogbonna & Sulaimon F Abimbade, 2025. "Modelling epidemiological dynamics with pseudo-recovery via fractional-order derivative operator and optimal control measures," PLOS ONE, Public Library of Science, vol. 20(1), pages 1-24, January.
    • Handle: RePEc:plo:pone00:0318080
    DOI: 10.1371/journal.pone.0318080
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    References listed on IDEAS

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    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. Ghosh, M. & Olaniyi, S. & Obabiyi, O.S., 2020. "Mathematical analysis of reinfection and relapse in malaria dynamics," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    3. 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.
    4. Sajjad, Assad & Farman, Muhammad & Hasan, Ali & Nisar, Kottakkaran Sooppy, 2023. "Transmission dynamics of fractional order yellow virus in red chili plants with the Caputo–Fabrizio operator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 347-368.
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