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Threshold and stability results in a periodic model for malaria transmission with partial immunity in humans

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  • Ibrahim, Mahmoud A.
  • Dénes, Attila

Abstract

We develop a periodic compartmental population model for the spread of malaria, dividing the human population into two classes: non-immune and semi-immune. The effect of seasonal changes in weather on the malaria transmission is considered by applying a non-autonomous model where mosquito birth, death and biting rates are time-dependent. We show that the global dynamics of the system is determined by the basic reproduction number, which we define as the spectral radius of a linear integral operator. For values of the basic reproduction number less than unity, the disease-free periodic solution is globally asymptotically stable, while if R0>1, then the disease remains endemic in the population. We show simulations in accordance with the analytic results. Finally, we show that the time-average reproduction rate gives an underestimation for malaria transmission risk.

Suggested Citation

  • Ibrahim, Mahmoud A. & Dénes, Attila, 2021. "Threshold and stability results in a periodic model for malaria transmission with partial immunity in humans," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    • Handle: RePEc:eee:apmaco:v:392:y:2021:i:c:s0096300320306640
    DOI: 10.1016/j.amc.2020.125711
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    Citations

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    Cited by:

    1. 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).
    2. Fawaz K. Alalhareth & Mohammed H. Alharbi & Mahmoud A. Ibrahim, 2023. "Modeling Typhoid Fever Dynamics: Stability Analysis and Periodic Solutions in Epidemic Model with Partial Susceptibility," Mathematics, MDPI, vol. 11(17), pages 1-26, August.
    3. Mahmoud A. Ibrahim & Attila Dénes, 2023. "Stability and Threshold Dynamics in a Seasonal Mathematical Model for Measles Outbreaks with Double-Dose Vaccination," Mathematics, MDPI, vol. 11(8), pages 1-20, April.

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