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Analyzing the Dynamics of a Periodic Typhoid Fever Transmission Model with Imperfect Vaccination

Author

Listed:
  • Mohammed H. Alharbi

    (Department of Mathematics, College of Science, University of Jeddah, Jeddah 21589, Saudi Arabia
    These authors contributed equally to this work.)

  • Fawaz K. Alalhareth

    (Department of Mathematics, College of Arts & Sciences, Najran University, Najran 61441, Saudi Arabia
    These authors contributed equally to this work.)

  • Mahmoud A. Ibrahim

    (Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720 Szeged, Hungary
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
    These authors contributed equally to this work.)

Abstract

We present a nonautonomous compartmental model that incorporates vaccination and accounts for the seasonal transmission of typhoid fever. The dynamics of the system are governed by the basic reproductive number R 0 . This demonstrates the global stability of the disease-free solution if R 0 < 1 . On the contrary, if R 0 > 1 , the disease persists and positive periodic solutions exist. Numerical simulations validate our theoretical findings. To accurately fit typhoid fever data in Taiwan from 2008 to 2023, we use the model and estimate its parameters using Latin hypercube sampling and least squares techniques. A sensitivity analysis reveals the significant influence of parameters such as infection rates on the reproduction number. Increasing vaccination coverage, despite challenges in developing countries, reduces typhoid cases. Accessible and highly effective vaccines play a critical role in suppressing the epidemic, outweighing concerns about the efficacy of the vaccine. Investigating possible parameter changes in Taiwan highlights the importance of monitoring and managing transmission rates to prevent recurring annual epidemics.

Suggested Citation

  • Mohammed H. Alharbi & Fawaz K. Alalhareth & Mahmoud A. Ibrahim, 2023. "Analyzing the Dynamics of a Periodic Typhoid Fever Transmission Model with Imperfect Vaccination," Mathematics, MDPI, vol. 11(15), pages 1-26, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3298-:d:1203479
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    References listed on IDEAS

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    1. Abboubakar, Hamadjam & Racke, Reinhard, 2021. "Mathematical modeling, forecasting, and optimal control of typhoid fever transmission dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 149(C).
    2. Shaikh, Amjad S. & Sooppy Nisar, Kottakkaran, 2019. "Transmission dynamics of fractional order Typhoid fever model using Caputo–Fabrizio operator," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 355-365.
    3. Tilahun, Getachew Teshome & Makinde, Oluwole Daniel & Malonza, David, 2018. "Co-dynamics of Pneumonia and Typhoid fever diseases with cost effective optimal control analysis," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 438-459.
    4. Abboubakar, Hamadjam & Kombou, Lausaire Kemayou & Koko, Adamou Dang & Fouda, Henri Paul Ekobena & Kumar, Anoop, 2021. "Projections and fractional dynamics of the typhoid fever: A case study of Mbandjock in the Centre Region of Cameroon," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    5. Andrea Saltelli, 2002. "Sensitivity Analysis for Importance Assessment," Risk Analysis, John Wiley & Sons, vol. 22(3), pages 579-590, June.
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