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A Proposed Analytical and Numerical Treatment for the Nonlinear SIR Model via a Hybrid Approach

Author

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  • Abdulrahman B. Albidah

    (Department of Mathematics, College of Science, Majmaah University, Al-Majmaah 11952, Saudi Arabia)

Abstract

This paper re-analyzes the nonlinear Susceptible–Infected–Recovered (SIR) model using a hybrid approach based on the Laplace–Padé technique. The proposed approach is successfully applied to extract several analytic approximations for the infected and recovered individuals. The domains of applicability of such analytic approximations are addressed. In addition, the present results are validated through various comparisons with the Runge–Kutta numerical method. The obtained analytical results agree with the numerical ones for a wide range of numbers of contacts featured in the studied model. The efficiency of the present analysis reveals that it can be implemented to deal with other systems describing real-life phenomena.

Suggested Citation

  • Abdulrahman B. Albidah, 2023. "A Proposed Analytical and Numerical Treatment for the Nonlinear SIR Model via a Hybrid Approach," Mathematics, MDPI, vol. 11(12), pages 1-15, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2749-:d:1173413
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    References listed on IDEAS

    as
    1. Huda O. Bakodah & Abdelhalim Ebaid, 2018. "Exact Solution of Ambartsumian Delay Differential Equation and Comparison with Daftardar-Gejji and Jafari Approximate Method," Mathematics, MDPI, vol. 6(12), pages 1-10, December.
    2. Aneefah H. S. Alenazy & Abdelhalim Ebaid & Ebrahem A. Algehyne & Hind K. Al-Jeaid, 2022. "Advanced Study on the Delay Differential Equation y ′( t ) = ay ( t ) + by ( ct )," Mathematics, MDPI, vol. 10(22), pages 1-13, November.
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    Cited by:

    1. Reinhard Schlickeiser & Martin Kröger, 2024. "Mathematics of Epidemics: On the General Solution of SIRVD, SIRV, SIRD, and SIR Compartment Models," Mathematics, MDPI, vol. 12(7), pages 1-45, March.
    2. Martin Kröger & Reinhard Schlickeiser, 2024. "On the Analytical Solution of the SIRV-Model for the Temporal Evolution of Epidemics for General Time-Dependent Recovery, Infection and Vaccination Rates," Mathematics, MDPI, vol. 12(2), pages 1-19, January.

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