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A Hermite Polynomial Approach for Solving the SIR Model of Epidemics

Author

Listed:
  • Aydin Secer

    (Department of Mathematical Engineering, Yildiz Technical University, Istanbul 34200, Turkey)

  • Neslihan Ozdemir

    (Department of Mathematical Engineering, Yildiz Technical University, Istanbul 34200, Turkey)

  • Mustafa Bayram

    (Department of Computer Engineering, Gelisim University, Istanbul 34315, Turkey)

Abstract

In this paper, the problem of the spread of a non-fatal disease in a population is solved by using the Hermite collocation method. Mathematical modeling of the problem corresponds to a three-dimensional system of nonlinear ODEs. The presented scheme reduces the problem to a nonlinear algebraic equation system by expanding the approximate solutions by using Hermite polynomials with unknown coefficients. These coefficients of the Hermite polynomials are computed by using the matrix operations of derivatives together with the collocation method. Maple software is used to carry out the computations. In addition, comparison of our method with the Homotopy perturbation method (HPM) and Laplece-Adomian decomposition method (LADM) proves accuracy of solution.

Suggested Citation

  • Aydin Secer & Neslihan Ozdemir & Mustafa Bayram, 2018. "A Hermite Polynomial Approach for Solving the SIR Model of Epidemics," Mathematics, MDPI, vol. 6(12), pages 1-11, December.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:12:p:305-:d:188149
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    References listed on IDEAS

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    1. Awawdeh, Fadi & Adawi, A. & Mustafa, Z., 2009. "Solutions of the SIR models of epidemics using HAM," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3047-3052.
    2. Hojjati, G. & Rahimi Ardabili, M.Y. & Hosseini, S.M., 2004. "A-EBDF: an adaptive method for numerical solution of stiff systems of ODEs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 66(1), pages 33-41.
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    Cited by:

    1. Şuayip Yüzbaşı & Gamze Yıldırım, 2023. "A Pell–Lucas Collocation Approach for an SIR Model on the Spread of the Novel Coronavirus (SARS CoV-2) Pandemic: The Case of Turkey," Mathematics, MDPI, vol. 11(3), pages 1-22, January.
    2. Burcu Gürbüz & Herman Mawengkang & Ismail Husein & Gerhard-Wilhelm Weber, 2022. "Rumour propagation: an operational research approach by computational and information theory," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(1), pages 345-365, March.

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