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Nonstandard Finite Difference Schemes for an SIR Epidemic Model

Author

Listed:
  • Mohammad Mehdizadeh Khalsaraei

    (Department of Mathematics, University of Maragheh, Maragheh 55181-83111, Iran)

  • Ali Shokri

    (Department of Mathematics, University of Maragheh, Maragheh 55181-83111, Iran)

  • Samad Noeiaghdam

    (Department of Applied Mathematics and Programming, South Ural State University, Lenin Prospect 76, 454080 Chelyabinsk, Russia
    Industrial Mathematics Laboratory, Baikal School of BRICS, Irkutsk National Research Technical University, 664074 Irkutsk, Russia)

  • Maryam Molayi

    (Department of Mathematics, University of Maragheh, Maragheh 55181-83111, Iran)

Abstract

This paper aims to present two nonstandard finite difference (NFSD) methods to solve an SIR epidemic model. The proposed methods have important properties such as positivity and boundedness and they also preserve conservation law. Numerical comparisons confirm that the accuracy of our method is better than that of other existing standard methods such as the second-order Runge–Kutta (RK2) method, the Euler method and some ready-made MATLAB codes.

Suggested Citation

  • Mohammad Mehdizadeh Khalsaraei & Ali Shokri & Samad Noeiaghdam & Maryam Molayi, 2021. "Nonstandard Finite Difference Schemes for an SIR Epidemic Model," Mathematics, MDPI, vol. 9(23), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3082-:d:691501
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    References listed on IDEAS

    as
    1. Ramos, Higinio & Popescu, Paul, 2018. "How many k-step linear block methods exist and which of them is the most efficient and simplest one?," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 296-309.
    2. Khalsaraei, Mohammad Mehdizadeh & Shokri, Ali & Ramos, Higinio & Heydari, Shahin, 2021. "A positive and elementary stable nonstandard explicit scheme for a mathematical model of the influenza disease," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 397-410.
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    Cited by:

    1. Vasily E. Tarasov, 2024. "Exact Finite-Difference Calculus: Beyond Set of Entire Functions," Mathematics, MDPI, vol. 12(7), pages 1-37, March.
    2. Agrawal, Khushbu & Kumar, Ranbir & Kumar, Sunil & Hadid, Samir & Momani, Shaher, 2022. "Bernoulli wavelet method for non-linear fractional Glucose–Insulin regulatory dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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