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Efficient Numerical Solutions to a SIR Epidemic Model

Author

Listed:
  • Mohammad Mehdizadeh Khalsaraei

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

  • Ali Shokri

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

  • Higinio Ramos

    (Scientific Computing Group, Universidad de Salamanca, Plaza de la Merced, 37008 Salamanca, Spain)

  • Shao-Wen Yao

    (School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China)

  • Maryam Molayi

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

Abstract

Two non-standard predictor-corrector type finite difference methods for a SIR epidemic model are proposed. The methods have useful and significant features, such as positivity, basic stability, boundedness and preservation of the conservation laws. The proposed schemes are compared with classical fourth order Runge–Kutta and non-standard difference methods (NSFD). The stability analysis is studied and numerical simulations are provided.

Suggested Citation

  • Mohammad Mehdizadeh Khalsaraei & Ali Shokri & Higinio Ramos & Shao-Wen Yao & Maryam Molayi, 2022. "Efficient Numerical Solutions to a SIR Epidemic Model," Mathematics, MDPI, vol. 10(18), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3299-:d:912368
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
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    Cited by:

    1. Svetozar Margenov & Nedyu Popivanov & Iva Ugrinova & Tsvetan Hristov, 2023. "Differential and Time-Discrete SEIRS Models with Vaccination: Local Stability, Validation and Sensitivity Analysis Using Bulgarian COVID-19 Data," Mathematics, MDPI, vol. 11(10), pages 1-26, May.

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