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Dynamics of SEIR epidemic model by optimal auxiliary functions method

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  • Marinca, Bogdan
  • Marinca, Vasile
  • Bogdan, Ciprian

Abstract

The aim of the present work is to establish an approximate analytical solution for the nonlinear Susceptible, Exposed, Infected, Recovered (SEIR) model applied to novel coronavirus COVID-19. The mathematical model depending of five nonlinear differential equations, is studied and approximate solutions are obtained using Optimal Auxiliary Functions Method (OAFM). Our technique ensures a fast convergence of the solutions after only one iteration. The nonstandard part of OAFM is described by the presence of so-called auxiliary functions and of the optimal convergence-control parameters. We have a great freedom to select the auxiliary functions and the number of optimal convergence-control parameters which are optimally determined. Our approach is independent of the presence of small or large parameters in the governing equations or in the initial/boundary conditions, is effective, simple and very efficient.

Suggested Citation

  • Marinca, Bogdan & Marinca, Vasile & Bogdan, Ciprian, 2021. "Dynamics of SEIR epidemic model by optimal auxiliary functions method," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    • Handle: RePEc:eee:chsofr:v:147:y:2021:i:c:s0960077921003039
    DOI: 10.1016/j.chaos.2021.110949
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    References listed on IDEAS

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    1. Piovella, Nicola, 2020. "Analytical solution of SEIR model describing the free spread of the COVID-19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. Asier Ibeas & Manuel de la Sen & Santiago Alonso-Quesada, 2014. "Robust Sliding Control of SEIR Epidemic Models," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-11, March.
    3. Annas, Suwardi & Isbar Pratama, Muh. & Rifandi, Muh. & Sanusi, Wahidah & Side, Syafruddin, 2020. "Stability analysis and numerical simulation of SEIR model for pandemic COVID-19 spread in Indonesia," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    4. A. Harir & S. Melliani & H. El Harfi & L. S. Chadli, 2020. "Variational Iteration Method and Differential Transformation Method for Solving the SEIR Epidemic Model," International Journal of Differential Equations, Hindawi, vol. 2020, pages 1-7, July.
    5. Nicolae Herisanu & Vasile Marinca & Gheorghe Madescu & Florin Dragan, 2019. "Dynamic Response of a Permanent Magnet Synchronous Generator to a Wind Gust," Energies, MDPI, vol. 12(5), pages 1-11, March.
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    Cited by:

    1. Nicolae Herisanu & Bogdan Marinca & Livija Cveticanin & Vasile Marinca, 2023. "Analysis of the Vibro-Impact Nonlinear Damped and Forced Oscillator in the Dynamics of the Electromagnetic Actuation," Mathematics, MDPI, vol. 11(9), pages 1-24, May.
    2. Nicolae Herisanu & Vasile Marinca, 2021. "Analytical Study of Nonlinear Vibration in a Rub-Impact Jeffcott Rotor," Energies, MDPI, vol. 14(24), pages 1-15, December.

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