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Dynamical Analysis of a Caputo Fractional Order SIR Epidemic Model with a General Treatment Function

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Analysis of Infectious Disease Problems (Covid-19) and Their Global Impact

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Abstract

In this work, a fractional order SIR epidemic model is proposed. We first prove the existence, uniqueness, non-negativity and boundedness of solutions to the considered model. We also study the existence of equilibrium points. Some sufficient conditions are derived to ensure, in terms of the basic reproduction number, the global asymptotic stability of the disease free equilibrium point and endemic equilibrium point. Finally, numerical simulations are illustrated to verify the validity of our theoretical results.

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Acknowledgements

The authors wish to thank the reviewers for careful reading and valuable suggestions to improve the quality of the paper.The support from Moulay Ismail University of Meknes (project UMI 2018) and Covid-19 project (Analyse épidémique du Covid-19 au Maroc par modélisation dynamique et intelligence artificielle) jointly funded by CNRST and the Moroccan Ministry of Higher Education and Scientific Research, is acknowledged. P. Agarwal was very thankful to the SERB (project TAR/2018/000001), DST (project DST/INT/DAAD/P-21/2019, INT/RUS/RFBR/308) and NBHM (project 02011/12/ 2020NBHM(R.P)/R& D II/7867) for their necessary support for providing the necessary facility.

Author information

Authors and Affiliations

  1. Moulay Ismail University of Meknes, FST Errachidia, MAIS Laboratory, MAMCS Group, Meknes, Morocco

    A. Lamrani Alaoui & M. Tilioua

  2. Moulay Ismail University of Meknes, FST Errachidia MAIS Laboratory, AMNEA Group, Meknes, Morocco

    M. R. Sidi Ammi

  3. Department of Mathematics, Anand International College of Engineering, Jaipur, 303012, Rajasthan, India

    P. Agarwal

  4. Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE

    P. Agarwal

Authors
  1. A. Lamrani Alaoui
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  2. M. Tilioua
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  3. M. R. Sidi Ammi
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  4. P. Agarwal
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Corresponding author

Correspondence to M. R. Sidi Ammi .

Editor information

Editors and Affiliations

  1. Anand International College of Engineering, Jaipur, Rajasthan, India

    Praveen Agarwal

  2. Institute of Mathematics, University of Santiago de Compostela, Santiago, Spain

    Juan J. Nieto

  3. Mathematical Sciences, Queen Mary University of London, London, UK

    Michael Ruzhansky

  4. Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Delfim F. M. Torres

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Alaoui, A.L., Tilioua, M., Sidi Ammi, M.R., Agarwal, P. (2021). Dynamical Analysis of a Caputo Fractional Order SIR Epidemic Model with a General Treatment Function. In: Agarwal, P., Nieto, J.J., Ruzhansky, M., Torres, D.F.M. (eds) Analysis of Infectious Disease Problems (Covid-19) and Their Global Impact. Infosys Science Foundation Series(). Springer, Singapore. https://doi.org/10.1007/978-981-16-2450-6_2

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