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Complex dynamics of a Caputo derivative-based fractional-order SIR model incorporating saturated incidence and recovery

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Abstract

In the current study, we develop and analyze a Caputo derivative-based fractional-order SIR-type epidemic model. The exact value of the basic reproduction number and its importance in the model system has also been discussed. Then, we provide a mathematical analysis of this model focused on endemic and infection-free states. Next, the global behavior of the model, along with the existence of the Backward and Hopf bifurcations, has been extensively studied. The impacts of the model parameters on the system are analyzed. Also, we have formulated an optimum control problem incorporating a time-dependent treatment control variable and studied the effects of the control parameter on the disease dynamics. To confirm the obtained analytical results, the model is also numerically simulated using the predictor-corrector approach.

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Acknowledgements

The authors would like to thank Dr. Pushpendra Kumar, Guest Editor of the journal and organizer committee member of ICFCTAN-2023, for his continuous assistance regarding the preparation of this article. In addition, the authors would like to thank the handling editor Jian-Qiao Sun, Editor in Chief, International Journal of Dynamics and Control, and reviewers for their useful suggestions and constructive comments to improve the manuscript significantly.

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Author notes

  1. Soovoojeet Jana, Anupam Khatua, Dibyendu Biswas, Biswajit Mondal, Anupam De have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, Durgapur Government College, Durgapur, Paschim Bardhaman, WB, 713214, India

    Sibaji Rit

  2. Department of Mathematics, Ramsaday College, Amta, Howrah, WB, 711401, India

    Soovoojeet Jana

  3. Department of Applied Sciences and Humanities, NIAMT, Ranchi, Jharkhand, 834003, India

    Anupam Khatua

  4. Department of Mathematics, City College of Commerce and Business Administration, Kolkata, WB, 700012, India

    Dibyendu Biswas

  5. Department of Mathematics, Raja Narendra Lal Khan Women’s College, Medinipur, Paschim Medinipur, WB, 721102, India

    Biswajit Mondal

  6. School of Applied Science and Humanities, Haldia Institute of Technology, Haldia, Purba Medinipur, WB, 721657, India

    Anupam De

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  1. Sibaji Rit
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Rit, S., Jana, S., Khatua, A. et al. Complex dynamics of a Caputo derivative-based fractional-order SIR model incorporating saturated incidence and recovery. Int. J. Dynam. Control 12, 246–258 (2024). https://doi.org/10.1007/s40435-023-01294-3

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  • DOI: https://doi.org/10.1007/s40435-023-01294-3

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