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.
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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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DOI: https://doi.org/10.1007/978-981-16-2450-6_2
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