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SEIRS epidemic model with Caputo–Fabrizio fractional derivative and time delay: dynamical analysis and simulation

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Abstract

SEIRS epidemic model with Caputo–Fabrizio fractional derivative, a general incidence rate, and the time delay is considered. The main target of this work is to analyze the stability behavior and develop a numerical simulation of the fractional SEIRS model. The reproduction number \({R}_{0}\) and the order of the fractional derivative \(\beta \) play an important role in controlling the stability of the equilibrium points of the model, where it was shown that the disease-free equilibrium point \({P}_{0}\) is asymptotically stable if \({R}_{0}<1\) and unstable for \({R}_{0}>1\). The proper choice of the system parameters alongside the order of differentiation guarantee that the epidemic equilibrium point \({P}_{1}\) is asymptotically stable. The presence of a time delay in treatment and its effect on the stability behavior of the model is considered. Also, bifurcation analysis of the model depending on the time delay, \( \beta \) and the treatment rate is discussed. Numerical simulations based on a three-step Adams–Bashforth predictor technique for supporting and validating the theoretical results have been illustrated.

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Authors and Affiliations

  1. Departement of Engineering Physics and Mathematics, Faculty of Engineering, Tanta University, Tanta, Egypt

    M. M. Hikal, T. E. M. Atteya & W. K. Zahra

  2. Department of Basic Sciences, Higher Institute of Engineering and Technology Kafrelsheikh, Kafrelsheikh, Egypt

    M. M. Hikal

  3. Departement of Mathematics, Common First Year Deanship, Umm Alqura University, Mecca, Saudi Arabia

    T. E. M. Atteya

  4. Departement of Computers and Control Engineering, Faculty of Engineering, Tanta University, Tanta, Egypt

    Hamed M. Hemeda

  5. Departement of Electronics Engineering and Electrical Communications, Higher Institute of Engineering and Technology, Kafrelsheikh, Egypt

    Hamed M. Hemeda

  6. Department of Mathematics, Institute of Basic and Applied Sciences, Egypt-Japan University of Science and Technology (E-JUST), New Borg El-Arab City, 21934, Alexandria, Egypt

    W. K. Zahra

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  1. M. M. Hikal
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  2. T. E. M. Atteya
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Correspondence to W. K. Zahra.

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Hikal, M.M., Atteya, T.E.M., Hemeda, H.M. et al. SEIRS epidemic model with Caputo–Fabrizio fractional derivative and time delay: dynamical analysis and simulation. Ricerche mat 73, 1085–1119 (2024). https://doi.org/10.1007/s11587-021-00643-8

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  • DOI: https://doi.org/10.1007/s11587-021-00643-8

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