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Modeling and Analysis of Fractional Leptospirosis Model Using Atangana–Baleanu Derivative

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Fractional Derivatives with Mittag-Leffler Kernel

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 194))

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Abstract

In this chapter, a fractional epidemic model for the leptospirosis disease with Atangana–Baleanu (AB) derivative is formulated. Initially, we present the model equilibria and basic reproduction number. The local stability of disease free equilibrium point is proved using fractional Routh Harwitz criteria. The Picard–Lindelof method is applied to show the existence and uniqueness of solutions for the model. A numerical scheme using Adams–Bashforth method for solving the proposed fractional model involving the AB derivative is presented. Finally, numerical simulations are performed in order to validate the importance of the arbitrary order derivative. The numerical result shows that the fractional order plays an important role to better understand the dynamics of disease.

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Authors and Affiliations

  1. Department of Mathematics, University of Peshawar, Peshawar, KP, Pakistan

    Saif Ullah

  2. Department of Mathematics, City University of Science and Information Technology, Peshawar, KP, Pakistan

    Muhammad Altaf Khan

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  1. Saif Ullah
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  2. Muhammad Altaf Khan
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Correspondence to Muhammad Altaf Khan .

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Editors and Affiliations

  1. CONACYT-Tecnológico Nacional de México, Centro Nacional de Investigación y Desarrollo Tecnológico, Cuernavaca, Morelos, Mexico

    José Francisco Gómez

  2. CONACYT-Instituto de Ingeniería, Universidad Nacional Autónoma de México, Mexico City, Mexico

    Lizeth Torres

  3. Tecnológico Nacional de México, Centro Nacional de Investigación y Desarrollo Tecnológico, Cuernavaca, Morelos, Mexico

    Ricardo Fabricio Escobar

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Ullah, S., Khan, M.A. (2019). Modeling and Analysis of Fractional Leptospirosis Model Using Atangana–Baleanu Derivative. In: Gómez, J., Torres, L., Escobar, R. (eds) Fractional Derivatives with Mittag-Leffler Kernel. Studies in Systems, Decision and Control, vol 194. Springer, Cham. https://doi.org/10.1007/978-3-030-11662-0_4

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  • DOI: https://doi.org/10.1007/978-3-030-11662-0_4

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