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Erschienen in:
Reproducing Kernel Method for Fractional Derivative with Non-local and Non-singular Kernel Kapitel lesen Erstes Kapitel lesen

2019 | OriginalPaper | Buchkapitel

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

verfasst von : Saif Ullah, Muhammad Altaf Khan

Erschienen in: Fractional Derivatives with Mittag-Leffler Kernel

Verlag: Springer International Publishing

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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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Vorheriges Kapitel Variable Order Mittag–Leffler Fractional Operators on Isolated Time Scales and Application to the Calculus of Variations
Nächstes Kapitel Dual Fractional Analysis of Blood Alcohol Model Via Non-integer Order Derivatives
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Metadaten
Titel
Modeling and Analysis of Fractional Leptospirosis Model Using Atangana–Baleanu Derivative
verfasst von
Saif Ullah
Muhammad Altaf Khan
Copyright-Jahr
2019
Buch
Fractional Derivatives with Mittag-Leffler Kernel

Print ISBN: 978-3-030-11661-3

Electronic ISBN: 978-3-030-11662-0

Copyright-Jahr: 2019

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

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