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

  • Saif Ullah
  • Muhammad Altaf KhanEmail author
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 194)

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.

Keywords

Fractional calculus Atangana–Baleanu fractional derivative Leptospirosis model 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of PeshawarPeshawarPakistan
  2. 2.Department of MathematicsCity University of Science and Information TechnologyPeshawarPakistan

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