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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