A mathematical analysis of a system of Caputo–Fabrizio fractional differential equations for the anthrax disease model in animals

• Main Authors: Shahram Rezapour, Sina Etemad, Hakimeh Mohammadi
• Format: Article
• Language: English
• Published: SpringerOpen 2020-09-01
• Series: Advances in Difference Equations
• Subjects: Anthrax disease; Homotopy analysis method; Mathematical modeling; Numerical simulation; The Caputo–Fabrizio derivative
• Online Access: http://link.springer.com/article/10.1186/s13662-020-02937-x

Abstract We study a fractional-order model for the anthrax disease between animals based on the Caputo–Fabrizio derivative. First, we derive an existence criterion of solutions for the proposed fractional CF $\mathcal {CF}$ -system of the anthrax disease model by utilizing the Picard–Lindelof technique. By obtaining the basic reproduction number R 0 $\mathcal{R}_{0}$ of the fractional CF $\mathcal{CF}$ -system we compute two disease-free and endemic equilibrium points and check the asymptotic stability property. Moreover, by applying an iterative approach based on the Sumudu transform we investigate the stability of the fractional CF $\mathcal{CF}$ -system. We obtain approximate series solutions of this system by means of the homotopy analysis transform method, in which we invoke the linear Laplace transform. Finally, after the convergence analysis of the numerical method HATM, we present a numerical simulation of the CF $\mathcal{CF}$ -fractional anthrax disease model and review the dynamical behavior of the solutions of this CF $\mathcal {CF}$ -system during a time interval.