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

Abstract

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 $\mathcal {CF}$ CF -system of the anthrax disease model by utilizing the Picard–Lindelof technique. By obtaining the basic reproduction number $\mathcal{R}_{0}$ R0 of the fractional $\mathcal{CF}$ 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 $\mathcal{CF}$ 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 $\mathcal{CF}$ CF -fractional anthrax disease model and review the dynamical behavior of the solutions of this $\mathcal {CF}$ CF -system during a time interval.