Numerical Treatment of Delay Salmonella Fractional Model with Atangana–Baleanu Derivative

Mathematical modelling of Salmonella disease played a significant role in the understanding of the transmission of this epidemic. In this article, we study numerically a fractional dynamical, with time-delay, Salmonella disease model. The introduced model is written as a system of fractional-order delay differential equations. The fractional operator is defined in the Atangana–Baleanu–Caputo sense, where the parameters are varied regarding the fractional-order derivative. We study, for any time delay, the stability of the disease-free equilibrium point and the endemic equilibrium point. Implicit nonstandard finite difference method is introduced to simulate numerically the proposed model. The obtained schema was unconditionally stable. Some comparison with our numerical simulations is introduced to show the effectiveness and applicability of the introduced approach for approximating the solutions of such stiff problems of fractional delay differential equations. Our simulations confirm the theoretical studies in this paper. © 2020, Springer Nature India Private Limited.