Dynamical Behavior of Fractional Order Breast Cancer Model: an Analytical and Numerical Stud

Abstract

In this paper, we investigate the dynamical behavior of the fractional-order breast cancer model with modified parameters. In this fractional-order model (FOM), we replaced the integer-order derivatives with the fractional-order derivatives on both sides. In physics, this means that the memory of a biological process is examined and transferred from one part to another while maintaining balance. The positivity of solutions of this FOM is proved. Also, the equilibrium points and stability of disease-free and endemic cases for this FOM are studied. Furthermore, the basic reproduction number (R0) is computed and sensitivity analysis concerning the parameters is achieved. We solve this FOM by two methods one of them gives an analytic-approximate solution called generalized Mittag-Leffler function method (GMLFM) and another method gives a numerical solution called predictor-corrector method (PCM). The simulations for the suggested model are presented to verify the obtained theoretical results.