Using the Modified Decomposition Method Associated with Mohand Transforms for a Numerical Simulation of the Mathematical Model for Breast Cancer

Abstract

We know that mathematical modeling is an important tool for understanding the dynamics of breast cancer (BC) development, spread and reduce new therapeutic approaches. So, in the current article, we have investigated the analytical solution of the mathematical model for BC by using the modified Adomian decomposition method (MADM). The MADM is based on the
integral transform (Mohand transform) with the Adomian decomposition procedure. The MADM provides a series of solutions that converge quickly to the exact solution for the proposed problem. The convergence of this method is discussed. Through this work, a numerical simulation was presented to solve the mathematical model under study with several values of the approximation order, rate of the estrogen source, and effectiveness of anti-cancer drugs, to understand the extent of their effect on the numerical solution and then on the nature and dynamics of the system, and to provide some recommendations to reduce the impact of this malignant tumor. In addition, we presented a comparison between the solution generated by the proposed technique and that numerical solution by utilizing the Runge-Kutta method (RK4M). Finally, the proposed method can also be extended to solving other models in the applied sciences.