Fractal Fractional Operator Method on HER2+ Breast Cancer Dynamics

Abstract

In this paper, an in vitro model of HER2+ breast cancer cells dynamics resulting from various dosages and timings of paclitaxel and trastuzumab combination regimens is considered. Since, the combined in vitro results and development of dynamics of drug synergy has a potential to evaluate and improve standard of care, then combination therapies in timings of paclitaxel and trastuzumab combination regimens, thus, HER2+ breast cancer cells dynamics are extended to a system of fractal fractional partial differential equations in order to enable one to capture the dynamics of the deadly breast cancer in terms of combination of the two therapies. Moreover, the well-posedness of solutions is presented and the extended dynamics are analysed to that effect. Since it is not that easy to obtain the analytic solution a novel numerical method based on fractal fractional derivatives is design, implemented and the results with respect to the stability conditions are presented.