Cancer treatment by stem cells and chemotherapy as a mathematical model with numerical simulations

The main idea of this work, is to introduce a new mathematical model of stem cells and chemotherapy to treat cancer, as an autonomous system. Local stability of the equilibrium points before and after the treatment are discussed. Numerical simulation and graphic for the concentra-tion of cells along the time are explored the effects of the therapies on the decay rate of tumor cells and on the growth rate of effector cells to modify the immune system of the cancer patient and hence hope a cure by helping Medical scientists take highlight action to start the screening process. (C) 2019 The Author. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).