NUMERICAL SIMULATION OF MATHEMATICAL MODEL FOR CANCER TREATMENTS BY STEM CELLS AND CHEMOTHERAPY USING CAPUTO-FABRIZIO FRACTIONAL DERIVATIVE

The high rate of mortality caused by cancer diseases has attracted much attention from various disciplines to come up with better preventive measures and treatment strategies that will lessen cancer development and increase survival rate. Several comprehensive mathematical analyses were carried out using the well-known Banach fixed point theorem/contracting principle to study the behaviour and stability of the cancer disease models. With these models a lot of numerical estimates of biological knowledge of the parameters have been obtained, a number of phenomena interpreted, and predictions were made in order to gain further knowledge of cancer development and possible treatment. In this study, simulation of the cancer mathematical model using Caputo-Frabrizio fractional derivative to see the effects of the combined treatment of cancer disease by stem cells and chemotherapy were performed. From the graphical representation of results presented one can clearly see the effects of the application of the stem cells and the chemotherapy involved in the treatment of cancer tumor. In the past, most of the cancer treatment were done by conventional chemotherapy, radiotherapy, hormone therapy, molecularly targeted therapies and surgery which were used either singly or in combination with one another or other therapies and all played vital role except the side effects that these therapies incur in the normal tissues and organs. Thus, from the recent research carried out by some researchers, it is now clear that in many cases they do not represent complete cure. Hence, the need to address not only the preventative measures of cancer disease, but also more successful treatment can be achieved using combination of stem cells and chemotherapy.