# Fractional-order mathematical modelling of cancer cells-cancer stem cells-immune system interaction with chemotherapy

## Keywords:

Fractional-order differential equations, cancer stem cells, immune system, numerical solutions, memory effect, existence and uniqueness

## Abstract

In this paper, we present a mathematical model of stem cells and chemotherapy for cancer treatment, in which the model is represented by fractional-order differential equations. Local stability of equilibrium points is discussed. Then, the existence and uniqueness of the solution are studied. In addition, in order to point out the advantages of the fractional-order modeling, memory trace and hereditary traits are taken into consideration. Numerical simulations have been used to investigate how the fractional-order derivative and different parameters affect the population dynamics, the graphs have been illustrated according to different values of fractional order $\alpha$ and different parameter values. Moreover, we have examined the effect of chemotherapy on tumor cells and stem cells over time. Furthermore, we concluded that the memory effect occurs as the $\alpha$ decreases from 1 and the chemotherapy drug is quite effective on the populations. We hope that this work will contribute to helping medical scientists take the necessary measures during the screening process and treatment.

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2021-12-13

## How to Cite

Özköse, F., Şenel, M. T. ., & Habbireeh, R. (2021). Fractional-order mathematical modelling of cancer cells-cancer stem cells-immune system interaction with chemotherapy. Mathematical Modelling and Numerical Simulation With Applications, 1(2), 67–83. https://doi.org/10.53391/mmnsa.2021.01.007

## Section

Research Articles