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

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, the 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 α 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 α 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.

Three-dimensional fractional system with the stability condition and chaos control

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Stability characterization of a fractional-order viral system with the non-cytolytic immune assumption

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An optimal control strategy and Grünwald-Letnikov finite-difference numerical scheme for the fractional-order COVID-19 model

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