On Fractional Order Model of Tumor Growth with Cancer Stem Cell

• Published in: Fractal and fractional Vol. 7; no. 1; p. 27
• Main Authors: Aliasghari, Ghazaleh, Mesgarani, Hamid, Nikan, Omid, Avazzadeh, Zakieh
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-12-2022
• Subjects: Analysis; Calculus; Cancer; cancer stem cell; Cancer therapies; Differential equations; Finite difference method; Fixed points (mathematics); fixed-point theory; fractional derivative; Growth; Mathematical functions; Mathematical models; Mittag-Leffler function; Numerical analysis; Stem cells; system of integro-differential equation; tumor growth paradox; Tumors
• ISSN: 2504-3110; 2504-3110
• DOI: 10.3390/fractalfract7010027

This paper generalizes the integer-order model of the tumour growth into the fractional-order domain, where the long memory dependence of the fractional derivative can be a better fit for the cellular response. This model describes the dynamics of cancer stem cells and non-stem (ordinary) cancer cells using a coupled system of nonlinear integro-differential equations. Our analysis focuses on the existence and boundedness of the solution in correlation with the properties of Mittag-Leffler functions and the fixed point theory elucidating the proof. Some numerical examples with different fractional orders are shown using the finite difference scheme, which is easily implemented and reliably accurate. Finally, numerical simulations are employed to investigate the influence of system parameters on cancer progression and to confirm the evidence of tumour growth paradox in the presence of cancer stem cells.