Mathematical modelling of multi-mutation and drug resistance model with fractional derivative

Abstract

We understand that the methods by which the therapeutic approaches with regard to drug induced resistance are still posing a big challenge, thus, we extend a model that expresses intrinsic drug resistances to include spatial effects of the involved cells, establish the physiological levels and asymptotic stability condition(s) of the equilibrium points of both models. Obviously, it is very difficult to solve the extended model analytically, therefore, we propose a well posed numerical method based on fractional derivative operator. We present our solutions for comparison purpose with regard to the stability condition.

Keywords

• Fractional operator
• Cancer conjoint cell growth
• Chemotherapy
• Drug resistance
• Stability analysis
• Numerical method