Fractional operator method on a multi-mutation and intrinsic resistance model

Abstract

Our focus in this work is to expand the studies on a tumour-host model with chemotherapy application, by considering a model which includes terms that can express both intrinsic drug resistance and drug-induced resistance. Thus, we extend a model that expresses both drug and drug-induced resistances to include spatial effects of the involved cells, establish the physiological levels and asymptotic stability conditions of the equilibrium points of both models. Since it is not that easy to solve the extended model analytically we propose a well posed numerical method based on fractional derivatives. We present our solutions for comparison purpose with regard to the stability conditions.

Keywords

• Cancer modeling
• Conjoint cell growth
• Drug resistance
• Intrinsic-drug resistance
• Mutation
• Asymptotic stability