Mathematical modelling of tumour chemotherapy by continuous infusion drug

Abstract

We present a theoretical framework based on logistic growth and Michaelis-Menten kinetics for describing the interaction between tumour density and drug concentration, through an infusion pump. According to the logistics growth and Michaelis-Menten kinetics, the growth rate of tumours increases with the availability of drugs only up to a certain point.  Cancer chemotherapy by continuous infusion pump has the advantage of achieving large concentrations of the drug at the tumour site while minimising adverse effects on the rest of the body, in contrast to conventional methods. The model in this work has aspects of logistic growth, which cover a method for determining tumour density and drug concentrations that will eliminate the tumour. Stability analysis is done by solving nonlinear equations and finding stable and unstable points, where the coordinates of the stable points represent the tumour density and the amount of drug. The stability of the equilibrium point for the model and illustrative numerical examples are provided to show the accuracy of the model.