A Model of Effector–Tumor Cell Interactions Under Chemotherapy: Bifurcation Analysis

Abstract

This paper studies the dynamic behavior of a three-dimensional mathematical model of effector–tumor cell interactions that incorporates the impact of chemotherapy. The well-known logistic function is used to model tumor growth. Elementary concepts of singularity theory are used to classify the model steady-state equilibria. I show that the model can predict hysteresis, isola/mushroom, and pitchfork singularities. Useful branch sets in terms of model parameters are constructed to delineate the domains of such singularities. I examine the effect of chemotherapy on bifurcation solutions, and I discuss the efficiency of chemotherapy treatment. I also show that the model cannot predict a periodic behavior for any model parameters.

Keywords

• cancer
• effectors–tumor cells
• chemotherapy
• singularity
• bifurcation
• periodic