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

Rubayyi T. Alqahtani ()
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Rubayyi T. Alqahtani: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh, Saudi Arabia

Mathematics, 2025, vol. 13, issue 7, 1-21

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; hysteresis; isola/mushroom; pitchfork (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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