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

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  • Rubayyi T. Alqahtani

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh, Saudi Arabia)

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.

Suggested Citation

  • Rubayyi T. Alqahtani, 2025. "A Model of Effector–Tumor Cell Interactions Under Chemotherapy: Bifurcation Analysis," Mathematics, MDPI, vol. 13(7), pages 1-21, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:7:p:1032-:d:1617974
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