A Mathematical Tumor Model with Immune Resistance and Drug Therapy: An Optimal Control Approach

TLDR

The study develops a competition model of tumor growth incorporating immune response and drug therapy to simulate Jeffs phenomenon and identify improved chemotherapy protocols. The authors construct a four‑population model of tumor, host, immune, and drug dynamics, analyze drug‑free equilibrium stability, and apply constrained optimal control with simulations to derive new therapy schedules. The model successfully reproduces the asynchronous Jeffs phenomenon, and the optimal control protocols generate larger tumor oscillations yet achieve a smaller final tumor size with minimal impact on normal cells compared to traditional pulsed therapy.

Abstract

We present a competition model of cancer tumor growth that includes both the immune system response and drug therapy. This is a four‐population model that includes tumor cells, host cells, immune cells, and drug interaction. We analyze the stability of the drug‐free equilibria with respect to the immune response in order to look for target basins of attraction. One of our goals was to simulate qualitatively the asynchronous tumor‐drug interaction known as “Jeffs phenomenon.” The model we develop is successful in generating this asynchronous response behavior. Our other goal was to identify treatment protocols that could improve standard pulsed chemotherapy regimens. Using optimal control theory with constraints and numerical simulations, we obtain new therapy protocols that we then compare with traditional pulsed periodic treatment. The optimal control generated therapies produce larger oscillations in the tumor population over time. However, by the end of the treatment period, total tumor size is smaller than that achieved through traditional pulsed therapy, and the normal cell population suffers nearly no oscillations.