A Mathematical Model of Cancer Transmission with Immune Response Dynamics and Optimal Drug Dosing
DOI:
https://doi.org/10.48165/gjs.2026.3103Keywords:
Mathematical model, Basic reproduction number Stability analysis, Optimal control, Numerical simulationAbstract
Cancer arises from intricate interactions among tumor cell proliferation, immune system dynamics, and therapeutic interventions. In this study, we develop a mathematical model that incorporates tumor growth, immune stimulation and suppression, as well as drug dynamics. The disease-free and endemic equilibria, and the basic reproduction number (R0) are computed to study the dynamics of the disease. Stability analysis is conducted to determine the conditions under which malignant cells either persist or are eradicated. Furthermore, the model is extended by introducing an optimal control parameter for drug infusion, with Pontryagin’s Maximum Principle applied to characterize the optimal therapeutic strategy. This study shows the theoretical insights into the delicate balance between tumor suppression and immune exhaustion, thereby providing guidance for the design of an effective treatment strategy.
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