Local Controllability Analysis for a Tumor Dynamics Model
DOI:
https://doi.org/10.5433/1679-0375.2025.v46.53579Keywords:
cancer modeling, controllability theory, Kalman rank condition, mathematical oncologyAbstract
This study investigates the local controllability of a mathematical model describing tumor dynamics, incorporating cellular competition and external interventions represented by a control variable. The model analyzed is a modified version of the formulation proposed by Gatenby (1996), and its dynamics are explored through linearization around equilibrium points. Using the Kalman rank condition, we establish the circumstances under which the system exhibits local controllability. The results provide a theoretical foundation for understanding how external stimuli can steer the system between distinct biological states, particularly in the context of interactions between healthy and tumor cells. The work bridges concepts from control theory and mathematical oncology, aiming to support the development of more effective clinical intervention strategies. Our analysis offers insights into identifying scenarios in which treatment, modeled as an external control input, can effectively stabilize or even reverse tumor growth.
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