The North Carolina Journal of Mathematics and Statistics

Mathematical Analysis of Tumor-Immune Interactions based on Michaelis-Menten Kinetics with CAR-T Immunotherapy

Erik J. Xie, Harish Ramasamy, Wei Feng


In this paper, we study the dynamics of tumor growth under immune system surveillance with a mathematical model based on Michaelis-Menten kinetics. In our three-component differential equation system, we accounted for the factor of immunotherapy, its effect on tumor population, and synergy with immune cells. CAR-T, or Chimeric Antigen Receptor T cell, therapy is chosen to be incorporated into the model as a form of immunotherapy due to its promising clinical applications. The stability of the steady-state equilibria of the system is analyzed with parameters from referred sources, and the various patterns of dynamics are demonstrated through numerical simulations. The analysis shows different outcomes of the tumor population given different parameters and initial values, which provides insights into the clinical practicability of CAR-T treatment. Earlier stages of tumor progression at which therapy begins, a critical time frame of therapeutic injection to prevent tumor relapse, and improvement of antigen affinity of the receptors are found to be factors that can enhance CAR-T efficiency and cancer patients' life span. For further analysis, we also propose an expanded system to investigate the potential off-target toxic effects of CAR-T cells on normal host cells. Our instability results and oscillating numerical patterns  suggest non-cooperation between the cell types, posing potential clinical challenges to the therapy.


tumor-immune, immunTumotherapy, CAR-T, Michaelis-Menten, Mathematical biology.

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