| Abstract: |
| Chimeric Antigen Receptor (CAR) T cell therapy has shown remarkable success in treating B cell malignancies, yet the long term dynamics of CAR T cells, tumor cells, and healthy B cells remain incompletely understood. We present a mathematical model of CAR T cell therapy for leukemia that incorporates a constant influx of healthy B cells from the bone marrow, a source term previously neglected, as well as CAR T cell inactivation by tumor cells. The model is analyzed as a system of nonlinear ordinary differential equations. We characterize the existence, uniqueness, and local and global stability of steady states, revealing how the interplay between CAR T cell activation and tumor burden determines outcomes such as remission or relapse. Bifurcation analysis identifies critical thresholds for treatment success. For periodic treatment protocols, we prove the existence of periodic solutions and derive conditions for tumor eradication. Additionally, we analyze an impulsive treatment regimen and obtain criteria for local stability of tumor free periodic solutions. Our results highlight the dual role of healthy B cells in sustaining CAR T cell activity and provide a theoretical framework for optimizing treatment strategies. |
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