This review examines recent developments in modeling the interaction between tumor cells and the immune system, with a specific focus on the application of delay differential equations (DDEs). The models serve as crucial tools to simulate and predict the immune response to tumor proliferation, thus facilitating a more effective evaluation of clinical and therapeutic strategies before their implementation. This approach enables the hypothetical testing of various interventions, thus resulting in significant time and resource savings. The central theme is the integration of DDEs to represent biologically realistic time delays. These delays—inherent in biological processes such as the activation and migration of immune cells to the tumor site—are essential for a more accurate and dynamic representation of the system. Furthermore, this document acknowledges the inherent limitations of these mathematical models, which are simplified representations of complex biological phenomena by nature. The precision and practical utility of these models depend on the use of biologically plausible delay formulations, the validation of parameters with empirical data, and the alignment of model predictions with clinical outcomes. Ultimately, this work underscores the considerable potential and significant challenges of employing mathematical models as a bridge between theoretical understanding and applied oncology.
Citation: John A. Arredondo, Andrés Rivera. Recent advances in ODEs modeling of tumor-immune responses: a focus on delay effects[J]. Mathematical Biosciences and Engineering, 2025, 22(12): 3060-3087. doi: 10.3934/mbe.2025113
This review examines recent developments in modeling the interaction between tumor cells and the immune system, with a specific focus on the application of delay differential equations (DDEs). The models serve as crucial tools to simulate and predict the immune response to tumor proliferation, thus facilitating a more effective evaluation of clinical and therapeutic strategies before their implementation. This approach enables the hypothetical testing of various interventions, thus resulting in significant time and resource savings. The central theme is the integration of DDEs to represent biologically realistic time delays. These delays—inherent in biological processes such as the activation and migration of immune cells to the tumor site—are essential for a more accurate and dynamic representation of the system. Furthermore, this document acknowledges the inherent limitations of these mathematical models, which are simplified representations of complex biological phenomena by nature. The precision and practical utility of these models depend on the use of biologically plausible delay formulations, the validation of parameters with empirical data, and the alignment of model predictions with clinical outcomes. Ultimately, this work underscores the considerable potential and significant challenges of employing mathematical models as a bridge between theoretical understanding and applied oncology.
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John A. Arredondo, Andrés Rivera. Recent advances in ODEs modeling of tumor-immune responses: a focus on delay effects[J]. Mathematical Biosciences and Engineering, 2025, 22(12): 3060-3087. doi: 10.3934/mbe.2025113
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