Mathematical Validation of a Cancer Model

Understanding cancer cell differentiation is essential for advancing its detection, diagnosis, and treatment. Mathematical models significantly contribute to this by providing a theoretical framework to understand the complex interactions between cancer stem cells, differentiated cancer cells, and immune system components. Such models depend on experimental data and computational simulations to predict tumor dynamics, offering insights into how different cell populations evolve over time. However, to ensure their realistic and consistent outcomes, rigorous mathematical analysis is required, including verification of solution uniqueness, stability, viability, positivity, and boundedness. Such validation guarantees that model's results can be used in both oncological research and clinical applications. In this study, we conduct a comprehensive analysis of an integrative mathematical model of cancer cell differentiation, with a particular focus on its interactions with immune cells. The model captures the dynamic balance between cancer stem cell self-renewal, differentiation into mature tumor cells, and immune-mediated elimination. By employing analytical and numerical techniques, we assess the model's feasibility, stability, and long-term behavior under various biological conditions. Our findings demonstrate that immune system engagement can significantly influence tumor composition and growth, highlighting potential therapeutic targets. This work not only advances theoretical cancer modeling but also provides a foundation for future experimental validation and the development of combined differentiation-immunotherapy approaches. The results underscore the importance of interdisciplinary collaboration in the fight against cancer.