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Model reduction aims to simplify complex models by decreasing the number of equations, variables, or parameters while preserving key characteristics. This approach enhances accessibility, comprehensibility, and computational efficiency, enabling a more focused analysis of relevant variables. In this study, we describe the reduction process of a population model that incorporates cancer cell differentiation and its interaction with the immune system, maintaining the fundamental dynamics and evolution of the original model. This led to a substantial reduction in variables and parameters, creating a more efficient model suitable for computational simulations, mathematical analysis, and quantitative understanding of population dynamics. Additionally, we performed a global sensitivity analysis of model parameters using the Sobol and eFast methods, revealing insights into differences and similarities in results from a biological perspective. Our findings emphasize the critical importance of understanding and controlling parameters related to the reproduction and death rates of differentiated cancer cells, as small variations in these parameters can have significant effects on model outcomes. This underscores the importance of thoroughly understanding these essential biological variables and processes in cancer treatment, as they have a significant impact on model outcomes and, consequently, on the development of more effective therapies. [ABSTRACT FROM AUTHOR]