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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]

Complex natural systems present characteristics of scalar invariance. This behavior has been experimentally verified and a large related bibliography has been reported. Multifractal Formalism is a way to evaluate this kind of behavior. In the past years, different numerical methods to estimate the multifractal spectrum have been proposed. These methods could be classified into those that originated from the wavelet analysis and others from numerical approximations like the Multifractal Detrended Fluctuation Analysis (MFDFA), proposed by Kantelhardt and Stanley. Recently, S. Jaffard and co-workers proposed the Wavelet Leaders (WL) method that exploits the potential of wavelet analysis and the efficiency of the Multiresolution Wavelet Schema. In a previous work, we checked that both methods are equivalent for estimating fractal properties in a series from singular measures. Now, we apply MFDFA and WL to natural signals with self-similar structures, but unknown multifractal spectrum. We observe that some differences appear in their respective estimations, particularly when the signals are corrupted with fractional Gaussian noise. [ABSTRACT FROM AUTHOR]