Wavelet-Based Mathematical Modelling of Regulatory T-Cell Dynamics: A Novel Framework for Understanding Immune Dysregulation in Autoimmune Disorders

Autoimmune disorders arise from the breakdown of immune tolerance, resulting in abnormal immune responses against the body's own tissues. Despite significant advancements in immunology and molecular biology, understanding the complex dynamics of immune regulation, particularly the role of Regulatory T (Treg) cells, remains a major challenge. Treg-mediated immune regulation involves temporal variability, spatial heterogeneity, and nonlinear feedback mechanisms that are difficult to capture using conventional mathematical approaches. This hypothesis-based research proposes a novel wavelet-based mathematical modelling framework to investigate immune dysregulation and autoimmune disease dynamics. The study integrates mathematical immunology, functional analysis, and computational wavelet techniques to examine interactions between Treg cells, effector T cells, and cytokine signalling pathways. Coupled nonlinear ordinary and partial differential equations (ODEs and PDEs) will be formulated to represent immune system interactions. Their solutions will be analysed within appropriate Hilbert spaces using orthonormal wavelet bases, enabling localized decomposition of immune responses across different temporal and spatial scales. The computational performance of the proposed framework will also be compared with conventional numerical methods to evaluate its accuracy and efficiency. This approach is hypothesized to improve the understanding of localized immune fluctuations, abrupt inflammatory transitions, and loss of immune tolerance. Ultimately, the proposed framework may contribute to improved disease monitoring, early risk stratification, and the development of personalized immunomodulatory strategies for autoimmune disorders.