Title : Mathematics of atopic dermatitis
Abstract:
Atopic dermatitis (AD) is a chronic inflammatory skin disease influenced by genetic, immunological, and environmental factors. Clinical observations show that AD symptoms vary significantly among individuals, with some experiencing spontaneous remission while others suffer from persistent flare-ups. Understanding this variability requires a quantitative approach that captures the complex dynamics of disease progression. In this presentation, I will introduce a mathematical model based on ordinary differential equations (ODEs) that describes the immune response and skin barrier interactions in AD. The model reveals that AD exhibits multistable states, meaning that disease outcomes depend strongly on initial immune conditions and genetic background. These multiple stable states explain why some individuals experience chronic AD, while others transition toward spontaneous remission. Through bifurcation analysis and dynamical systems theory, we identify tipping points where small changes in immune activity or external triggers can lead to dramatic shifts in disease states. The mathematical framework provides insights into how and when AD may naturally resolve and how interventions can be optimized to guide the system toward remission. By demonstrating the power of mathematical modeling in dermatology, this research highlights the potential for predicting disease progression, optimizing treatments, and developing personalized therapeutic strategies. The results emphasize that AD is not a simple linear condition but a complex, nonlinear system, where mathematical tools can provide valuable clinical insights.
