Controlling severe atopic dermatitis dynamics

Atopic dermatitis (AD) is a pervasive inflammatory skin disease, with severe forms constituting a refractory phenotype that devastates quality of life through relentless pruritus, widespread lesions, and resistance to standard therapies. A central clinical challenge is to steer the disease away from chronic inflammation and sustain remission. Framed in dynamical terms, this amounts to controlling the remission dynamics of AD. We establish a mathematical framework for the canonical two-phase clinical strategy: the "Get Control" (GC) phase, where antibiotics are administered to suppress acute inflammation, and the "Keep Control" (KC) phase, where emollients are applied to maintain remission. A key question of therapeutic relevance is: what are the minimal drug doses required for each phase to succeed? Our analysis reveals scaling laws that tie the control amplitude (drug dose) directly to two fundamental determinants of severe AD: barrier permeability and immune clearance capacity. These laws delineate the antibiotic dosage required to exit chronic inflammation in GC and the emollient level needed to sustain remission in KC. The uncovered scaling principles elevate treatment design from heuristic to quantitative, leading to a theoretical framework for precision, phase-based analysis of treatment control in severe AD. By aligning clinical intervention with the dynamical structure of the disease, the framework points toward personalized, optimally dosed strategies for overcoming refractory cases.