A new study published in Chaos by AIP Publishing reports on Mar. 17 that researchers from Pusan National University in Korea and Arizona State University have used nonlinear dynamics to determine the minimal dose of medication needed to treat atopic dermatitis, commonly known as eczema.
The research is significant because chronic illnesses like eczema are unpredictable, with periods of remission interrupted by sudden flare-ups. Understanding how small physiological changes can lead to large effects may help improve treatment outcomes for patients.
Nonlinear dynamics is a branch of mathematics that studies systems where relationships between variables are not proportional. In health care, this approach has been applied to diseases in neurology, cardiology, endocrinology, and immunology. "These applications illustrate a broader principle: Many chronic diseases can be interpreted as nonlinear dynamical systems operating near critical thresholds, where small physiological changes may lead to qualitatively different outcomes," said author Yoseb Kang.
The researchers divided their mathematical approach into two regimes: one focused on suppressing active flare-ups and another aimed at maintaining long-term remission. They found that while the amount of antibiotics required during flare-ups scales predictably with skin permeability and immune response, the maintenance phase is highly nonlinear. "In this regime, relatively small physiological changes can significantly increase the maintenance burden," said Kang.
Kang also said, "Instead of only describing disease evolution, we aimed to determine the minimal intervention required to deliberately move the system from a chronic state into remission and then maintain stability." He added that tying treatment outcomes not just to medication dosage but also to patient-specific attributes could provide clarity for both patients and providers. "This framework may help explain why some patients require strong early intervention and why maintaining remission can sometimes demand sustained effort even after visible improvement," Kang said. "In the longer term, if measurements of barrier function or immune markers are incorporated into models, treatment intensity could be adjusted more precisely to a patient's physiological state."
The findings suggest that mathematical modeling could play an important role in personalizing treatments for chronic conditions like eczema.
