WASHINGTON, March 17, 2026 — Anyone with a chronic illness understands the struggle of living with a disease that is deeply unpredictable. Many such illnesses are characterized by long periods of remission broken up by sudden, debilitating flare-ups. Sometimes these flare-ups have obvious causes, but often they seem to come out of nowhere, which can be frustrating and unpleasant.
The solution might come from a complex field of mathematics called nonlinear dynamics. This field involves changing systems where the relationships between variables are not proportional. In a nonlinear system, a small change in one area might lead to a very large change somewhere else, something colloquially known as the butterfly effect. This makes nonlinear systems difficult to predict and challenging to study.
In Chaos, by AIP Publishing, a pair of researchers from Pusan National University in Korea and Arizona State University used the principles of nonlinear dynamics to calculate the minimal dose of medication required to treat atopic dermatitis, commonly referred to as eczema.
In health care, nonlinear dynamics are applied to study 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 used their understanding of nonlinear dynamics to explore why eczema flare-ups happen and how to improve treatment outcomes.
"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," said Kang.
The duo divided their mathematical approach into two regimes: In the first, the goal of treatment is to suppress an active flare-up. The second regime is a long-term effort to keep eczema in remission and prevent future flare-ups. In both treatments, patients use medications to control the condition, and the amount of medication required is determined by the skin's permeability and the patient's immune response.
However, the researchers found the specifics were drastically different between the two regimes. In the first phase, the amount of antibiotics required scales proportionally and predictably with permeability and immune response.
But in the second phase, the relationship is highly nonlinear.
"In this regime, relatively small physiological changes can significantly increase the maintenance burden," said Kang.
Tying treatment outcomes not just to medication dosage but also to patient-specific attributes can provide clarity to both patients and providers, and the predictive power of this analysis could help identify appropriate treatment plans.
"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," said Kang. "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."
