A nonlinear transient-dynamics approach to atopic dermatitis: Role of spontaneous remission

Atopic dermatitis (AD) is a common skin disease that can occur in all age groups. An intriguing phenomenon associated with AD is spontaneous remission, in which the symptoms can disappear even without any treatment, especially for patients at a young age. From the point of view of dynamical evolution, spontaneous remission in AD is a transient phenomenon. A clinic implication is that, if the transient time is short, then aggressive treatment may not be necessary. A key question is thus, statistically, how long the transient time can be? Due to the lack of clinic data, mathematical modeling is a viable approach to addressing this question. Modeling AD as a nonsmooth dynamical system and regarding the disease as a transient phenomenon with spontaneous remission marking the end of the transient, we obtain a quantitative understanding of the statistical characteristics of AD. In particular, we find that, depending on the immune state, two different types of transient behaviors can arise. For type-I spontaneous remission characterized by a healthy immune level with its skin state exhibiting mild oscillations, the transient time is short, which typically occurs in patients between infancy and childhood. In contrast, type-II spontaneous remission is characterized by a low immune level and its skin state exhibits severe oscillations with a long recovering time. Quantitatively, a scaling relation exists between the average transient time (or recovery time) and some key physiological parameters, revealing that the transient is superpersistent in the sense that its average lifetime can diverge in a drastic way: e∞ as a bifurcation parameter approaches a critical value. In this case, the disease is essentially permanent, thereby requiring and justifying active treatment.