Complexity and multistability of a nonsmooth atopic dermatitis system

Abstract

Atopic dermatitis (AD) has been known as the most common allergic inflammatory skin disease and its immunopathogenetic network is very complex. In this paper, to investigate the complexity of AD, we study a in silico AD model based on the mechanisms of AD disease pathogenesis, which is described by a nonsmooth system with three switches. We uncover a new oscillating behavior Os called Serious Oscillation, which can make a clear distinction between oscillating behaviors. It thus makes possible to classify AD attractors, which is very similar to AD clinical symptoms used in SCORAD index. A striking finding is that by investigating the existence and the stability of all found attractors on the parameter space for Barrier permeability κP and Immune responses αI, there exist many different types of bi- and multistability: four and five different types of bistability and multistability, respectively. By characterizing these different types of bi- and multistability, we finally conclude that the complexity of AD is caused by multistability detected in too much wide parameter ranges. In addition, we show a peculiar bifurcation phenomenon occurred in nonsmooth dynamical system. Our results suggest that the existence of multistability will make it possible to better understand the complexity of AD, which can be applicable in the development of new therapy strategies.