Abstract
Atopic dermatitis (AD) is a common inflammatory skin disease, whose incidence is currently increasing worldwide. AD has a complex etiology, involving genetic, environmental, immunological, and epidermal factors, and its pathogenic mechanisms have not yet been fully elucidated. Identification of AD risk factors and systematic understanding of their interactions are required for exploring effective prevention and treatment strategies for AD. We recently developed a mathematical model for AD pathogenesis to clarify mechanisms underlying AD onset and progression. This model describes a dynamic interplay between skin barrier, immune regulation, and environmental stress, and reproduced four types of dynamic behaviour typically observed in AD patients in response to environmental triggers. Here, we analyse bifurcations of the model to identify mathematical conditions for the system to demonstrate transitions between different types of dynamic behaviour that reflect respective severity of AD symptoms. By mathematically modelling effects of topical application of antibiotics, emollients, corticosteroids, and their combinations with different application schedules and doses, bifurcation analysis allows us to mathematically evaluate effects of the treatments on improving AD symptoms in terms of the patients’ dynamic behaviour. The mathematical method developed in this study can be used to explore and improve patient-specific personalised treatment strategies to control AD symptoms.
Highlights
Atopic dermatitis (AD), known as atopic eczema, is one of the most common chronic skin diseases, whose prevalence is around 10–20% in developed countries and is rapidly increasing in developing countries (Flohr and Mann, 2014; Guo et al, 2016; Weidinger and Novak, 2016)
By modelling the effects of three major treatments for AD, namely topical application of antibiotics (Lin et al, 2007), emollients (Simpson et al, 2014), and corticosteroids (Leyden et al, 1974; Nilsson et al, 1992), we evaluate the effects of different treatments, at different doses and combinations, on dynamic phenotypes, via bifurcation analysis of the model of AD pathogenesis
We assume G(t) to be constant, either at Goff or Gon, as we focus on the bifurcation diagram for each of these cases, rather than the progression of AD
Summary
Atopic dermatitis (AD), known as atopic eczema, is one of the most common chronic skin diseases, whose prevalence is around 10–20% in developed countries and is rapidly increasing in developing countries (Flohr and Mann, 2014; Guo et al, 2016; Weidinger and Novak, 2016). In order to systematically explore the patient-specific effects of different therapeutic interventions, here we derive mathematical conditions that determine whether and how the system can be perturbed by treatments to transition to a more physiological dynamic phenotype, for example, from the asymptomatic-butsusceptible oscillation to the healthy recovery dynamic phenotypes. We obtain analytical parameter conditions for transitions between different dynamic phenotypes. The method developed in this study, based on bifurcation analysis, enables us to systematically stratify the patients with different dynamic phenotypes and to evaluate patient-specific optimal treatment strategies (the types and combinations of drugs and application schedules) that improve prevention and control of AD by achieving preferable transition of dynamic phenotypes
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