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Appl. Sci. 2016, 6(9), 252;

Chronic Inflammation in the Epidermis: A Mathematical Model

Institute of Industrial Science, University of Tokyo, Tokyo 153-8505, Japan
College of Science and Engineering, Aoyama Gakuin University, Kanagawa 252-5258, Japan
Department of Mathematical Sciences, Ulsan National Institute of Science and Technology, Ulsan 44919, Korea
Department of Radiology, Seoul National University Hospital, Seoul 03080, Korea
Department of Mathematics, Konkuk University, Seoul 05029, Korea
Department of Mathematics, Ohio State University, Columbus, OH 43210, USA
Author to whom correspondence should be addressed.
Academic Editor: Yang Kuang
Received: 11 June 2016 / Revised: 31 August 2016 / Accepted: 31 August 2016 / Published: 9 September 2016
(This article belongs to the Special Issue Dynamical Models of Biology and Medicine)
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The epidermal tissue is the outmost component of the skin that plays an important role as a first barrier system in preventing the invasion of various environmental agents, such as bacteria. Recent studies have identified the importance of microbial competition between harmful and beneficial bacteria and the diversity of the skin surface on our health. We develop mathematical models (M1 and M2 models) for the inflammation process using ordinary differential equations and delay differential equations. In this paper, we study microbial community dynamics via transcription factors, protease and extracellular cytokines. We investigate possible mechanisms to induce community composition shift and analyze the vigorous competition dynamics between harmful and beneficial bacteria through immune activities. We found that the activation of proteases from the transcription factor within a cell plays a significant role in the regulation of bacterial persistence in the M1 model. The competition model (M2) predicts that different cytokine clearance levels may lead to a harmful bacteria persisting system, a bad bacteria-free state and the co-existence of harmful and good bacterial populations in Type I dynamics, while a bi-stable system without co-existence is illustrated in the Type II dynamics. This illustrates a possible phenotypic switch among harmful and good bacterial populations in a microenvironment. We also found that large time delays in the activation of immune responses on the dynamics of those bacterial populations lead to the onset of oscillations in harmful bacteria and immune activities. The mathematical model suggests possible annihilation of time-delay-driven oscillations by therapeutic drugs. View Full-Text
Keywords: epidermis; mathematical model; bacterial inflammation; bacterial competition epidermis; mathematical model; bacterial inflammation; bacterial competition

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Nakaoka, S.; Kuwahara, S.; Lee, C.H.; Jeon, H.; Lee, J.; Takeuchi, Y.; Kim, Y. Chronic Inflammation in the Epidermis: A Mathematical Model. Appl. Sci. 2016, 6, 252.

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