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Pattern dynamics of the reaction-diffusion immune system

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  • Qianqian Zheng
  • Jianwei Shen
  • Zhijie Wang

Abstract

In this paper, we will investigate the effect of diffusion, which is ubiquitous in nature, on the immune system using a reaction-diffusion model in order to understand the dynamical behavior of complex patterns and control the dynamics of different patterns. Through control theory and linear stability analysis of local equilibrium, we obtain the optimal condition under which the system loses stability and a Turing pattern occurs. By combining mathematical analysis and numerical simulation, we show the possible patterns and how these patterns evolve. In addition, we establish a bridge between the complex patterns and the biological mechanism using the results from a previous study in Nature Cell Biology. The results in this paper can help us better understand the biological significance of the immune system.

Suggested Citation

  • Qianqian Zheng & Jianwei Shen & Zhijie Wang, 2018. "Pattern dynamics of the reaction-diffusion immune system," PLOS ONE, Public Library of Science, vol. 13(1), pages 1-11, January.
    • Handle: RePEc:plo:pone00:0190176
    DOI: 10.1371/journal.pone.0190176
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    References listed on IDEAS

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    1. Li, Meifeng & Han, Bo & Xu, Li & Zhang, Guang, 2013. "Spiral patterns near Turing instability in a discrete reaction diffusion system," Chaos, Solitons & Fractals, Elsevier, vol. 49(C), pages 1-6.
    2. Duccio Fanelli & Claudia Cianci & Francesca Patti, 2013. "Turing instabilities in reaction-diffusion systems with cross diffusion," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 86(4), pages 1-8, April.
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