Lee Seongwon, Kim Se-Woong, Oh Youngmin, Hwang Hyung Ju
National Institute for Mathematical Sciences, Daejeon, Republic of Korea.
Pohang University of Science and Technology, Pohang, Republic of Korea.
J Math Biol. 2017 Nov;75(5):1101-1131. doi: 10.1007/s00285-017-1108-7. Epub 2017 Feb 27.
In this paper, we study how chemotaxis affects the immune system by proposing a minimal mathematical model, a reaction-diffusion-advection system, describing a cross-talk between antigens and immune cells via chemokines. We analyze the stability and instability arising in our chemotaxis model and find their conditions for different chemotactic strengths by using energy estimates, spectral analysis, and bootstrap argument. Numerical simulations are also performed to the model, by using the finite volume method in order to deal with the chemotaxis term, and the fractional step methods are used to solve the whole system. From the analytical and numerical results for our model, we explain not only the effective attraction of immune cells toward the site of infection but also hypersensitivity when chemotactic strength is greater than some threshold.
在本文中，我们通过提出一个最小数学模型——一个反应扩散对流系统，来研究趋化性如何影响免疫系统，该系统描述了抗原与免疫细胞之间通过趋化因子的相互作用。我们分析了趋化性模型中出现的稳定性和不稳定性，并通过能量估计、谱分析和自举论证找到了不同趋化强度下的条件。还对该模型进行了数值模拟，使用有限体积法来处理趋化项，并使用分步方法求解整个系统。从我们模型的分析和数值结果中，我们不仅解释了免疫细胞向感染部位的有效吸引，还解释了趋化强度大于某个阈值时的超敏反应。
