Mathematical Analysis of a Kinetic Model for Cell Movement in Network Tissues

From Kinetic Theory of Multicellular Systems to Hyperbolic Tissue Equations: Asymptotic Limits and Computing

This paper deals with the analysis of the asymptotic limit toward the derivation of macroscopic equations for a class of equations modeling complex multicellular systems by methods of the kinetic theory. After having chosen an appropriate scaling of time and space, a Chapman-Enskog expansion is combined with a closed, by minimization, technique to derive hyperbolic models at the macroscopic level. The resulting macroscopic equations show how the macroscopic tissue behavior can be described by hyperbolic systems which seem the most natural in this context. We propose also an asymptotic-preservi…

关于组织再生的数学模型

On a mathematical model for tissue regeneration

本文提出了一个用于组织再生的PDE-ODE模型，通过对介观尺度细胞动力学输运方程进行抛物线尺度升级获得宏观反应-扩散-趋化方程，证明了解的全局存在性并通过稳定性和分岔分析揭示了趋化驱动的模式形成。

Hypocoercivity and Fast Reaction Limit for Linear Reaction Networks with Kinetic Transport

The long time behavior of a model for a first order, weakly reversible chemical reaction network is considered, where the movement of the reacting species is described by kinetic transport. The reactions are triggered by collisions with a nonmoving background with constant temperature, determining the post-reactional equilibrium velocity distributions. Species with different particle masses are considered, with a strong separation between two groups of light and heavy particles. As an approximation, the heavy species are modeled as nonmoving. Under the assumption of at least one moving species…

细胞运动模型中的时空分数扩散与延迟

Space-time fractional diffusion in cell movement models with delay

本文研究了细胞运动中时空分数扩散模型，通过引入幂律分布的运行和等待时间，推导出非局部扩散方程，探讨了搜索策略和趋化反应对寻找稀有目标时间的影响。

人口 compartmental 感染模型的动力学表述

Kinetic formulation of compartmental epidemic models

本文提出了一种将人口运动与病原体动态耦合的动力学模型，证明其与SIRS模型的兼容性，并探讨了其在流行病学中的应用。

贝叶斯框架下趋化性逆问题的多尺度收敛性

Multiscale convergence of the inverse problem for chemotaxis in the Bayesian setting

本文在贝叶斯框架下探讨了趋化性宏观和微观逆问题间的关系，通过寻求生物体群体转向核的后验分布，证明了两个后验分布的渐近等价性。