具扩散性的病原体-宿主免疫模型的Turing不稳性

Turing Instability in a Pathogen-Host Immune Model with Diffusion

为了研究在病原体与宿主免疫细胞相互作用过程中存在的扩散因素对其动力学的影响,建立了带有齐次Neumann边界条件的病原体-宿主免疫反应扩散模型。以病原体与免疫细胞的扩散比率ρ为参数,利用偏微分方程理论,讨论了在正平衡解处线性化系统特征根的分布,得到模型在正平衡解处经历Turing不稳性的临界条件。并利用Matlab数值模拟了病原体-宿主免疫模型经历Turing不稳性的动力学现象,进一步讨论了Turing不稳性的动力学现象所蕴含的病原体与免疫细胞的扩散机理。

In order to study the effects of diffusion function on the dynamics between pathogens and host immune cells,a reaction-diffusion model of pathogen-host immune with homogeneous Neumann boundary condition is constructed.Taking the diffusion ratioρof pathogens and immune cells as a parameter,the critical conditions of Turing instability are obtained by using partial differential equation theories to discuss the characteristic root distribution of the linearized system at the positive equilibrium solution.Matlab numerical simulations are performed to show the dynamic phenomenon of Turing instability in the pathogen-host immune model.Furthermore,diffusion mechanisms of the pathogen and immune cell in the dynamic phenomenon of Turing instability are discussed.