具时滞扩散效应的病原体-免疫模型的稳定性及分支  

Stability and Bifurcation of a Pathogen-Immune Model with Delay and Diffusion Effects

作　　者：王晶囡[1] 杨德中 Wang Jingnan;Yang Dezhong(Department of Applied Mathematics,Harbin University of Science and Technology,Harbin 150080)

机构地区：[1]哈尔滨理工大学应用数学系,哈尔滨150080

出　　处：《数学物理学报（A辑）》2021年第4期1204-1217,共14页Acta Mathematica Scientia

基　　金：国家自然科学基金(11801122);黑龙江省自然科学基金(A2018008)。

摘　　要：为了了解病原体与免疫细胞相互作用过程中存在的扩散因素与时滞因素对其动力学行为的影响,建立了带有齐次Neumann边界条件的具时滞病原体-免疫反应扩散模型.以病原体与免疫细胞的扩散比率和免疫时滞为参数,通过分析该模型在正稳态解处线性化系统特征根的分布,并利用泛函微分方程分支理论,得到正稳态解经历Turing失稳的充要条件以及经历Hopf分支的条件.利用Matlab数值模拟直观地展示了病原体与宿主免疫在临界点附近经历Turing失稳和Hopf分支的动力学行为,并解释了动力学行为所对应的生物医学意义,为控制病原体生长提供了一定的理论支持.In order to understand the effects of diffusion and time-delay factors on the dynamics between pathogens and immune cells,a delayed pathogen-immune reaction diffusion model with homogeneous Neumann boundary condition is established.By using the diffusion ratio of pathogen-immune cells and immune delay as two parameters,the characteristic root distribution of the linearized system at the positive steady state is analyzed and the necessary and sufficient conditions for the positive steady state to undergo Turing instability and Hopf bifurcation are obtained by using the bifurcation theory of functional differential equations.In addition,the dynamic behavior close to the critical value of Turing instability and Hopf bifurcation is intuitively shown by Matlab numerical simulation.The biological and medicinal significance of corresponding dynamic behaviors are discussed.Furthermore,the obtained results provide certain theoretical support for controlling the growth of pathogen.

关 键 词：病原体免疫 反应扩散 时滞 Turing分支 HOPF分支 

分 类 号：O175.29[理学—数学]