发表机构
Fujian Medical University; Boston University; Chinese Academy of Sciences; University of Chinese Academy of Sciences; Northeastern University（福建医科大学; 波士顿大学; 中国科学院; 中国科学院大学; 东北大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究肿瘤细胞、免疫效应细胞和趋化因子信号通过反应-扩散-趋化系统相互作用，建立计算肿瘤学模型，经无量纲化等处理，进行线性稳定性分析并验证相关结果。
AI 中文摘要
空间肿瘤-免疫异质性是实体肿瘤进展、免疫浸润和免疫排斥的关键特征。我们开发了一个计算肿瘤学模型，其中肿瘤细胞、免疫效应细胞和趋化因子信号通过具有无通量边界的有界组织域上的反应-扩散-趋化系统相互作用。趋化因子由肿瘤细胞和肿瘤-免疫接触产生，招募免疫细胞并引导趋化迁移。无量纲化后，我们建立了正性、肿瘤密度界和免疫/趋化因子质量估计。我们确定了无肿瘤平衡，推导了免疫控制阈值σ₀>δ，并将共存简化为一个标量方程。关于共存的线性稳定性分析产生了一个模式色散关系，其中趋化作用表现为波数放大耦合，在临界灵敏度以上产生有限波长不稳定性。具有迎风趋化通量的保守有限体积格式验证了阈值、主导不稳定模式、灵敏度图、正性、收敛性和残差一致性。
英文摘要
We develop a reaction--diffusion--chemotaxis model for spatial tumour--immune--chemokine dynamics that couples logistic tumour growth, immune-mediated killing, chemokine-dependent immune recruitment, chemotactic migration, and signal production. For the nondimensional system, we establish local classical solvability, nonnegativity, a uniform tumour-density bound, and global mass estimates for the immune and chemokine components. The tumour-free equilibrium is stable precisely when the baseline immune-control index satisfies \(σ_0/δ>1\), whereas positive homogeneous coexistence is characterized by a scalar nonlinear equation. Linearization in the Neumann Laplacian eigenbasis yields a mode-dependent cubic dispersion relation, showing that chemotaxis does not alter the tumour-invasion threshold but can destabilize homogeneous coexistence through a finite-wavelength oscillatory instability above a critical sensitivity \(ξ_c\). A conservative finite-volume discretization with upwind chemotactic fluxes and implicit backward differentiation formula time integration is used to test these predictions. Numerical experiments recover the analytical equilibria and growth rates, identify the dominant unstable mode, reproduce the transition to spatial heterogeneity, and quantify the effects of immune recruitment, decay, and diffusion on the stability boundary. Grid-refinement, mass-balance, residual, and nonnegativity diagnostics support the computational reliability of the results.
