从SIR/SEIR/SVEIR模型到趋化系统：爱因斯坦范式内感染传播的时空机制分析
From the SIR/SEIR/SVEIR Model to a Chemotactic System: Analysis of Spatiotemporal Mechanisms of Infection Spread within the Einstein Paradigm
- Department of Automation for Scientific Research, Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University（莫斯科国立大学计算数学与Cybernetics学院自动化科研系）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究以SIR/SEIR/SVEIR等传染病模型为基础，构建含恐惧/规避效应的扩散-趋化PDE系统，结合数值方法分析感染传播的时空机制，其参数经真实流感数据校准验证。
AI中文摘要：
本研究考察SIR/SEIR模型类及其扩展为基于常微分方程（ODE）的SVEIR系统，该系统的参数通过真实流感暴发数据进行校准与验证。理论部分借助皮卡-林德勒夫（Picard-Lindelöf）定理确立SVEIR模型解的存在性与唯一性，并分析容许区域的不变性。为描述城市环境中感染的时空传播，将SIR框架扩展为扩散-趋化偏微分方程（PDE）系统，引入额外项以表征系统动力学中的恐惧/规避效应。提出的数值工作流包含网格离散化、镜像延拓实现的诺伊曼边界条件、半隐式IMEX时间步进格式及稀疏线性求解；计算正确性通过检查总人口守恒等方式进行监控。
英文摘要：
This work investigates the class of SIR/SEIR models and their extension to an ODE-based SVEIR system, whose parameters are calibrated and validated using real influenza outbreak data. The theoretical part establishes existence and uniqueness of solutions for the SVEIR model via the Picard-Lindelof theorem and analyzes invariance of the admissible region. To describe spatiotemporal infection spread in an urban setting, a diffusion-chemotaxis extension of the SIR framework is formulated as a PDE system; an additional term is introduced to represent fear/avoidance effects in the system dynamics. A numerical workflow is proposed, including grid discretization, Neumann boundary conditions enforced by mirror extension, a semi-implicit IMEX time-stepping scheme, and sparse linear solves; computational correctness is monitored, in particular, by checking conservation of the total population.
