发表机构
University of Naples “Federico II”; Istituto Nazionale di Alta Matematica “F. Severi”; University of Palermo; Parthenope University of Naples; University of Trento（那不勒斯费德里科二世大学; F·塞韦里高等数学国家研究所; 巴勒莫大学; 那不勒斯帕耳忒诺佩大学; 特伦托大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究分析具有缓慢免疫丧失的空间SIRS流行病模型，利用几何奇异摄动理论揭示其行波前的快慢结构，经数值模拟验证理论，明确行波前由多段连接构成。
AI 中文摘要
我们研究受感染种群的扩散作用下的空间SIRS流行病模型中行波前解的出现。该模型因存在控制免疫丧失的小参数而呈现出自然的快慢结构，这会诱导动力学中的尺度分离。通过行波约化，偏微分方程组被转化为奇异摄动常微分方程组，我们在几何奇异摄动理论框架内对其进行分析。在奇异极限下，我们研究由层问题控制的快速偏移，以及靠近临界流形的慢演化。特别地，我们识别出追踪慢、快状态之间转变的进入-退出机制，并推导出进入-退出动力学的定量表征。对完整系统的数值模拟证实了所提出的几何图像的有效性。行波前被证明由局部、快速和慢速段的连接组成，与理论分析一致。
英文摘要
We investigate the emergence of traveling front solutions in a spatial SIRS epidemic model with diffusion acting on the infected population. The model exhibits a natural slow-fast structure due to the presence of a small parameter governing the loss of immunity, which induces a separation of scales in the dynamics. Using a traveling wave reduction, the PDE system is transformed into a singularly perturbed system of ODEs, which we analyze within the framework of Geometric Singular Perturbation Theory. In the singular limits, we study the fast excursions governed by the layer problem, and the slow evolution close to the critical manifold. In particular, we identify an entry-exit mechanism tracking the transitions between slow and fast regimes, and derive a quantitative characterization of the entry-exit dynamics. Numerical simulations of the full system confirm the validity of the proposed geometric picture. The traveling front is shown to consist of a concatenation of local, fast, and slow segments, in agreement with the theoretical analysis.
Comments20 pages, 7 figures
