Dynamics for a Diffusive Epidemic Model With a Free Boundary: Spreading Speed

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics Pub Date : 2024-11-27 DOI:10.1111/sapm.12796

Xueping Li, Lei Li, Mingxin Wang

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引用次数: 0

Abstract

We study the spreading speed of a diffusive epidemic model proposed by Li et al. [Dynamics for a diffusive epidemic model with a free boundary: spreading-vanishing dichotomy, Zeitschrift für Angewandte Mathematik und Physik 75 (2024): Article No. 202], where the Stefan boundary condition is imposed at the right boundary, and the left boundary is subject to the homogeneous Dirichlet and Neumann condition, respectively. A spreading-vanishing dichotomy and some sharp criteria were obtained in Li et al. In this paper, when spreading happens, we not only obtain the exact spreading speed of the spreading front described by the right boundary, but derive some sharp estimates on the asymptotical behavior of solution component $(u, v)$ . Our arguments depend crucially on some detailed understandings for a corresponding semi-wave problem and a steady-state problem.

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具有自由边界的扩散性流行病模型的动力学：传播速度

我们研究了 Li 等人提出的扩散流行病模型的传播速度[Dynamics for a diffusive epidemic model with a free boundary: spreading-vanishing dichotomy, Zeitschrift für Angewandte Mathematik und Physik 75 (2024)：文章编号 202]，其中右边界施加斯特凡边界条件，左边界分别施加同质迪里夏特条件和诺依曼条件。在本文中，当扩散发生时，我们不仅得到了右边界描述的扩散前沿的精确扩散速度，而且推导出了解分量 ( u , v ) $(u,v)$ 的渐近行为的一些尖锐估计。我们的论证关键取决于对相应的半波问题和稳态问题的一些详细理解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Studies in Applied Mathematics 数学-应用数学

CiteScore

4.30

自引率

3.70%

发文量

审稿时长

>12 weeks

期刊介绍： Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.