一类带有饱和治愈率的SEIR格微分动力系统的行波解

doi:10.6040/j.issn.1671-9352.0.2023.188

《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (8): 106-115.doi: 10.6040/j.issn.1671-9352.0.2023.188

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一类带有饱和治愈率的SEIR格微分动力系统的行波解

李敖宇

西安电子科技大学数学与统计学院, 陕西西安 710071

发布日期:2025-07-25
基金资助:
陕西省杰出青年科学基金项目(2020JC-24)

Traveling wave solutions of a class of SEIR lattice differential equations with saturated recovery rate

LI Aoyu

School of Mathematics and Statistics, Xidian University, Xian 710071, Shaanxi, China

Published:2025-07-25

摘要/Abstract

摘要： 研究一类具有饱和治愈率和双线性发生率的离散扩散SEIR模型行波解的存在性。首先利用上下解的方法结合Schauder不动点定理证明截断问题的解的存在性; 其次, 通过极限方法证明当R0>1, c>c^*时, 系统存在连接无病平衡点和正平衡点的行波解, 通过分析证明行波解在无穷远处的渐近行为。

关键词: 饱和治愈率, SEIR模型, 行波解, 格微分方程

Abstract: In this paper, the existence of traveling wave solutions for a kind of discrete diffusion SEIR model with saturated recovery rate and bilinear occurrence rate is studied. Firstly, the existence of solutions for truncationproblem is proved by using the method of upper and lower solutions and the Schauder fixed point theorem; Secondly, it is proved by the limit method that when R0>1, c>c^*, the system has traveling wave solutions connecting the disease-free equilibrium point and the positive equilibrium point. Finally, the asymptotic behavior of traveling wave solution at infinity is proved.

Key words: saturated recovery rate, SEIR model, traveling wave solution, lattice differential equation

中图分类号:

O175

李敖宇. 一类带有饱和治愈率的SEIR格微分动力系统的行波解[J]. 《山东大学学报(理学版)》, 2025, 60(8): 106-115.

LI Aoyu. Traveling wave solutions of a class of SEIR lattice differential equations with saturated recovery rate[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(8): 106-115.

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一类带有饱和治愈率的SEIR格微分动力系统的行波解

Traveling wave solutions of a class of SEIR lattice differential equations with saturated recovery rate

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