对于周期性非局部分散操作员和应用程序的基本复制号的非对称行为
Yan-Xia Feng1, Wan-Tong Li2, Yuan Lou3
1School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, Gansu, China.
Journal of mathematical biology
|February 3, 2025
概括
本研究分析了使用非本地运营商在时间周期性环境中的基本复制数. 它发现复制数是单调的频率,但不总是分散率,建立单调性条件和证明本地溶液的存在.
科学领域:
- 数学流行病学数学流行病学
- 动态系统理论 动态系统理论
- 非局部分散建模模型
背景情况:
- 基本繁殖数 (R0) 对于预测流行病传播至关重要.
- 非局部分散运算符和时间周期性环境带来了独特的数学挑战.
- 证明特有溶液存在的标准方法往往无法应用于非本地系统.
研究的目的:
- 在时间周期设置中研究非局部分散运算符的基本复制数 (R0) 的非对称行为.
- 分析频率和分散率对R0.0的影响.
- 在一个时间周期性SIS模型中确定特有周期性溶液的存在和非对称配置文件.
主要方法:
- 对基本复制数 (R0) 的非对称行为分析.
- 对R0的单调性条件的推导,与频率和分散率有关.
- 应用非对称固定点定理和库拉托夫斯基测量非紧度来证明固有解决方案的存在.
主要成果:
- 基本的复制数 (R0) 是一个单调的频率函数.
- 一般来说,R0与散射速率不是单调的,但对于高频率或散射速率来说,单调性是得到的.
- 根据一个时间周期的SIS模型,确定了特有周期性溶液的存在和非对称配置文件.
结论:
- 该研究提供了复杂的流行病学模型中基本繁殖数的全面分析.
- 新的数学技术被用来克服与非局部系统相关的挑战.
- 这些发现有助于更深入地了解不同时间和空间结构的人群中的流行病动态.
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