在复杂网络上的时空传染病模型的模式动态分析和参数识别
Tao Yang1, Linhe Zhu1, Shuling Shen2
1School of Mathematical Sciences, Jiangsu University, Zhenjiang, China.
Mathematical biosciences
|July 18, 2025
概括
这项研究模拟了传染病在网络上传播的模式,其中有道和延迟. 高级网络和宣传影响动态,有助于准确预测疾病传播.
科学领域:
- 数学生物学 数学生物学
- 网络科学 网络科学
- 流行病学 流行病学
背景情况:
- 反应-扩散系统对于建模空间现象至关重要.
- 导向和时间延迟显著影响系统动态,特别是在生物环境中.
- 网络结构为了解疾病传播中的复杂相互作用提供了一个框架.
研究的目的:
- 研究在离散网络上具有向导的反应-扩散系统.
- 开发一种包含时间延迟的传染病传播模型.
- 分析网络拓和导向对疾病动态的影响.
主要方法:
- 对平衡点存在的分析和时间延迟的线性近似.
- 图灵不稳定条件的确定.
- 构建低级和高级网络结构.
- 为参数识别应用最佳控制的应用.
- 广泛的数值模拟.
主要成果:
- 确定了平衡和图灵不稳定的条件.
- 证明了导向和网络顺序对系统动态的影响.
- 在复杂网络中成功应用了对参数识别的最佳控制.
- 验证了模型对现实世界的数据匹配和预测的有效性.
结论:
- 宣传和更高层次的网络在塑造疾病传播动态方面发挥着至关重要的作用.
- 开发的模型有效地捕捉了复杂的时空模式.
- 该方法为流行病学建模和预测提供了一个强大的框架.
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