一个离散的生态流行病学模型的分支和混合控制与霍林格型III
Lizhi Fei1,2, Hengmin Lv1,3, Heping Wang1,2
1College of Science, Nanchang Institute of Technology, Nanchang, Jiangxi, P. R. China.
PloS one
|July 18, 2024
概括
这项研究引入了一个3D离散的生态流行病学模型,采用霍林格型III反应. 该研究分析了模型稳定性,分叉,并应用混合控制策略来管理复杂的动态.
科学领域:
- 数学生物学 数学生物学
- 生态生态学 生态生态学
- 流行病学 流行病学
背景情况:
- 生态流行病学模型对于了解人口中的疾病动态至关重要.
- 霍林的III型功能反应是模拟捕食者-猎物和宿主-病原体相互作用的关键组成部分.
- 离散时间模型提供了对不同时间间隔的人口动态的见解.
研究的目的:
- 提出和分析一个三维离散的生态流行病学模型,包括霍林格型III功能反应.
- 研究解决方案的局限性,所有固定点的存在和稳定性.
- 探索分叉现象,特别是跨临界,尼马克-萨克和翻转分叉,并控制尼马克-萨克分叉.
主要方法:
- 制定一个三维离散的生态流行病学模型.
- 解决方案的局限性的分析.
- 使用线性化对固定点稳定性的研究.
- 双叉理论的应用,以识别跨临界,尼马克-萨克和翻转双叉.
- 开发和应用混合控制策略 (参数扰动和状态反).
- 数字模拟用于验证分析结果.
主要成果:
- 确定了拟议模型的解决方案的局限性.
- 确定了所有固定点存在和稳定的条件.
- 确定了跨临界分叉表面.
- 该系统被证明在正定点上表现出Neimark-Sacker和翻转分叉.
- 一种混合控制策略成功地应用于管理Neimark-Sacker分叉.
- 数字模拟证实了分析结果.
结论:
- 拟议的离散生态流行病学模型表现出丰富的动态行为,包括各种分叉.
- 稳定性分析和分叉调查为模型的复杂性提供了更深入的理解.
- 开发的混合控制策略为稳定系统和控制分叉提供了一种有效的方法.
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