卡普托分数顺序SEIR模型的动态分析,具有一般发病率
1School of Mathematics and Information Science, North Minzu University, Yinchuan, 750021, Ningxia, People's Republic of China. xuluck2001@163.com.
本研究引入了一种新的分数顺序SEIR模型,以准确捕捉复杂的传染病动态,包括无症状传播和记忆效应. 该模型比疾病控制策略的传统方法提供了更高的准确性.
科学领域:
- 流行病学 流行病学
- 数学生物学 数学生物学
- 动态系统 动态系统
背景情况:
- 传统的整数顺序SEIR模型往往过于简化了复杂的疾病传播动态.
- 传染病表现出记忆效应和非局部传播特征,这些特征并未完全被标准模型所捕获.
研究的目的:
- 开发和分析一个包含无症状感染和记忆效应的分数顺序SEIR模型.
- 调查普遍发病率对流行病传播动态的影响.
- 严格分析无病和特有平衡的稳定性.
主要方法:
- 利用卡普托的分数导数来模拟记忆效应和非局部性.
- 运用利亚普诺夫函数对平衡点进行严格的稳定性分析.
- 进行敏感性分析以确定关键的流行病学参数.
- 进行数值模拟以验证理论发现.
主要成果:
- 在特定条件下 () 证明了无疾病平衡的全球非对称稳定性.
- 在不同的条件下,证明了在不同条件下为特有平衡的全球非对称稳定性 ().
- 证明分数顺序模型捕捉了整数顺序模型错过的复杂动态.
结论:
- 开发的分数顺序SEIR模型为传染病动态提供了更准确的表示.
- 分数计算在流行病学中为模拟非局部和记忆依赖现象提供了优势.
- 研究结果为优化复杂传染病的控制策略提供了见解.
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