在非线性分数红疹模型中分析最佳控制技术
W Ahmad1, M A Nazir1, M Rafiq2
1Department of Mathematics, Government College University, Lahore, 54000, Pakistan.
Computers in biology and medicine
|August 30, 2025
概括
这项研究引入了一种使用阿坦甘纳-巴莱努衍生物 (ABC) 改善疫情控制的新型分数红疹模型. 时间依赖的疫苗接种和治疗策略被证明在管理红疹疫情方面更有效和更具成本效益.
科学领域:
- 数学流行病学
- 分数计算
- 疾病建模
背景情况:
- 红疹疫情在全球面临重大健康,社会和经济挑战.
- 有效的疾病控制和了解对于根除疾病的努力至关重要.
- 传统的流行病学模型可能无法完全捕捉复杂的疾病动态,包括记忆效应.
研究的目的:
- 使用卡普托框架 (ABC) 中的阿坦加纳-巴莱努衍生模型开发和分析非线性风疹病例,以结合记忆和遗传效应.
- 使用分数顺序方法调查红疹的传播方式,风险因素和长期影响.
- 制定和解决红疹管理的微分最佳控制问题.
主要方法:
- 开发一个分数顺序的SEITR模型与ABC导数.
- 模型属性的分析:存在,独特性,积极性,局限性.
- 使用莱普诺夫理论的基本复制数和平衡的稳定性分析.
- 分叉分析和灵敏度分析以确定关键值和影响性参数.
- 使用Pontryagin的最大原则制定和解决一个分数最佳控制问题.
- 使用Toufik-Atangana方法进行数值模拟.
主要成果:
- 分数模型成功地捕捉了红疹传播的记忆和遗传效应.
- 分析和数值方法证实了无红疹和流行病的稳定性.
- 敏感性分析确定了影响疾病传播的关键参数.
- 时间依赖的最佳控制策略 (疫苗接种和治疗) 证明比常规控制更有效和更具成本效益.
- 数字模拟显示,随着干预覆盖范围的增加,感染率和成本显著降低.
结论:
- 分数顺序模型,特别是ABC导数,为了解和管理卢贝拉提供了更现实的方法.
- 最佳的防控策略,尤其是依赖时间的策略,对于具有成本效益的疫情控制至关重要.
- 这项研究强调了将先进的数学工具整合为加强对抗红疹的公共卫生干预的重要性.
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