麻疹感染的分数顺序流行病模型
Philip N A Akuka1, Baba Seidu2, Eric Okyere3
1Department of Mathematics, Bongo Senior High School, Bongo, Ghana.
Scientifica
|October 18, 2024
概括
这项研究引入了分数级麻疹模型来分析疾病传播. 研究结果显示,通过疫苗接种,隔离和治疗,通过减少感染和暴露的人口,有效控制麻疹.
科学领域:
- 流行病学建模的流行病学建模.
- 分数微积分的应用.
- 传染病的动态传染病的动态
背景情况:
- 麻疹在全球范围内仍然是一个重大的公共卫生问题.
- 数学模型对于理解和控制传染病至关重要.
- 分数顺序导数提供了一个更细致的方法,用记忆效应来建模疾病动态.
研究的目的:
- 开发和分析一个非线性,分数顺序的SEVIQR麻疹流行病模型.
- 确定模型平衡的存在,独特性和稳定性.
- 调查预防措施对麻疹传播的影响.
主要方法:
- 卡普托分数级SEVIQR麻疹模型的构建.
- 模型平衡的分析使用雅可比式决定函数和利亚普诺夫函数.
- 使用亚当斯类型预测器-校正器方案的数值模拟.
主要成果:
- 确立了无病和特有平衡的存在,独特性和全球非对称稳定性.
- 基本的复制数 (R0) 通过雅可比定数法确定.
- 数字模拟表明,疫苗接种,隔离和治疗可以减少感染和暴露的人口.
结论:
- 分数顺序建模为麻疹动态提供了宝贵的见解.
- 疫苗接种,隔离和治疗等预防策略是有效控制麻疹的.
- 建议为疫苗分发提供财政支持,以加强疾病控制工作.
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