在Caputo运营商下建模疫苗接种和环境传播对病毒动态的影响
Emmanuel Addai1,2, Mercy Ngungu3, Musibau Abayomi Omoloye4
1College of Biomedical Engineering, Taiyuan University of Technology, Shanxi Taiyuan 030024, China.
Mathematical biosciences and engineering : MBE
|June 16, 2023
概括
数学建模显示,疫苗接种和卫生习惯显著减少了麻疹的传播. 这项研究表明,分数计算为控制麻风的动态提供了新的见解.
科学领域:
- 流行病学 流行病学
- 数学生物学 数学生物学
- 分数微积分的计算.
背景情况:
- 病毒传播动态需要强大的分析模型.
- 了解疫苗接种和环境因素等干预措施的影响至关重要.
研究的目的:
- 用卡普托的分数顺序来制定和分析感染传播的数学模型.
- 研究疫苗接种和环境因素对疾病动态的影响.
- 探索微积分计算在控制水的潜力.
主要方法:
- 开发一个包含卡普托分数导数的数学模型.
- 分析模型以确定基本复制号码.
- 评估本地和全球对无病平衡的非对称稳定性.
- 固定点定理的应用,以确保解决方案的存在和独特性.
- 数字模拟以获得轨迹并分析参数灵敏度.
主要成果:
- 确定了无病平衡的基本繁殖数和稳定条件.
- 解决方案的存在和独特性是在卡普托分数顺序下确立的.
- 数字轨迹证明了各种参数对麻疹传播的影响.
- 提出了一个假设,认为分数顺序 (记忆指数) 可以控制传输.
结论:
- 疫苗接种,公共卫生教育,个人卫生和消毒有效地减少了水病例.
- 分数计算为理解和潜在控制麻疹传播动态提供了一个框架.
- 分数模型中的"记忆指数"可能为传染病提供一种新的控制策略.
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