用高效的有限差异方法分析登革热和COVID-19共流的双菌株的非整数顺序数学模型
Emeka F Obiajulu1, Andrew Omame2, Simeon C Inyama3
1Department of Mathematics, Nnamdi Azikiwe University, P.O. Box 5025, Awka, 420110, Nigeria.
Scientific reports
|October 18, 2023
概括
一个新的分数顺序模型分析了登革热和COVID-19的共同循环. 数字结果显示,疾病控制取决于生殖数量,无论分数顺序如何.
科学领域:
- 流行病学 流行病学
- 数学生物学 数学生物学
- 计算科学 计算科学
背景情况:
- 登革热和COVID-19的共同流通构成了重大的公共卫生挑战.
- 数学建模对于理解和控制传染病动态至关重要.
研究的目的:
- 开发和分析一种新的分数顺序数学模型,用于控制共同流通的登革热和COVID-19菌株.
- 调查模型解决方案的存在,独特性和稳定性.
- 评估模型参数和控制措施对疾病传播的影响.
主要方法:
- 利用基于卡普托的分数导数的分数顺序数学模型.
- 用巴纳赫的固定点定理来证明存在和独特性.
- 应用非标准的有限差异 (NSFD) 方法用于数值解决方案.
- 通过平衡点分析和直接Lyapunov方法进行稳定性分析.
主要成果:
- 模型解决方案已被证明存在并且是独一无二的.
- 无感染平衡的非对称稳定性是在基本繁殖数低于单位时建立的.
- 数字模拟显示了基于基本繁殖数的疾病存在或无疾病平衡的趋同.
- 分数顺序和关键率显著影响疾病模式.
结论:
- 分数顺序模型提供了关于登革热和COVID-19联合循环动态的见解.
- 通过管理基本的繁殖数来实现疾病控制.
- 该研究强调了实施控制措施以减轻共传播的重要性.
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