一个分数顺序密码菌病流行病模型的统计估计
Nauman Ahmed1,2, Wissal Audah Alhilfi3, Hanan A Z AlMansury4
1Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan.
Scientific reports
|April 22, 2025
概括
这项研究使用分数顺序的流行病模型分析了密码菌病的动态. 一种新的数值方法确保了模型的稳定性和积极性,这对于了解疾病传播至关重要.
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:
- 密码化症是严重的公共卫生问题.
- 数学模型对于理解疾病传播动态至关重要.
- 分数顺序模型为流行病学研究提供了更细致的方法.
研究的目的:
- 开发和分析密码菌病的分数顺序流行病模型.
- 调查平衡点的稳定性 (无疾病和流行病).
- 设计和验证用于解决分数模型的数值方案.
主要方法:
- 分数计算应用于流行病模型.
- 稳定性分析的雅科比矩阵理论.
- 格伦瓦尔德-莱特尼科夫非标准有限差异 (GL-NSFD) 数值解方案.
- 拉普拉斯和逆拉普拉斯转换来证明积极性和有限性.
主要成果:
- 计算了基本生殖数 (R0) 并分析了其在疾病动态中的作用.
- GL-NSFD方案成功设计和模拟.
- 数值方案的正性和边界性属性被数学证明了.
- 确定了平衡点及其稳定性.
结论:
- 分数顺序模型为加密菌病的动态提供了一个强大的框架.
- 拟议的GL-NSFD方案是准确的,积极的,有界的,适合流行病学建模.
- 这项研究增强了对密码菌病传播和控制策略的理解.
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