型流行病模型的传播动态通过延迟效应的随机分析
Ali Raza1,2, Nauman Ahmed3, Muhammad Bilal Riaz4,5
1Center for Research & Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, Aveiro, 3810-193, Portugal. ali.raza@ua.pt.
Scientific reports
|October 9, 2025
概括
随机延迟建模为了解传染病传播提供了一种现实的方法. 本研究应用了随机延迟微分方程来建模疹传播动态,并评估控制策略.
科学领域:
- 流行病学 流行病学
- 数学生物学 数学生物学
- 随机过程 随机过程
背景情况:
- 仍然是一个全球性的健康问题,全世界有20%的年轻成年男性受到影响.
- 了解传播动态对于有效控制至关重要,尽管存在疫苗接种.
- 有延迟的随机建模提供了更现实的疾病传播表现.
研究的目的:
- 使用随机延迟微分方程 (SDDEs) 调查病传播动态.
- 分析随机性和延迟对疾病持续性和控制的影响.
- 在这种情况下,比较不同的数值方法解决SDDEs的有效性.
主要方法:
- 扩展一个确定性分区模型 (S,E,I,A,Q,R) 到一个SDDE框架.
- 对模型属性的分析,包括积极性,局限性,灭绝和持久性.
- 研究无病和特有平衡,稳定性和参数灵敏度的研究.
- 使用标准 (Euler Maruyama, RK) 和非标准的有限差异方法进行数值模拟.
主要成果:
- 该研究严格分析了疾病灭绝和持续的条件.
- 均衡的稳定性分析和灵敏性分析提供了对模型关键参数的见解.
- 数字模拟可视化了随机延迟对疹传播的影响.
- 非标准的数值方法表明非线性SDDEs的效率更高.
结论:
- 随机延迟建模为了解传染病动态提供了一个强大的工具.
- 非标准的数值方法对于分析复杂的随机延迟模型更有效.
- 这些发现可以为公众健康策略提供信息,以控制疹.
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