有交叉免疫和多次时间延迟的SIRC流行病模型
Shashank Goel1, Sumit Kaur Bhatia2, Jai Prakash Tripathi3
1Department of Mathematics, Jaypee Institute of Information Technology, Noida, Uttar Pradesh, India.
Journal of mathematical biology
|August 12, 2023
概括
本研究引入了多菌株疾病的数学模型,揭示了时间延迟和交叉免疫显著影响疾病动态和流行率. 增加疫苗接种和交叉免疫率有助于稳定系统并减少感染.
科学领域:
- 流行病学 流行病学
- 数学生物学 数学生物学
- 传染病建模 传染病建模
背景情况:
- 多菌株疾病可以诱导交叉免疫.
- 疾病进展的时间延迟和免疫力是流行病动态的关键因素.
研究的目的:
- 用多延迟SIRC模型研究化和免疫时间延迟对疾病动态的影响.
- 分析疫苗引发的部分/交叉免疫和交叉免疫的强度对疾病流行率的影响.
- 探索流行病模型与时间延迟的稳定性和分叉性质.
主要方法:
- 开发和分析多延迟的SIRC (易受感染-康复-感染) 流行病模型.
- 数学分析溶液的阳性,边界性和平衡点 (无病和特有).
- 基本繁殖数的导出和稳定性条件的分析,包括霍夫分叉.
- 数字模拟和参数灵敏度分析,包括基本复制号的全球灵敏度分析.
主要成果:
- 模型的解决方案被证明是积极的和有界的.
- 稳定性条件和Hopf分叉被分析为存在或不存在延迟的两个平衡点.
- 数字模拟证实,时间延迟,通过振荡和Hopf-分叉,改变系统动态.
- 参数灵敏度分析表明,疫苗接种和交叉免疫率的增加减少了受感染人群并稳定了系统.
结论:
- 时间延迟和交叉免疫是必须纳入流行病模型的关键因素,以准确理解疾病动态.
- 疫苗接种策略和了解交叉免疫力对于控制传染病传播至关重要.
- 该研究为分析延迟和疫情免疫力的复杂相互作用提供了定量框架.
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