网络上的随机SIRS模型:感染的平均值和差异
Tingting Chen1, Guirong Liu1,2, Zhen Jin3,2
1School of Mathematics and Statistics, Shanxi University, Taiyuan, Shanxi, 030006, China.
Infectious Disease Modelling
|April 29, 2025
概括
这项研究使用网络上的随机SIRS模型来模拟流行病的传播. 疫苗接种减少了感染,但增加了波动,高度联系的个人更容易受到感染.
科学领域:
- 流行病学 流行病学
- 数学生物学 数学生物学
- 网络科学 网络科学
背景情况:
- 由于接触异质性,流行病建模从网络结构中受益.
- 网络上的随机SIRS (易感-感染-恢复-易感) 模型准确地捕捉疾病动态.
- 马尔科夫链方法适用于离散的,随机的流行病事件.
研究的目的:
- 建立和分析在网络上接种疫苗的随机SIRS模型.
- 在大群体中调查易感和感染个体的平均值和差异.
- 了解疫苗接种对流行病动态和个体易感性的影响.
主要方法:
- 使用范坎潘的系统大小扩展来导出确定性和福克-普朗克方程.
- 应用定性分析和利亚普诺夫函数来确定平衡的稳定性.
- 分析福克-普朗克方程和利亚普诺夫方程用于方程近似.
主要成果:
- 如果基本的繁殖数 (R0) < 1,则无病平衡在全球上是异常稳定的.
- 如果R0>1.1,那么特有平衡在全球上是异常稳定的.
- 疫苗接种减少了感染,但增加了波动;具有较高网络度的个人更容易受到感染.
结论:
- 网络上的随机SIRS模型为流行病分析提供了强大的框架.
- 疫苗接种策略可以通过网络结构和R0值来告知.
- 网络拓显著影响疾病传播和个体感染风险.
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