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对于复杂网络上的流行过程,离散和连续时间平均场理论的准确性
Diogo H Silva1, Francisco A Rodrigues1, Silvio C Ferreira2,3
1Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos, SP 13566-590, Brazil.
Physical review. E
|August 20, 2024
概括
在复杂的网络上对易受感染易受感染 (SIS) 流行病的离散和连续时间模型进行比较,可以发现关键差异. 离散时间模型显示了不同流行流行病的临界指数,突出显示了网络流行病建模中时间步骤选择的重要性.
科学领域:
- 复杂系统科学 复杂系统科学
- 流行病学 流行病学
- 网络科学 网络科学
背景情况:
- 复杂网络上的动态过程通常使用离散或连续时间方法建模.
- 药物相互作用的异质性显著影响了这些动态.
- 清楚地了解离散和连续时间模型之间的差异对于准确的分析至关重要.
研究的目的:
- 调查和比较敏感-感染-敏感 (SIS) 流行病模型的离散和连续时间平均场理论.
- 分析时间分离对流行病局部化和流行率的影响.
- 为基于网络的流行病研究指导选择合适的建模方法.
主要方法:
- 开发并比较离散时间流行病链接方程 (ELE) 和连续时间对灭平均场 (PQMF) 理论.
- 使用随机模拟进行验证.
- 在具有权力法度分布的随机网络上使用逆参与率 (IPR) 进行了流行病局部化分析.
主要成果:
- 离散流行病链接方程 (ELE) 在时间步骤接近零时汇聚到连续对灭平均场 (PQMF) 理论中.
- 这两种理论都表现出类似的流行病本地化行为,取决于网络度指数 γ.
- 离散时间模型显示,较大的时间步骤导致更局部的流行病,并且与连续时间模型 (θ=1/(3-γ)) 相比,在临界值附近的流行病患病率的临界指数 (θ=1) 不一样.
结论:
- 在离散和连续时间模型之间的选择可以显著影响临界值附近预测的流行病流行率.
- 在离散时间模型中的时间分离化影响流行病局部化和临界指数.
- 在离散时间模型中,更大的时间步骤会导致更局部的流行病,与连续时间预测不同.
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