Noël Pierre-André, Allard Antoine, Hébert-Dufresne Laurent, Marceau Vincent, Dubé Louis J
University of California, Davis, CA, 95616, USA,
J Math Biol. 2014 Dec;69(6-7):1627-60. doi: 10.1007/s00285-013-0744-9. Epub 2013 Dec 24.
Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach is especially well adapted for modelling spreading processes and/or population dynamics. In particular, the generality of our framework and the fact that its assumptions are explicitly stated suggests that it could be used as a common ground for comparing existing epidemics models too complex for direct comparison, such as agent-based computer simulations. We provide many examples for the special cases of susceptible-infectious-susceptible and susceptible-infectious-removed dynamics (e.g., epidemics propagation) and we observe multiple situations where accurate results may be obtained at low computational cost. Our perspective reveals a subtle balance between the complex requirements of a realistic model and its basic assumptions.
从马尔可夫随机过程的角度考虑网络动力学。我们通过网络基序部分描述系统状态，并利用可用信息推断任何缺失数据。这种通用方法特别适用于对传播过程和/或种群动态进行建模。特别是，我们框架的通用性以及其假设被明确阐述这一事实表明，它可以作为一个共同基础，用于比较过于复杂而无法直接比较的现有流行病模型，例如基于主体的计算机模拟。我们针对易感-感染-易感和易感-感染-移除动态（例如，流行病传播）的特殊情况提供了许多示例，并且我们观察到在多种情况下可以以低计算成本获得准确结果。我们的观点揭示了现实模型的复杂要求与其基本假设之间的微妙平衡。
