Kim Kiseong, Lee Sangyeon, Lee Doheon, Lee Kwang Hyung
Department of Bio and Brain Engineering, KAIST, Daejeon, South Korea.
Bio-Synergy Research Center, Daejeon, South Korea.
BMC Bioinformatics. 2017 May 31;18(Suppl 7):250. doi: 10.1186/s12859-017-1643-7.
Pandemic is a typical spreading phenomenon that can be observed in the human society and is dependent on the structure of the social network. The Susceptible-Infective-Recovered (SIR) model describes spreading phenomena using two spreading factors; contagiousness (β) and recovery rate (γ). Some network models are trying to reflect the social network, but the real structure is difficult to uncover.
We have developed a spreading phenomenon simulator that can input the epidemic parameters and network parameters and performed the experiment of disease propagation. The simulation result was analyzed to construct a new marker VRTP distribution. We also induced the VRTP formula for three of the network mathematical models.
We suggest new marker VRTP (value of recovered on turning point) to describe the coupling between the SIR spreading and the Scale-free (SF) network and observe the aspects of the coupling effects with the various of spreading and network parameters. We also derive the analytic formulation of VRTP in the fully mixed model, the configuration model, and the degree-based model respectively in the mathematical function form for the insights on the relationship between experimental simulation and theoretical consideration.
We discover the coupling effect between SIR spreading and SF network through devising novel marker VRTP which reflects the shifting effect and relates to entropy.
大流行是一种典型的传播现象，可在人类社会中观察到，且取决于社会网络的结构。易感-感染-康复（SIR）模型使用两个传播因素来描述传播现象，即传染性（β）和康复率（γ）。一些网络模型试图反映社会网络，但真实结构难以揭示。
我们开发了一种传播现象模拟器，它可以输入疫情参数和网络参数，并进行疾病传播实验。对模拟结果进行分析，以构建一个新的标记VRTP分布。我们还推导了三种网络数学模型的VRTP公式。
我们提出了新的标记VRTP（转折点上的康复值）来描述SIR传播与无标度（SF）网络之间的耦合，并观察其与各种传播和网络参数的耦合效应。我们还分别以数学函数形式推导出完全混合模型、配置模型和基于度的模型中VRTP的解析公式，以深入了解实验模拟与理论考量之间的关系。
我们通过设计反映转移效应并与熵相关的新型标记VRTP，发现了SIR传播与SF网络之间的耦合效应。
