Trapman Pieter
Faculty of Veterinary Medicine, Utrecht University, The Netherlands.
Theor Popul Biol. 2007 Mar;71(2):160-73. doi: 10.1016/j.tpb.2006.11.002. Epub 2006 Dec 5.
One way to describe the spread of an infection on a network is by approximating the network by a random graph. However, the usual way of constructing a random graph does not give any control over the number of triangles in the graph, while these triangles will naturally arise in many networks (e.g. in social networks). In this paper, random graphs with a given degree distribution and a given expected number of triangles are constructed. By using these random graphs we analyze the spread of two types of infection on a network: infections with a fixed infectious period and infections for which an infective individual will infect all of its susceptible neighbors or none. These two types of infection can be used to give upper and lower bounds for R(0), the probability of extinction and other measures of dynamics of infections with more general infectious periods.
描述感染在网络上传播的一种方法是通过用随机图来近似该网络。然而，构建随机图的通常方法无法对图中三角形的数量进行任何控制，而这些三角形在许多网络中（例如社交网络）会自然出现。本文构建了具有给定度分布和给定预期三角形数量的随机图。通过使用这些随机图，我们分析了网络上两种类型感染的传播：具有固定感染期的感染以及感染个体将感染其所有易感邻居或一个都不感染的感染。这两种类型的感染可用于给出(R(0))（灭绝概率）以及具有更一般感染期的感染动态的其他度量的上下界。
