有限网络上病毒传播的期望总感染数
On the Expected Total Number of Infections for Virus Spread on a Finite Network
摘要：
本文考虑了一个简单的病毒感染传播模型，该模型是在由邻域结构连接的有限$n$代理种群上建立的。给定一个在$n$顶点上的图$G$，我们从一些固定数目的初始感染顶点开始。在每个离散时间步，一个被感染的顶点试图以$β\in (0,1)$的概率感染它的邻居，然后它就消失了。这个过程一直持续到所有被感染的顶点消失。我们专注于获得适当的下界的预期数量的曾经感染的顶点。我们得到一个简单的下界，使用\textit{breadth-first search}算法，并表明，对于一个大类的图，可以被归类为那些局部“看起来像”一棵树的意义上的\emph{local weak convergence}，这个下界给出了更好的近似比一些已知的近似通过矩阵方法为基础的上界由Draief，Ganesh和Massoulie在2008年。
英文摘要：
In this paper we consider a simple virus infection spread model on a finite population of $n$ agents connected by some neighborhood structure. Given a graph $G$ on $n$ vertices, we begin with some fixed number of initial infected vertices. At each discrete time step, an infected vertex tries to infect its neighbors with probability $β\in (0,1)$ independently of others and then it dies out. The process continues till all infected vertices die out. We focus on obtaining proper lower bounds on the expected number of ever infected vertices. We obtain a simple lower bound, using \textit{breadth-first search} algorithm and show that for a large class of graphs which can be classified as the ones which locally "look like" a tree in sense of the \emph{local weak convergence}, this lower bound gives better approximation than some of the known approximations through matrix-method based upper bounds derived by Draief, Ganesh and Massoulie in 2008.
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