分数(化学)
渗透(认知心理学)
极限(数学)
统计物理学
渗流阈值
流行病模型
巨型组件
中心极限定理
感染率
GSM演进的增强数据速率
物理
数学
组合数学
统计
作者
G. Machado,G. J. Baxter
出处
期刊:Physical review
日期:2022-07-21
卷期号:106 (1)
标识
DOI:10.1103/physreve.106.014307
摘要
We consider the effect of a nonvanishing fraction of initially infected nodes (seeds) on the susceptible-infected-recovered epidemic model on random networks. This is relevant when the number of arriving infected individuals is large, or to the spread of ideas with publicity campaigns. This model is frequently studied by mapping to a bond percolation problem, in which edges are occupied with the probability $p$ of eventual infection along an edge. This gives accurate measures of the final size of the infection and epidemic threshold in the limit of a vanishingly small seed fraction. We show, however, that when the initial infection occupies a nonvanishing fraction, $f$, of the network, this method yields ambiguous results, as the correspondence between edge occupation and contagion transmission no longer holds. We propose instead to measure the giant component of recovered individuals within the original contact network. We derive exact equations for the size of the epidemic and the epidemic threshold in the infinite size limit in heterogeneous sparse random networks, and we confirm them with numerical results. We observe that the epidemic threshold correctly depends on $f$, decreasing as $f$ increases. When the seed fraction tends to zero, we recover the standard results.
科研通智能强力驱动
Strongly Powered by AbleSci AI