论文标题
网络上的流行，预防性重新布线
Epidemics on networks with preventive rewiring
论文作者
论文摘要
分析了在社交网络上定义的随机先生（易感$ \ to $感染$ \至$恢复）的流行模型。基本的社交网络由Erdős-rényi随机图描述，但是在流行病的过程中，与传染性邻居相关的易感人可能会降低或重新连接这种联系。该模型的较大人口限制是为早期分支过程样行为提供的收敛结果，并且假设大爆发是流行过程的主要阶段，该过程是融合到确定性模型的主要阶段，该模型等同于某个配对近似模型。还获得了大型爆发的最终规模（即感染的个体总数）的大量结果。两个结果脱颖而出（对于一系列参数设置有效）：（i）在感染率$λ$ $λ$ $λ_c$的感染率$λ_c$（因此，从$ 0 $上升到严格的正数）和（II）在重新注射时，如果$ nibected $ dibection $ dibection $ nibected nignive $λc $，如果$ nibected $ dibemption nibimimimimimimimimimimimimimim，则可能是不连续的（因此，从$ 0 $上升到一个严格的正数）。 $ 1 $ AS $λ$通过$λ_C$通过。
A stochastic SIR (susceptible $\to$ infective $\to$ recovered) epidemic model defined on a social network is analysed. The underlying social network is described by an Erdős-Rényi random graph but, during the course of the epidemic, susceptible individuals connected to infectious neighbours may drop or rewire such connections. Large population limits of the model are derived giving both convergence results for the early branching process-like behaviour, and, assuming a major outbreak, the main phase of the epidemic process which converges to a deterministic model that is equivalent to a certain pair approximation model. Law of large numbers results are also obtained for the final size (i.e. total number of individuals infected) of a major outbreak. Two results stand out (valid for a range of parameter set-ups): (i) the limiting final fraction infected may be discontinuous in the infection rate $λ$ at its threshold $λ_c$ (thus making a discrete jump from $0$ to a strictly positive number) and (ii) for the situation when rewiring is necessarily to uninfected individuals, if it is discontinuous, the limiting final fraction infected jumps from $0$ to $1$ as $λ$ passes through $λ_c$.
