论文标题
在不断发展的图上易感的流行病
Susceptible-Infected Epidemics on Evolving Graphs
论文作者
论文摘要
Evosir模型是对图形$ g $通常的SIR进程的修改，其中$ s-i $连接以$ρ$打破，$ s $连接到随机选择的顶点。 Evosi模型与Evosir相同，但恢复是不可能的。 In \cite{DOMath} the critical value for evoSIR was computed and simulations showed that when $G$ is an Erd\H os-Rényi graph with mean degree 5, the system has a discontinuous phase transition, i.e., as the infection rate $λ$ decreases to $λ_c$, the fraction of individuals infected during the epidemic does not converge to 0. In this paper we study evoSI dynamics on graphs generated通过配置模型。我们表明，有一个数量$δ$确定由度分布的前三矩确定，因此，如果$Δ> 0 $，则相变是不连续的，并且如果$Δ<0 $连续。
The evoSIR model is a modification of the usual SIR process on a graph $G$ in which $S-I$ connections are broken at rate $ρ$ and the $S$ connects to a randomly chosen vertex. The evoSI model is the same as evoSIR but recovery is impossible. In \cite{DOMath} the critical value for evoSIR was computed and simulations showed that when $G$ is an Erd\H os-Rényi graph with mean degree 5, the system has a discontinuous phase transition, i.e., as the infection rate $λ$ decreases to $λ_c$, the fraction of individuals infected during the epidemic does not converge to 0. In this paper we study evoSI dynamics on graphs generated by the configuration model. We show that there is a quantity $Δ$ determined by the first three moments of the degree distribution, so that the phase transition is discontinuous if $Δ>0$ and continuous if $Δ<0$.
