在這篇論文裡面，我們探討了一個在配置網路模型(configuration model)將接觸者追蹤以及隔離一起考慮的SEIR模型。利用度近似，我們可以得到此模型的若干個微分方程式此微分方程組雖然不能解出一個解析解(closed form)，但我們提出了早期傳染病近似分析(early-time approximate solution)用於判定此傳染病會在網路上大流行與否，並且針對於此模型的近似微分方程組來降低微分方程組的複雜度。同時我們也將這個考慮接觸者追蹤以及隔離的SEIR模型用於模擬真實世界的網路以展示接觸者追蹤以及隔離對於控制疫情是有幫助的。

In this paper we study a susceptible infectious recovered (SIR) model
with asymptomatic patients, contact tracing and isolation on a configuration network. Using degree based approximation, we derive a system of
differential equations for this model. This system can not be solved analytically. We present an early-time analysis for the model. The early-time
analysis produces an epidemic threshold. On one side of the threshold,
the disease dies out quickly. On the other side, a significant fraction of
population are infected. The threshold only depends on the parameters
of the disease, the mean access degree of the network, and the fraction of
asymptomatic patients. The threshold does not depend on the parameter
of contact tracing and isolation policy. This implies that contact tracing
and isolation can not prevent a disease from spreading widely. It reduces
the size of the epidemic, if the disease spreads widely. We also present an
approximate analysis which reduces computation complexity. We simulate the SIR model with contact tracing and isolation on five real-world
networks. Simulation results show that contact tracing and isolation are
useful to contain epidemics.

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