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In this paper we study a susceptible infectious recovered (SIR) model withasymptomatic patients, contact tracing and isolation on a configurationnetwork. Using degree based approximation, we derive a system of differentialequations for this model. This system can not be solved analytically. Wepresent an early-time analysis for the model. The early-time analysis producesan epidemic threshold. On one side of the threshold, the disease dies outquickly. On the other side, a significant fraction of the population areinfected. The threshold only depends on the parameters of the disease, the meanaccess degree of the network, and the fraction of asymptomatic patients. Thethreshold does not depend on the parameter of contact tracing and isolationpolicy. We present an approximate analysis which greatly reduces computationalcomplexity. The nonlinear system derived from the approximation is not almostlinear. We present a stability analysis for this system. We simulate the SIRmodel with contact tracing and isolation on five real-world networks.Simulation results show that contact tracing and isolation are useful tocontain epidemics.

A Degree Based Approximation of an SIR Model with Contact Tracing and Isolation