  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 the 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. We present an approximate analysis which greatly reduces computational
complexity. The nonlinear system derived from the approximation is not almost
linear. We present a stability analysis for this system. 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.
