  Case isolation, that is, detection and isolation of infected individuals in
order to prevent spread, is a strategy to curb infectious disease epidemics.
Here, we study the efficiency of a case isolation strategy subject to time
delays in terms of its ability to stabilize the epidemic spread in
heterogeneous contact networks. For an SIR epidemic model, we characterize the
stability boundary analytically and show how it depends on the time delay
between infection and isolation as well as the heterogeneity of the
inter-individual contact network, quantified by the variance in contact rates.
We show that network heterogeneity accounts for a restricting correction factor
to previously derived stability results for homogeneous SIR models (with
uniform contact rates), which are therefore too optimistic on the relevant time
scales. We illustrate the results and the underlying mechanisms through
insightful numerical examples.
