Limitations of time-delayed case isolation in heterogeneous SIR models

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.