Compartmental Model for Epidemics with Contact Tracing and Isolation under Arbitrary Degree Distribution

The recent COVID-19 epidemic demonstrated the need and importance of epidemic models as a tool for policy-making during times of uncertainty, allowing the decision-makers to test different intervention techniques and scenarios. Furthermore, tools such as large-scale contact tracing became technologically feasible for the first time. While large-scale agent-based simulations are nowadays part of the toolboxes, good analytical models allow for much faster testing of scenarios. Unfortunately, good models that consider contact tracing and quarantine, and allow for different degree distributions do not exist. To overcome these shortcomings of existing models we propose a new simple compartmental model that integrates quarantine and contact tracing into the SIR compartmental models with arbitrary degree distribution of nodes to better understand the dynamics of the disease under various parameters of intervention and contagion. Consequently, we analytically derive the epidemic threshold as a function of the degree distribution and the model parameters when both quarantine and contact tracing are used. Simulation results demonstrate and quantify the benefits of quarantine and contact tracing and show the effectiveness of such measures over a large range of epidemic parameters.