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

TL;DR

This paper develops a degree-based approximation for an SIR epidemic model with contact tracing and isolation on networks, deriving a differential equation system, analyzing thresholds, and validating with simulations on real networks.

Contribution

It introduces a novel degree-based approximation for an SIR model with contact tracing and isolation, including threshold analysis and reduced computational complexity.

Findings

Contact tracing and isolation help contain epidemics.

The epidemic threshold depends on disease parameters and network degree, not tracing policies.

Simulations on real networks confirm the effectiveness of contact tracing.

Abstract

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.