Recovery rate affects the effective epidemic threshold with synchronous updating

TL;DR

This paper investigates how arbitrary recovery rates influence the epidemic threshold and outbreak size in SIR models on complex networks, revealing that recovery rate impacts the threshold and outbreak size under synchronous updating.

Contribution

It derives a theoretical effective epidemic threshold considering arbitrary recovery rates and validates it through extensive simulations, extending existing models.

Findings

Recovery rate decreases the epidemic threshold under synchronous updating.

Final outbreak size increases with higher recovery rates.

Theoretical predictions align well with numerical simulations on various networks.

Abstract

Accurate identification of effective epidemic threshold is essential for understanding epidemic dynamics on complex networks. The existing studies on the effective epidemic threshold of the susceptible-infected-removed (SIR) model generally assume that all infected nodes immediately recover after the infection process, which more or less does not conform to the realistic situation of disease. In this paper, we systematically study the effect of arbitrary recovery rate on the SIR spreading dynamics on complex networks. We derive the theoretical effective epidemic threshold and final outbreak size based on the edge-based compartmental theory. To validate the proposed theoretical predictions, extensive numerical experiments are implemented by using asynchronous and synchronous updating methods. When asynchronous updating method is used in simulations, recovery rate does not affect the final state of spreading dynamics. But with synchronous updating, we find that the effective epidemic threshold decreases with recovery rate, and final outbreak size increases with recovery rate. A good agreement between the theoretical predictions and numerical results are observed on both synthetic and real-world networks. Our results extend the existing theoretical studies, and help us to understand the phase transition with arbitrary recovery rate.