Die-out Probability in SIS Epidemic Processes on Networks

TL;DR

This paper proposes a simple, accurate formula for the probability that an SIS epidemic will die out on a network, based on key network and infection parameters, and validates it across different graph types.

Contribution

It introduces a novel approximate formula for die-out probability in SIS epidemics that depends on only three parameters, enhancing predictive accuracy.

Findings

The formula matches well with exact probabilities in various network types.

It effectively incorporates die-out probability into the N-Intertwined Mean-Field Approximation.

The approach simplifies understanding epidemic die-out dynamics on complex networks.

Abstract

An accurate approximate formula of the die-out probability in a SIS epidemic process on a network is proposed. The formula contains only three essential parameters: the largest eigenvalue of the adjacency matrix of the network, the effective infection rate of the virus, and the initial number of infected nodes in the network. The die-out probability formula is compared with the exact die-out probability in complete graphs, Erd\H{o}s-R\'enyi graphs, and a power-law graph. Furthermore, as an example, the formula is applied to the $N$-Intertwined Mean-Field Approximation, to explicitly incorporate the die-out.