Influence of individual nodes for continuous-time Susceptible-Infected-Susceptible dynamics on synthetic and real-world networks

TL;DR

This paper analyzes how the initial infected node's position affects epidemic spread in continuous-time SIS models on both synthetic and real-world networks, providing analytical predictions and validating them with simulations.

Contribution

It introduces analytical methods to predict the influence of initial seed location on epidemic outcomes in SIS dynamics across various network types.

Findings

Analytical predictions match well with simulations on random networks.

The approach extends to real-world network topologies.

Network features influence deviations from theoretical predictions.

Abstract

In the study of epidemic dynamics a fundamental question is whether a pathogen initially affecting only one individual will give rise to a limited outbreak or to a widespread pandemic. The answer to this question crucially depends not only on the parameters describing the infection and recovery processes but also on where, in the network of interactions, the infection starts from. We study the dependence on the location of the initial seed for the Susceptible-Infected-Susceptible epidemic dynamics in continuous time on networks. We first derive analytical predictions for the dependence on the initial node of three indicators of spreading influence (probability to originate an infinite outbreak, average duration and size of finite outbreaks) and compare them with numerical simulations on random uncorrelated networks, finding a very good agreement. We then show that the same theoretical approach works fairly well also on a set of real-world topologies of diverse nature. We conclude by briefly investigating which topological network features determine deviations from the theoretical predictions.