How network properties and epidemic parameters influence stochastic SIR dynamics on scale-free random networks

TL;DR

This paper investigates how network structure and disease parameters affect stochastic SIR epidemic dynamics on scale-free networks, highlighting the impact of network connectivity and initial node degree on disease spread outcomes.

Contribution

It provides a theoretical analysis of disease extinction probability and explores stochastic simulation results on how epidemic indices vary with network and disease parameters.

Findings

Higher network connectivity increases epidemic spread.

Initial node degree significantly influences epidemic indices.

Theoretical extinction probability aligns with stochastic simulation results.

Abstract

With the premise that social interactions are described by power-law distributions, we study a SIR stochastic dynamic on a static scale-free random network generated via configuration model. We verify our model with respect to deterministic considerations and provide a theoretical result on the probability of the extinction of the disease. Based on this calibration, we explore the variability in disease spread by stochastic simulations. In particular, we demonstrate how important epidemic indices change as a function of the contagiousness of the disease and the connectivity of the network. Our results quantify the role of starting node degree in determining these indices, commonly used to describe epidemic spread.