A Novel Metric to Quantify the Real-Time Robustness of Complex Networks With Respect to Epidemic Models

Xu Wang,Yurong Song,Junming Yang,Y. Jay Guo,Guo-Ping Jiang,Bo Song

doi:10.3389/fphy.2021.805674

Abstract

Spread velocity, epidemic threshold, and infection density at steady state are three non-negligible features describing the spread of epidemics. Combining these three features together, a new network robustness metric with respect to epidemics was proposed in this paper. The real-time robustness of the network was defined and analyzed. By using the susceptible–infected (SI) and susceptible–infected–susceptible (SIS) epidemic models, the robustness of different networks was analyzed based on the proposed network robustness metric. The simulation results showed that homogeneous networks present stronger robustness than do heterogeneous networks at the early stage of the epidemic, and the robustness of the heterogeneous networks becomes stronger than that of the homogeneous ones with the progress of the epidemic. Moreover, the irregularity of the degree distribution decreases the network robustness in homogeneous networks. The network becomes more vulnerable as the average degree grows in both homogeneous and heterogeneous networks.

Highlights

Nowadays, various dynamic phenomena exist in real networks, many of which are harmful and bring great damage to real life
In [13], a new measure incorporating the fraction of infected nodes at the steady state and the epidemic threshold to assess the robustness of the complex networks with respect to the spread of epidemic has been proposed and proven to be effective in modeling epidemics with different final infection densities
At the early stage of the epidemic, the BA network is more fragile than the WS network because of the higher epidemic threshold and faster spread velocity

Summary

INTRODUCTION

Various dynamic phenomena exist in real networks, many of which are harmful and bring great damage to real life. Epidemic propagation models have been recently used to analyze network robustness against virus attacks, and the robustness of different networks has been studied [10,11,12,13,14]. In this paper, combining spread velocity, infection density at steady state, and the epidemic threshold, a novel metric was proposed to measure real-time robustness with respect to epidemics in complex networks. Network robustness with respect to the spread of the susceptible–infected (SI) [15] and susceptible–infected–susceptible (SIS) models [16] was analyzed based on the new metric, and some interesting results are presented in our paper. In Network Robustness With Respect to Epidemic Models, we analyze the necessity of proposing the new metric to measure the network robustness against diseases. The simulation results in different networks are presented and analyzed in Results, and the main conclusions and the direction for future studies are summarized in Discussion

RELATED WORK

RESULTS

DISCUSSION