Impact of the distribution of recovery rates on disease spreading in complex networks

Guilherme Ferraz De Arruda,Yamir Moreno,Francisco A Rodrigues,Giovanni Petri

doi:10.1103/physrevresearch.2.013046

Abstract

We study a general epidemic model with arbitrary recovery rate distributions. This simple deviation from the standard setup is sufficient to prove that heterogeneity in the dynamical parameters can be as important as the more studied structural heterogeneity. Our analytical solution is able to predict the shift in the critical properties induced by heterogeneous recovery rates. We find that the critical value of infectivity tends to be smaller than the one predicted by quenched mean-field approaches in the homogeneous case and that it can be linked to the variance of the recovery rates. Our findings also illustrate the role of dynamical-structural correlations, where we allow a power-law network to dynamically behave as a homogeneous structure by an appropriate tuning of its recovery rates. Overall, our results demonstrate that heterogeneity in the recovery rates, eventually in all dynamical parameters, is as important as the structural heterogeneity.

Highlights

Heterogeneity, whether in the nature of the components or the pattern of connections, is a key characteristic of complex systems
Our results demonstrate that heterogeneity in the recovery rates, eventually in all dynamical parameters, is as important as the structural heterogeneity
We have analyzed the impact of introducing heterogeneity in the recovery rates of an SIS disease dynamics

Summary

INTRODUCTION

Heterogeneity, whether in the nature of the components or the pattern of connections, is a key characteristic of complex systems. It was mainly studied for the SIR model: A message-passing formalism was proposed in [19,20] and a heterogeneous mean-field approach in [21] In the latter, the authors performed numerical experiments showing that the population can be more vulnerable in the scenario with dynamical heterogeneity. The authors performed numerical experiments showing that the population can be more vulnerable in the scenario with dynamical heterogeneity This problem was investigated on temporal networks [22] using an SIS process, which was described within the quenched mean-field (QMF) formalism and mainly focusing on spreading rates [23,24]. Our results complement previous evidence on the SIR model [21] and imply that proper characterization of the dynamical parameters is of utmost importance for a better understanding of spreading processes, and for many practical applications, such as surveillance, forecasting, resource management, and network reconstruction, among many others

THE SIS MODEL WITH HETEROGENEOUS RECOVERIES

SYNTHETIC NETWORKS

REAL-WORLD NETWORKS

EFFECTS OF DYNAMICS-STRUCTURE CORRELATIONS

CONCLUSION