Suppression of epidemic spreading in complex networks by local information based behavioral responses.

Ying-Cheng Lai,Ming Tang,Jia-Rong Xie,Hai-Feng Zhang

doi:10.1063/1.4896333

Abstract

The interplay between individual behaviors and epidemic dynamics in complex networks is a topic of recent interest. In particular, individuals can obtain different types of information about the disease and respond by altering their behaviors, and this can affect the spreading dynamics, possibly in a significant way. We propose a model where individuals' behavioral response is based on a generic type of local information, i.e., the number of neighbors that has been infected with the disease. Mathematically, the response can be characterized by a reduction in the transmission rate by a factor that depends on the number of infected neighbors. Utilizing the standard susceptible-infected-susceptible and susceptible-infected-recovery dynamical models for epidemic spreading, we derive a theoretical formula for the epidemic threshold and provide numerical verification. Our analysis lays on a solid quantitative footing the intuition that individual behavioral response can in general suppress epidemic spreading. Furthermore, we find that the hub nodes play the role of “double-edged sword” in that they can either suppress or promote outbreak, depending on their responses to the epidemic, providing additional support for the idea that these nodes are key to controlling epidemic spreading in complex networks.

Highlights

Epidemic spreading in complex networks often occurs in an extremely interactive manner
Our work reinforces the idea that hub nodes are key to controlling epidemic dynamics
A general result from previous works is that the local information-based responses can enhance the epidemic threshold and reduce its prevalence, but global informationbased awareness, being capable of altering the epidemic size, has little effect on the threshold.6,24,25. In these works on the interplay between epidemic spreading in complex networks and human behavioral responses, a tacit hypothesis24–26,28 is that local information-based behavioral response is a function of the density of infection among the local neighborhood, denoted as s/k, where s is the number of infected neighbors among a total of k neighbors

Summary

INTRODUCTION

Epidemic spreading in complex networks often occurs in an extremely interactive manner. A general result from previous works is that the local information-based responses can enhance the epidemic threshold and reduce its prevalence, but global informationbased awareness, being capable of altering the epidemic size, has little effect on the threshold.. A general result from previous works is that the local information-based responses can enhance the epidemic threshold and reduce its prevalence, but global informationbased awareness, being capable of altering the epidemic size, has little effect on the threshold.6,24,25 In these works on the interplay between epidemic spreading in complex networks and human behavioral responses, a tacit hypothesis is that local information-based behavioral response is a function of the density of infection among the local neighborhood, denoted as s/k, where s is the number of infected neighbors among a total of k neighbors.

MODELING BEHAVIORAL RESPONSE

SIS dynamics

SIR dynamics

CONCLUSIONS