Interplay between the local information based behavioral responses and the epidemic spreading in complex networks

TL;DR

This paper introduces a new $S^F$ state in the $SIR$ model to account for human behavioral responses, showing that increased protective behavior raises the epidemic threshold and reduces prevalence, with theoretical and simulation validation.

Contribution

It develops a novel $S^F$ state in epidemic modeling to incorporate local behavioral responses, providing analytical formulas for epidemic threshold and prevalence.

Findings

Higher response rates increase epidemic threshold.

Protective behaviors reduce epidemic prevalence.

Mean field methods may underestimate the impact of behavioral responses.

Abstract

The spreading of an infectious disease can trigger human behavior responses to the disease, which in turn plays a crucial role on the spreading of epidemic. In this study, to illustrate the impacts of the human behavioral responses, a new class of individuals, $S^F$, is introduced to the classical susceptible-infected-recovered ($SIR$) model. In the model, $S^F$ state represents that susceptible individuals who take self-initiate protective measures to lower the probability of being infected, and a susceptible individual may go to $S^F$ state with a response rate when contacting an infectious neighbor. Via the percolation method, the theoretical formulas for the epidemic threshold as well as the prevalence of epidemic are derived. Our finding indicates that, with the increasing of the response rate, the epidemic threshold is enhanced and the prevalence of epidemic is reduced. The analytical results are also verified by the numerical simulations. In addition, we demonstrate that, because the mean field method neglects the dynamic correlations, a wrong result based on the mean field method is obtained---the epidemic threshold is not related to the response rate, i.e., the additional $S^F$ state has no impact on the epidemic threshold.