Network Behavioral-Feedback SIR Epidemic Model

TL;DR

This paper introduces a novel network behavioral-feedback SIR epidemic model that incorporates heterogeneity and endogenous behavioral responses, analyzing stability and transient dynamics to inform control strategies.

Contribution

It develops a new feedback-based epidemic model capturing behavioral responses and heterogeneity, analyzing stability and unimodal infection curves for improved epidemic control insights.

Findings

Stability of equilibria depends on interaction matrix structure.

Existence of unimodal infection curves for rank-1 interaction matrices.

Insights for designing effective epidemic control strategies.

Abstract

We propose a network behavioral-feedback Susceptible-Infected-Recovered (SIR) epidemic model in which the interaction matrix describing the infection rates across subpopulations depends in feedback on the current epidemic state. This model captures both heterogeneities in individuals mixing, contact frequency, aptitude to contract and spread the infection, and endogenous behavioral responses such as voluntary social distancing and the adoption of self-protective measures. We study the stability of the equilibria and illustrate through several examples how the shape of the stability region depends on the structure of the interaction matrix, providing insights for the design of effective control strategies. We then analyze the transient behavior of the dynamics, showing that, for a special class of rank-1 interaction matrices, there always exists an aggregate infection curve that exhibits a unimodal behavior, expanding the results on the unimodality of infection curve known in the literature of epidemic models and paving the way for future control applications.