A mean-field analysis of a network behavioural-epidemic model

TL;DR

This paper develops a coupled epidemic-behavior model using mean-field analysis to understand how disease spread and population responses co-evolve, revealing conditions for disease eradication or persistent outbreaks.

Contribution

It introduces a novel coupled model combining epidemic dynamics with behavioral decision-making and provides a mean-field analysis of its long-term behavior and stability.

Findings

Conditions for global convergence to disease-free state

Characterization of endemic equilibria and their stability

Identification of parameter ranges leading to periodic outbreaks

Abstract

The spread of an epidemic disease and the population's collective behavioural response are deeply intertwined, influencing each other's evolution. Such a co-evolution typically has been overlooked in mathematical models, limiting their real-world applicability. To address this gap, we propose and analyse a behavioural-epidemic model, in which a susceptible-infected-susceptible epidemic model and an evolutionary game-theoretic decision-making mechanism concerning the use of self-protective measures are coupled. Through a mean-field approach, we characterise the asymptotic behaviour of the system, deriving conditions for global convergence to a disease-free equilibrium and characterising the endemic equilibria of the system and their (local) stability. Interestingly, for a certain range of the model parameters, we prove global convergence to a limit cycle, characterised by periodic epidemic outbreaks.