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arXiv · 2203.04016

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

Kathinka Frieswijk·Lorenzo Zino·Mengbin Ye·Alessandro Rizzo·Ming Cao
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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.

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Kathinka Frieswijk, Lorenzo Zino, Mengbin Ye, Alessandro Rizzo, Ming Cao. 2022-03-08. A mean-field analysis of a network behavioural-epidemic model. https://doi.org/10.1109/lcsys.2022.3168260

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