The spread of an epidemic disease and the population’s collective behavioral 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 behavioral–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 characterize the asymptotic behavior of the system, deriving conditions for global convergence to a disease-free equilibrium and characterizing the endemic equilibria of the system and their (local) stability properties. Interestingly, for a certain range of the model parameters, we prove global convergence to a limit cycle, characterized by periodic epidemic outbreaks and collective behavioral response.
A mean-field analysis of a network behavioral–epidemic model / Frieswijk, Kathinka; Zino, Lorenzo; Ye, Mengbin; Rizzo, Alessandro; Cao, Ming. - In: IEEE CONTROL SYSTEMS LETTERS. - ISSN 2475-1456. - ELETTRONICO. - 6:(2022), pp. 2533-2538. [10.1109/LCSYS.2022.3168260]
A mean-field analysis of a network behavioral–epidemic model
Lorenzo Zino;Alessandro Rizzo;
2022
Abstract
The spread of an epidemic disease and the population’s collective behavioral 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 behavioral–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 characterize the asymptotic behavior of the system, deriving conditions for global convergence to a disease-free equilibrium and characterizing the endemic equilibria of the system and their (local) stability properties. Interestingly, for a certain range of the model parameters, we prove global convergence to a limit cycle, characterized by periodic epidemic outbreaks and collective behavioral response.File | Dimensione | Formato | |
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2022 CSS-L A_Mean-Field_Analysis_of_a_Network_BehavioralEpidemic_Model.pdf
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https://hdl.handle.net/11583/2962200