A mean-field analysis of a network behavioural-epidemic model
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866913560224858112 |
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| author | Frieswijk, Kathinka Zino, Lorenzo Ye, Mengbin Rizzo, Alessandro Cao, Ming |
| author_facet | Frieswijk, Kathinka Zino, Lorenzo Ye, Mengbin Rizzo, Alessandro Cao, Ming |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_04016 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A mean-field analysis of a network behavioural-epidemic model Frieswijk, Kathinka Zino, Lorenzo Ye, Mengbin Rizzo, Alessandro Cao, Ming Dynamical Systems 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. |
| title | A mean-field analysis of a network behavioural-epidemic model |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2203.04016 |