Infinite dimensional metapopulation SIS model with generalized incidence rate
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917244721692672 |
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| author | Delmas, Jean-François Lefki, Kacem Zitt, Pierre-André |
| author_facet | Delmas, Jean-François Lefki, Kacem Zitt, Pierre-André |
| contents | We consider an infinite-dimension SIS model introduced by Delmas, Dronnier and Zitt, with a more general incidence rate, and study its equilibria. Unsurprisingly, there exists at least one endemic equilibrium if and only if the basic reproduction number is larger than 1. When the pathogen transmission exhibits one way propagation, it is possible to observe different possible endemic equilibria. We characterize in a general setting all the equilibria, using a decomposition of the space into atoms, given by the transmission operator. We also prove that the proportion of infected individuals converges to an equilibrium, which is uniquely determined by the support of the initial condition.We extend those results to infinite-dimensional SIS models with reservoir or with immigration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00034 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Infinite dimensional metapopulation SIS model with generalized incidence rate Delmas, Jean-François Lefki, Kacem Zitt, Pierre-André Analysis of PDEs Spectral Theory We consider an infinite-dimension SIS model introduced by Delmas, Dronnier and Zitt, with a more general incidence rate, and study its equilibria. Unsurprisingly, there exists at least one endemic equilibrium if and only if the basic reproduction number is larger than 1. When the pathogen transmission exhibits one way propagation, it is possible to observe different possible endemic equilibria. We characterize in a general setting all the equilibria, using a decomposition of the space into atoms, given by the transmission operator. We also prove that the proportion of infected individuals converges to an equilibrium, which is uniquely determined by the support of the initial condition.We extend those results to infinite-dimensional SIS models with reservoir or with immigration. |
| title | Infinite dimensional metapopulation SIS model with generalized incidence rate |
| topic | Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2408.00034 |