Longtime behaviors of an epidemic model with nonlocal diffusions and a free boundary: spreading-vanishing dichotomy
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911987586301952 |
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| author | Li, Xueping Li, Lei |
| author_facet | Li, Xueping Li, Lei |
| contents | We propose a nonlocal epidemic model whose spatial domain evolves over time and is represented by $[0,h(t)]$ with $h(t)$ standing for the spreading front of epidemic. It is assumed that the agents can cross the fixed boundary $x=0$, but they will die immediately if they do it, which implies that the area $(-\infty,0)$ is a hostile environment for the agents. We first show that this model is well posed, then prove that the longtime behaviors are governed by a spreading-vanishing dichotomy and finally give some criteria determining spreading and vanishing. Particularly, we obtain the asymptotical behaviors of the principal eigenvalue of a cooperative system with nonlocal diffusions without assuming the related nonlocal operator is self-adjoint, and the steady state problem of such cooperative system on half space $[0,\infty)$ is studied in detail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07356 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Longtime behaviors of an epidemic model with nonlocal diffusions and a free boundary: spreading-vanishing dichotomy Li, Xueping Li, Lei Analysis of PDEs We propose a nonlocal epidemic model whose spatial domain evolves over time and is represented by $[0,h(t)]$ with $h(t)$ standing for the spreading front of epidemic. It is assumed that the agents can cross the fixed boundary $x=0$, but they will die immediately if they do it, which implies that the area $(-\infty,0)$ is a hostile environment for the agents. We first show that this model is well posed, then prove that the longtime behaviors are governed by a spreading-vanishing dichotomy and finally give some criteria determining spreading and vanishing. Particularly, we obtain the asymptotical behaviors of the principal eigenvalue of a cooperative system with nonlocal diffusions without assuming the related nonlocal operator is self-adjoint, and the steady state problem of such cooperative system on half space $[0,\infty)$ is studied in detail. |
| title | Longtime behaviors of an epidemic model with nonlocal diffusions and a free boundary: spreading-vanishing dichotomy |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2408.07356 |