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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.10751 |
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| _version_ | 1866910310603948032 |
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| author | Hartarsky, Ivailo Lichev, Lyuben |
| author_facet | Hartarsky, Ivailo Lichev, Lyuben |
| contents | Brownian snails with removal is a spatial epidemic model defined as follows. Initially, a homogeneous Poisson process of susceptible particles on $\mathbb R^d$ with intensity $λ>0$ is deposited and a single infected one is added at the origin. Each particle performs an independent standard Brownian motion. Each susceptible particle is infected immediately when it is within distance 1 from an infected particle. Each infected particle is removed at rate $α>0$, and removed particles remain such forever. Answering a question of Grimmett and Li, we prove that in one dimension, for all values of $λ$ and $α$, the infection almost surely dies out. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_10751 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Brownian snails with removal die out in one dimension Hartarsky, Ivailo Lichev, Lyuben Probability Brownian snails with removal is a spatial epidemic model defined as follows. Initially, a homogeneous Poisson process of susceptible particles on $\mathbb R^d$ with intensity $λ>0$ is deposited and a single infected one is added at the origin. Each particle performs an independent standard Brownian motion. Each susceptible particle is infected immediately when it is within distance 1 from an infected particle. Each infected particle is removed at rate $α>0$, and removed particles remain such forever. Answering a question of Grimmett and Li, we prove that in one dimension, for all values of $λ$ and $α$, the infection almost surely dies out. |
| title | Brownian snails with removal die out in one dimension |
| topic | Probability |
| url | https://arxiv.org/abs/2305.10751 |