dorsal/arxiv
View SchemaSolution of an infection model near threshold
| Authors | David A. Kessler, Nadav M. Shnerb |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0701024 |
| URL | https://arxiv.org/abs/q-bio/0701024 |
| DOI | 10.1103/PhysRevE.76.010901 |
Abstract
We study the Susceptible-Infected-Recovered model of epidemics in the vicinity of the threshold infectivity. We derive the distribution of total outbreak size in the limit of large population size $N$. This is accomplished by mapping the problem to the first passage time of a random walker subject to a drift that increases linearly with time. We recover the scaling results of Ben-Naim and Krapivsky that the effective maximal size of the outbreak scales as $N^{2/3}$, with the average scaling as $N^{1/3}$, with an explicit form for the scaling function.
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"date_modified": "2026-03-02T18:01:35.413000Z",
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"abstract": "We study the Susceptible-Infected-Recovered model of epidemics in the\nvicinity of the threshold infectivity. We derive the distribution of total\noutbreak size in the limit of large population size $N$. This is accomplished\nby mapping the problem to the first passage time of a random walker subject to\na drift that increases linearly with time. We recover the scaling results of\nBen-Naim and Krapivsky that the effective maximal size of the outbreak scales\nas $N^{2/3}$, with the average scaling as $N^{1/3}$, with an explicit form for\nthe scaling function.",
"arxiv_id": "q-bio/0701024",
"authors": [
"David A. Kessler",
"Nadav M. Shnerb"
],
"categories": [
"q-bio.PE"
],
"doi": "10.1103/PhysRevE.76.010901",
"title": "Solution of an infection model near threshold",
"url": "https://arxiv.org/abs/q-bio/0701024"
},
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