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Solution of an infection model near threshold | David A. Kessler
; Nadav M. Shnerb
; | Date: |
17 Jan 2007 | Subject: | Populations and Evolution | 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. | Source: | arXiv, q-bio/0701024 | Other source: | [GID 555998] pmid17677403 | Services: | Forum | Review | PDF | Favorites |
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