期刊
JOURNAL OF APPLIED PROBABILITY
卷 45, 期 3, 页码 757-778出版社
APPLIED PROBABILITY TRUST
DOI: 10.1239/jap/1222441828
关键词
Infection; epidemic; SIS
资金
- Israel Science Foundation
We study the susceptible-infected-susceptible model of the spread of an endemic infection. We calculate an exact expression for the mean number of transmissions for all values of the population size (N) and the infectivity. We derive the large-N asymptotic behavior for the infectivitiy below, above, and in the critical region. We obtain an analytical expression for the probability distribution of the number of transmissions, it, in the critical region. We show that this distribution has an 17-3/2 singularity for small it and decays exponentially for large n. The exponent decreases with the distance from the threshold, diverging to infinity far below and approaching 0 far above.
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