Epidemic Size in the Sis Model of Endemic Infec- Tions

Details Epidemic Size in the Sis Model of Endemic Infec- Tions Epidemic Size in the Sis Model of Endemic Infec- Tions

2007-09-19

arxiv.org/abs/0709.3049v1

Biology

Quantitative Biology

Populations and Evolution

Scientific paper

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 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, n, in the critical region. We show that this distribution has a $n^3/2$ singularity for small n and decays exponentially for large n. The exponent decreases with the distance from threshold, diverging to infinity far below and approaching zero far above.

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