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Epidemic Size in the SIS Model of Endemic Infections

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

David A. Kessler
David A. Kessler*
Affiliation:
Bar-Ilan University
*
∗Postal address: Department of Physics, Bar-Ilan University, Ramat-Gan, IL52900, Israel. Email address: [email protected]
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Abstract

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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, n, in the critical region. We show that this distribution has an n-3/2 singularity for small n and decays exponentially for large n. The exponent decreases with the distance from the threshold, diverging to ∞ far below and approaching 0 far above.

Keywords

InfectionepidemicSIS

MSC classification

Secondary: 92D30: Epidemiology 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) 60J27: Continuous-time Markov processes on discrete state spaces
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 3 , September 2008 , pp. 757 - 778
Copyright
Copyright © Applied Probability Trust 2008 

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