Author: Marina Voinson; Alexandra Alvergne; Sylvain Billiard; Charline Smadi
Title: Stochastic dynamics of an epidemics with recurrent spillovers from an endemic reservoir Document date: 2017_11_3
ID: b2f3a8un_64
Snippet: The second excursion has a probability γ/βS 2 − 1 (γ/βS 2 ) c − 1 to be an outbreak. The number of susceptibles at the beginning of the third excursion is approximated by We now focus on the case R 0 = βN/γ > 1. In this case the approximating branching process will be supercritical and will go to infinity with a positive probability. In the case when the epidemic process describes small excursions, the branching process approximation is.....
Document: The second excursion has a probability γ/βS 2 − 1 (γ/βS 2 ) c − 1 to be an outbreak. The number of susceptibles at the beginning of the third excursion is approximated by We now focus on the case R 0 = βN/γ > 1. In this case the approximating branching process will be supercritical and will go to infinity with a positive probability. In the case when the epidemic process describes small excursions, the branching process approximation is still valid, but in the case when it describes a large excursion, then a large fraction of susceptible individuals will be consumed and the branching approximation will not be valid anymore. However, as all the quantities (susceptible, infected and recovered individuals) will be large, a mean field approximation will be a good approximation of the process. Here the mean field approximation will be the deterministic SIR process, whose dynamics is given by:
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