Selected article for: "branching process and outbreak excursion"
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_83
    Snippet: As the approximating branching process is subcritical, the probability p c is small. Hence, we pursue the approximation by saying As a consequence, we get P(excursion is an outbreak) ∼ mp c = 1 − βN γ −τ /β (γ/βN ) 2 − 1 (γ/βN ) c − 1 when mp 2 c is small. Hence, if mp c is small, few outbreaks will hit the treshold, and the number of outbreaks will be small. If mp c is large, (1−p c ) m is small and the outbreaks will be big,.....
    Document: As the approximating branching process is subcritical, the probability p c is small. Hence, we pursue the approximation by saying As a consequence, we get P(excursion is an outbreak) ∼ mp c = 1 − βN γ −τ /β (γ/βN ) 2 − 1 (γ/βN ) c − 1 when mp 2 c is small. Hence, if mp c is small, few outbreaks will hit the treshold, and the number of outbreaks will be small. If mp c is large, (1−p c ) m is small and the outbreaks will be big, consuming a large number of susceptible individuals.

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