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Article overview
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Epidemic extinction in a generalized contact process | Hanshuang Chen
; Feng Huang
; Haifeng Zhang
; Guofeng Li
; | Date: |
2 Sep 2016 | Abstract: | We study the extinction of epidemics in a generalized contact process, where
a susceptible individual becomes infected with the rate $lambda$ when
contacting $m$ infective individual(s) simultaneously, and an infected
individual spontaneously recovers with the rate $mu$. By employing WKB
approximation for the master equation, the problem is reduced to finding the
zero-energy trajectories in an effective Hamiltonian system, and the mean
extinction time $langle T
angle$ depend exponentially on the associated
action $mathcal {S}$ and the size of the population $N$, $langle T
angle
sim exp(Nmathcal {S})$. Because of qualitatively different bifurcation
features for $m=1$ and $mgeq2$, we derive independently the expressions of
$mathcal {S}$ as a function of the rescaled infection rate $lambda/mu$. For
the weak infection, $mathcal {S}$ scales to the distance to the bifurcation
with an exponent $2$ for $m=1$ and $3/2$ for $mgeq2$. Finally, a rare-event
simulation method is used to validate the theory. | Source: | arXiv, 1608.8715 | Services: | Forum | Review | PDF | Favorites |
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