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18 February 2025
 
  » arxiv » 1608.8715

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Epidemic extinction in a generalized contact process
Hanshuang Chen ; Feng Huang ; Haifeng Zhang ; Guofeng Li ;
Date 2 Sep 2016
AbstractWe 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
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