2011 | OriginalPaper | Chapter
Approximation of the Time to Extinction for the SIS Model
Author : Ingemar Nåsell
Published in: Extinction and Quasi-Stationarity in the Stochastic Logistic SIS Model
Publisher: Springer Berlin Heidelberg
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We noted in Sect. 3.4, (3.42), that the time to extinction $$ \tau_{\rm q}$$ from quasi-stationarity for a birth–death process with finite state space and with an absorbing state at the origin has an exponential distribution with expectation equal to $$ \rm E{\tau}_{Q}= 1 /(\mu_{1}\rm q_{1}).$$