Biology – Quantitative Biology – Populations and Evolution
Scientific paper
2004-01-10
Biology
Quantitative Biology
Populations and Evolution
20 pages, 6 figures
Scientific paper
We consider extinction times for a class of birth-death processes commonly found in applications, where there is a control parameter which determines whether the population quickly becomes extinct, or rather persists for a long time. We give an exact expression for the discrete case and its asymptotic expansion for large values of the population. We have results below the threshold, at the threshold, and above the threshold (where there is a quasi-stationary state and the extinction time is very long.) We show that the Fokker-Planck approximation is valid only quite near the threshold. We compare our analytical results to numerical simulations for the SIS epidemic model, which is in the class that we treat. This is an interesting example of the delicate relationship between discrete and continuum treatments of the same problem.
Doering Charles R.
Sander Leonard M.
Sargsyan Khachik V.
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