dorsal/arxiv
View SchemaExtinction times for birth-death processes: exact results, continuum asymptotics, and the failure of the Fokker-Planck approximation
| Authors | Charles R. Doering, Khachik V. Sargsyan, Leonard M. Sander |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0401016 |
| URL | https://arxiv.org/abs/q-bio/0401016 |
Abstract
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.
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"abstract": "We consider extinction times for a class of birth-death processes commonly\nfound in applications, where there is a control parameter which determines\nwhether the population quickly becomes extinct, or rather persists for a long\ntime. We give an exact expression for the discrete case and its asymptotic\nexpansion for large values of the population. We have results below the\nthreshold, at the threshold, and above the threshold (where there is a\nquasi-stationary state and the extinction time is very long.) We show that the\nFokker-Planck approximation is valid only quite near the threshold. We compare\nour analytical results to numerical simulations for the SIS epidemic model,\nwhich is in the class that we treat. This is an interesting example of the\ndelicate relationship between discrete and continuum treatments of the same\nproblem.",
"arxiv_id": "q-bio/0401016",
"authors": [
"Charles R. Doering",
"Khachik V. Sargsyan",
"Leonard M. Sander"
],
"categories": [
"q-bio.PE",
"cond-mat.stat-mech",
"physics.bio-ph"
],
"title": "Extinction times for birth-death processes: exact results, continuum asymptotics, and the failure of the Fokker-Planck approximation",
"url": "https://arxiv.org/abs/q-bio/0401016"
},
"schema_id": "dorsal/arxiv",
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