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020 _a9783642205309
_9978-3-642-20530-9
024 7 _a10.1007/978-3-642-20530-9
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aMAT029000
_2bisacsh
072 7 _aPBT
_2thema
072 7 _aPBWL
_2thema
082 0 4 _a519.2
_223
100 1 _aNåsell, Ingemar.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aExtinction and Quasi-Stationarity in the Stochastic Logistic SIS Model
_h[electronic resource] /
_cby Ingemar Nåsell.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2011.
300 _aXI, 199 p. 10 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aMathematical Biosciences Subseries,
_x2524-6771 ;
_v2022
505 0 _a1 Introduction -- 2 Model Formulation -- 3 A Birth-Death Process with Finite State Space and with an Absorbing State at the Origin -- 4 The SIS Model: First Approximations of the Quasi-Stationary Distribution -- 5 Some Approximations Involving the Normal Distribution -- 6 Preparations for the Study of the Stationary Distribution p(1) of the SIS Model -- 7 Approximation of the Stationary Distribution p(1) of the SIS Model -- 8 Preparations for the Study of the Stationary Distribution p(0) of the SIS Model -- 9 Approximation of the Stationary Distribution p(0) of the SIS Model -- 10 Approximation of Some Images UnderY for the SIS Model -- 11 Approximation of the Quasi-Stationary Distribution q of the SIS Model -- 12 Approximation of the Time to Extinction for the SIS Model -- 13 Uniform Approximations for the SIS Model -- 14 Thresholds for the SIS Model -- 15 Concluding Comments.
520 _aThis volume presents explicit approximations of the quasi-stationary distribution and of the expected time to extinction from the state one and from quasi-stationarity for the stochastic logistic SIS model. The approximations are derived separately in three different parameter regions, and then combined into a uniform approximation across all three regions. Subsequently, the results are used to derive thresholds as functions of the population size N.
650 0 _aDistribution (Probability theory.
650 0 _aLife sciences.
650 1 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
650 2 4 _aLife Sciences, general.
_0http://scigraph.springernature.com/things/product-market-codes/L00004
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642205293
776 0 8 _iPrinted edition:
_z9783642205316
830 0 _aMathematical Biosciences Subseries,
_x2524-6771 ;
_v2022
856 4 0 _uhttps://doi.org/10.1007/978-3-642-20530-9
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c10300
_d10300