Nåsell, Ingemar.
Extinction and Quasi-Stationarity in the Stochastic Logistic SIS Model [electronic resource] / by Ingemar Nåsell. - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2011. - XI, 199 p. 10 illus. in color. online resource. - Lecture Notes in Mathematics, 2022 0075-8434 ; . - Lecture Notes in Mathematics, 2022 .
1 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.
This 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.
9783642205309
10.1007/978-3-642-20530-9 doi
Mathematics.
Life sciences.
Distribution (Probability theory).
Mathematics.
Probability Theory and Stochastic Processes.
Life Sciences, general.
QA273.A1-274.9 QA274-274.9
519.2
Extinction and Quasi-Stationarity in the Stochastic Logistic SIS Model [electronic resource] / by Ingemar Nåsell. - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2011. - XI, 199 p. 10 illus. in color. online resource. - Lecture Notes in Mathematics, 2022 0075-8434 ; . - Lecture Notes in Mathematics, 2022 .
1 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.
This 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.
9783642205309
10.1007/978-3-642-20530-9 doi
Mathematics.
Life sciences.
Distribution (Probability theory).
Mathematics.
Probability Theory and Stochastic Processes.
Life Sciences, general.
QA273.A1-274.9 QA274-274.9
519.2