Extinction and quasi-stationarity in the stochastic logistic SIS model

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 auniform approximation across all three regions. Subsequently, the results areused to derive thresholds as functions of the population size N. INDICE: 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.

• ISBN: 978-3-642-20529-3
• Editorial: Springer Berlin Heidelberg
• Encuadernacion: Rústica
• Páginas: 196
• Fecha Publicación: 01/06/2011
• Nº Volúmenes: 1
• Idioma: Inglés