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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.
List of contents
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.
Summary
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.
