5 edition of **Extinction and quasi-stationarity in the stochastic logistic SIS model** found in the catalog.

Extinction and quasi-stationarity in the stochastic logistic SIS model

Ingemar NГҐsell

- 62 Want to read
- 25 Currently reading

Published
**2011**
by Springer Verlag in Heidelberg, New York
.

Written in English

- Population biology,
- Mathematical models,
- Stochastic models,
- Relicts (Biology),
- Biomathematics

**Edition Notes**

Statement | Ingemar Nåsell |

Series | Lecture notes in mathematics -- 2022, Mathematical biosciences subseries, Lecture notes in mathematics (Springer-Verlag), Lecture notes in mathematics (Springer-Verlag) -- 2022. |

Classifications | |
---|---|

LC Classifications | QH352 .N37 2011, QA3 .L28 no.2022 |

The Physical Object | |

Pagination | xi, 199 p. : |

Number of Pages | 199 |

ID Numbers | |

Open Library | OL25189626M |

ISBN 10 | 3642205291 |

ISBN 10 | 9783642205293, 9783642205309 |

LC Control Number | 2011930820 |

OCLC/WorldCa | 729346823 |

Our main concern in this monograph is with the quasi-stationary distribution and the time to extinction for the stochastic logistic SIS model. Explicit expressions are not available for these. Extinction and Quasi-stationarity in the Verhulst Logistic Model. Journal of Theoretical Biology, Vol. , Issue. 1, p. The quasi-stationary distribution of the closed stochastic SIS model changes drastically as the basic reproduction ratio R 0 passes the deterministic threshold value 1. Approximations are derived that describe these.

We study an open population stochastic epidemic model from the time of introduction of the disease, through a possible outbreak and to extinction. The model describes an SIS (susceptible-infective. Download Citation | ON THE QUASI-STATIONARY DISTRIBUTION OF SIS MODELS | In this paper, we propose a novel method for constructing upper bounds of the quasi-stationary distribution of SIS .

A. Lahrouz and L. Omari, Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence, Statist. Probabil. Lett. 83(4) () – Crossref, ISI, Google Scholar; D. Jiang, J. Yu, C. Ji et al. Asymptotic behavior of global positive solution to a stochastic SIR model. The stochastic aspects of the SIS model for infectious diseases have been studied by many authors. In [10], Cavender considered the SIS model as an example of a birth and death process, which is a stochastic population model used to model demographic stochasticity [8]. Norden [32] described the stochastic SIS model as a stochastic logistic.

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: Extinction and Quasi-Stationarity in the Stochastic Logistic SIS Model (Lecture Notes in Mathematics ()) (): Nåsell, Ingemar: BooksCited by: Extinction and Quasi-Stationarity in the Stochastic Logistic SIS Model book series (LNM, volume ) Also part of the Mathematical Biosciences Subseries book sub series -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. 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. Get this from a library. Extinction and quasi-stationarity in the stochastic logistic SIS model. [Ingemar Nåsell] -- "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.

An approximation is derived for the quasi-stationary distribution of the stochastic logistic epidemic in the intricate case where the transmission factor R 0 lies in the transition region near the deterministic threshold value 1.

An approximation for the expected time to extinction from quasi-stationarity in the same parameter region is also by: Nåsell I. () The SIS Model: First Approximations of the Quasi-stationary Distribution.

In: Extinction and Quasi-Stationarity in the Stochastic Logistic SIS Model. Lecture Notes in Mathematics, vol Nåsell I. () Approximation of the Quasi-stationary Distribution q of the SIS Model.

In: Extinction and Quasi-Stationarity in the Stochastic Logistic SIS Model. Lecture Notes in Mathematics, vol Extinction and Quasi-stationarity in the Verhulst Logistic Model C.

LEFÈVREOn the extinction of the SIS stochastic logistic epidemic. Appl. Probab., 27 (), pp. R.H. NORDENOn the distribution of the time to extinction in the stochastic logistic population model. ymptotic approximation, transition region, logistic model, SIS model, demographic stochasticity, stochastic fade-out.

The work reported here was stimulated by a study circle on biological models at the University of Stockholm during the spring term ofinitiated by H˚akan Andersson.

The study circle was focused on the book by Renshaw. Nåsell I. () Approximation of Some Images Under Ψ for the SIS Model. In: Extinction and Quasi-Stationarity in the Stochastic Logistic SIS Model. Lecture Notes in Mathematics, vol (English) In: EXTINCTION AND QUASI-STATIONARITY IN THE STOCHASTIC LOGISTIC SIS MODEL,p.

V-+ Chapter in book (Refereed) Place, publisher, year, edition, pages p. V-+ Series Kapitel i bok, del av antologi, ISSN National Category.

Extinction and Quasi-stationarity in the Verhulst Logistic Model The study circle was focused on the book by Renshaw. An early version of this paper was presented at the Conference on Mathematical Population Dynamics in Zakopane, Poland.

I thank Charles Mode for inviting me to. Get this from a library. Extinction and quasi-stationarity in the stochastic logistic SIS model. [Ingemar Nåsell] -- 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.

Cite this chapter as: Nåsell I. () Preparations for the Study of the Stationary Distribution p (1) of the SIS Model. In: Extinction and Quasi-Stationarity in the Stochastic Logistic SIS Model. springer, 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. This book presents 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.

These are derived and then combined into uniform approximation. The stochastic SIS model is a birth-and-death process with a finite state space, correspondent to the number of infected individuals I (t) ∈ {0, 1, 2,N} at time t.

The birth rate β is the probability, per unit of time, of one infected individual to have a contact with a susceptible one and to transmit the disease. (English) In: EXTINCTION AND QUASI-STATIONARITY IN THE STOCHASTIC LOGISTIC SIS MODEL, Springer Berlin/Heidelberg,p. Chapter in book (Refereed) Place, publisher, year, edition, pages Springer Berlin/Heidelberg, p.

Series, Lecture notes in. (English) In: EXTINCTION AND QUASI-STATIONARITY IN THE STOCHASTIC LOGISTIC SIS MODEL,p. Chapter in book (Refereed) Place, publisher, year, edition, pages p. Series Kapitel i bok, del av antologi, ISSN National Category.

EXTINCTION AND QUASI-STATIONARITY IN THE VERHULST LOGISTIC MODEL: WITH DERIVATIONS OF MATHEMATICAL RESULTS The time until extinction for the closed SIS stochastic logistic epidemic model is. () Extinction and persistence of a stochastic nonlinear SIS epidemic model with jumps.

Physica A: Statistical Mechanics and its Applications() Modelling the effect of telegraph noise in the SIRS epidemic model using Markovian switching. These results link the stochastic SIS epidemic model with a pure dynamical system, which can be solved and manipulated using standard analytical tools.

I. Extinction and quasi-stationarity .The first model is a two-strain generalization of the stochastic Susceptible-Infected-Susceptible (SIS) model. Here we extend previous results due to Parsons and Quince (), Parsons et al (