Extinction times in the subcritical stochastic SIS logistic epidemicCitation formats

Standard

Extinction times in the subcritical stochastic SIS logistic epidemic. / Brightwell, Graham; House, Thomas; Luczak, Malwina.

In: Journal of Mathematical Biology, Vol. 77, No. 2, 08.2018, p. 1-39.

Research output: Contribution to journalArticle

Harvard

Brightwell, G, House, T & Luczak, M 2018, 'Extinction times in the subcritical stochastic SIS logistic epidemic' Journal of Mathematical Biology, vol. 77, no. 2, pp. 1-39. https://doi.org/10.1007/s00285-018-1210-5

APA

Brightwell, G., House, T., & Luczak, M. (2018). Extinction times in the subcritical stochastic SIS logistic epidemic. Journal of Mathematical Biology, 77(2), 1-39. https://doi.org/10.1007/s00285-018-1210-5

Vancouver

Brightwell G, House T, Luczak M. Extinction times in the subcritical stochastic SIS logistic epidemic. Journal of Mathematical Biology. 2018 Aug;77(2):1-39. https://doi.org/10.1007/s00285-018-1210-5

Author

Brightwell, Graham ; House, Thomas ; Luczak, Malwina. / Extinction times in the subcritical stochastic SIS logistic epidemic. In: Journal of Mathematical Biology. 2018 ; Vol. 77, No. 2. pp. 1-39.

Bibtex

@article{e5dfe0e9f50b491087ed7ac5f4d7e1c7,
title = "Extinction times in the subcritical stochastic SIS logistic epidemic",
abstract = "Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights into the near-critical regime by considering the stochastic SIS logistic epidemic, a well-known birth-and-death chain used to model the spread of an epidemic within a population of a given size N. We study the behaviour of the process as the population size N tends to infinity. Our results cover the entire subcritical regime, including the “barely subcritical” regime, where the recovery rate exceeds the infection rate by an amount that tends to 0 as (Formula presented.) but more slowly than (Formula presented.). We derive precise asymptotics for the distribution of the extinction time and the total number of cases throughout the subcritical regime, give a detailed description of the course of the epidemic, and compare to numerical results for a range of parameter values. We hypothesise that features of the course of the epidemic will be seen in a wide class of other epidemic models, and we use real data to provide some tentative and preliminary support for this theory.",
keywords = "Birth-and-death chain, Near-critical epidemic, Stochastic SIS logistic epidemic, Time to extinction",
author = "Graham Brightwell and Thomas House and Malwina Luczak",
year = "2018",
month = "8",
doi = "10.1007/s00285-018-1210-5",
language = "English",
volume = "77",
pages = "1--39",
journal = "Journal of Mathematical Biology",
issn = "0303-6812",
publisher = "Springer Nature",
number = "2",

}

RIS

TY - JOUR

T1 - Extinction times in the subcritical stochastic SIS logistic epidemic

AU - Brightwell, Graham

AU - House, Thomas

AU - Luczak, Malwina

PY - 2018/8

Y1 - 2018/8

N2 - Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights into the near-critical regime by considering the stochastic SIS logistic epidemic, a well-known birth-and-death chain used to model the spread of an epidemic within a population of a given size N. We study the behaviour of the process as the population size N tends to infinity. Our results cover the entire subcritical regime, including the “barely subcritical” regime, where the recovery rate exceeds the infection rate by an amount that tends to 0 as (Formula presented.) but more slowly than (Formula presented.). We derive precise asymptotics for the distribution of the extinction time and the total number of cases throughout the subcritical regime, give a detailed description of the course of the epidemic, and compare to numerical results for a range of parameter values. We hypothesise that features of the course of the epidemic will be seen in a wide class of other epidemic models, and we use real data to provide some tentative and preliminary support for this theory.

AB - Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights into the near-critical regime by considering the stochastic SIS logistic epidemic, a well-known birth-and-death chain used to model the spread of an epidemic within a population of a given size N. We study the behaviour of the process as the population size N tends to infinity. Our results cover the entire subcritical regime, including the “barely subcritical” regime, where the recovery rate exceeds the infection rate by an amount that tends to 0 as (Formula presented.) but more slowly than (Formula presented.). We derive precise asymptotics for the distribution of the extinction time and the total number of cases throughout the subcritical regime, give a detailed description of the course of the epidemic, and compare to numerical results for a range of parameter values. We hypothesise that features of the course of the epidemic will be seen in a wide class of other epidemic models, and we use real data to provide some tentative and preliminary support for this theory.

KW - Birth-and-death chain

KW - Near-critical epidemic

KW - Stochastic SIS logistic epidemic

KW - Time to extinction

UR - http://www.scopus.com/inward/record.url?scp=85044943701&partnerID=8YFLogxK

U2 - 10.1007/s00285-018-1210-5

DO - 10.1007/s00285-018-1210-5

M3 - Article

VL - 77

SP - 1

EP - 39

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 2

ER -