The time to extinction for a stochastic SIS-household-epidemic model

Journal of Mathematical Biology
Tom Britton, Peter Neal

Abstract

We analyse a Markovian SIS epidemic amongst a finite population partitioned into households. Since the population is finite, the epidemic will eventually go extinct, i.e., have no more infectives in the population. We study the effects of population size and within household transmission upon the time to extinction. This is done through two approximations. The first approximation is suitable for all levels of within household transmission and is based upon an Ornstein-Uhlenbeck process approximation for the diseases fluctuations about an endemic level relying on a large population. The second approximation is suitable for high levels of within household transmission and approximates the number of infectious households by a simple homogeneously mixing SIS model with the households replaced by individuals. The analysis, supported by a simulation study, shows that the mean time to extinction is minimized by moderate levels of within household transmission.

References

Feb 24, 2001·Journal of Mathematical Biology·H Anderson, T Britton
Jun 3, 2004·Mathematical Biosciences·G GhoshalI M Sokolov
Jul 6, 2004·Journal of Theoretical Biology·T J HagenaarsN M Ferguson
Sep 9, 2004·American Journal of Epidemiology·Jacco Wallinga, Peter Teunis
Apr 28, 2006·Nature·Neil M FergusonDonald S Burke
Feb 22, 2008·Mathematical Biosciences·Mathias Lindholm
Apr 1, 2008·Mathematical Biosciences·Thomas House, Matt J Keeling

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Citations

Apr 7, 2015·Epidemics·Frank BallGianpaolo Scalia Tomba
Jul 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Vicenç MéndezWerner Horsthemke
Sep 9, 2017·Journal of Mathematical Biology·Yu-Jhe HuangHsin-Yu Wang
Jun 17, 2018·Physical Review. E·M GilsonG Zamora-López
Dec 10, 2020·Journal of the Royal Society, Interface·Maryam AlieeMatt J Keeling

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