The time to extinction for a stochastic SIS-household-epidemic model |
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| Authors: | Tom Britton Peter Neal |
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| Institution: | (1) Department of Mathematics and Faculty of Medicine, The University of Ottawa, 585 King Edward Ave, K1N 6N5 Ottawa, Ontario, Canada;(2) Department of Mathematics, The University of Ottawa, 585 King Edward Ave, K1N 6N5 Ottawa, Ontario, Canada;(3) Department of Radiology, University of Manitoba, R3A 1R9 Winnipeg, Manitoba, Canada;(4) Department of Mathematics & Statistics, York University, 4700 Keele St, M3J 1P3 Toronto, Ontario, Canada |
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| 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. |
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