Approximating the Quasi-stationary Distribution of the SIS Model for Endemic Infection

Damian Clancy () and Sang Taphou Mendy
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Damian Clancy: University of Liverpool
Sang Taphou Mendy: University of Liverpool

Methodology and Computing in Applied Probability, 2011, vol. 13, issue 3, 603-618

Abstract: Abstract Probably the simplest model for endemic infection is the susceptible-infected-susceptible (SIS) logistic model. Long-term behaviour of this model prior to disease extinction is described by the quasi-stationary distribution. This quasi-stationary distribution has been the subject of much previous work, including derivation of a variety of approximations, using both standard distributional forms and specialized approximating formulae. The aim of this paper is to carry out a systematic comparison between approximations. As well as comparing previously available approximations, we derive several new variants. Taking into account both accuracy (measured using total variation distance) and simplicity, and denoting by R 0 the basic reproduction number, our main findings are: (a) in the subcritical region R 0

Keywords: Stochastic infection model; Endemic disease; Cumulant equations; Moment closure; 60J28; 92D30 (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s11009-010-9177-8

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