Approximating the Quasi-stationary Distribution of the SIS Model for Endemic Infection |
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Authors: | Damian Clancy Sang Taphou Mendy |
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Institution: | 1.Department of Mathematical Sciences,University of Liverpool,Liverpool,England |
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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 < 1 a geometric distribution approximation is preferred; (b) in the supercritical region R
0 ≫ 1 a beta-binomial distribution is preferred. Both of these preferred approximations are new. |
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Keywords: | |
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