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

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  • Damian Clancy

    (University of Liverpool)

  • Sang Taphou Mendy

    (University of Liverpool)

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

Suggested Citation

  • Damian Clancy & Sang Taphou Mendy, 2011. "Approximating the Quasi-stationary Distribution of the SIS Model for Endemic Infection," Methodology and Computing in Applied Probability, Springer, vol. 13(3), pages 603-618, September.
    • Handle: RePEc:spr:metcap:v:13:y:2011:i:3:d:10.1007_s11009-010-9177-8
    DOI: 10.1007/s11009-010-9177-8
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    Citations

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    Cited by:

    1. van Doorn, Erik A. & Pollett, Philip K., 2013. "Quasi-stationary distributions for discrete-state models," European Journal of Operational Research, Elsevier, vol. 230(1), pages 1-14.
    2. Klauschies, Toni & Coutinho, Renato Mendes & Gaedke, Ursula, 2018. "A beta distribution-based moment closure enhances the reliability of trait-based aggregate models for natural populations and communities," Ecological Modelling, Elsevier, vol. 381(C), pages 46-77.
    3. A.H. Nzokem, 2021. "SIS Epidemic Model Birth-and-Death Markov Chain Approach," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(4), pages 1-10, July.

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