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A stochastic SIS infection model incorporating indirect transmission

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Damian Clancy
Damian Clancy*
Affiliation:
The University of Liverpool
*
∗Postal address: Department of Mathematical Sciences, The University of Liverpool, Liverpool L69 7ZL, UK. Email address: d.clancy@liv.ac.uk
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Abstract

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We describe a stochastic susceptible–infective–susceptible (SIS) model for transmission of infectious disease through a population, incorporating both direct host–host transmission and indirect transmission via free-living infectious stages (e.g. environmental bacteria). Existence of a quasi-stationary distribution conditional upon nonextinction of infection is established. A bivariate Ornstein–Uhlenbeck approximation is used to investigate the long-term behaviour of the process conditional upon nonextinction of infection. We show that indirect transmission leads to lower variability in the number of infected hosts present in quasi-stationarity and, consequently, to a greater tendency of infection to persist, compared with a model with direct transmission only and the same average individual infectivity. Some numerical work illustrating these results is presented.

Keywords

Quasi-stationary distributionnormal approximationfree-living infectious stagepiecewise-deterministic Markov process

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 92D30: Epidemiology
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 3 , September 2005 , pp. 726 - 737
Copyright
© Applied Probability Trust 2005 

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