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The SEIS model, or, the contact process with a latent stage

Part of: Markov processes Mathematical biology in general

Published online by Cambridge University Press:  24 October 2016

Eric Foxall
Eric Foxall*
Affiliation:
Arizona State University
*
* Postal address: School of Mathematical and Statistical Sciences, Arizona State University, PO Box 871804, Tempe, AZ, 85287-1804, USA. Email address: eric.foxall@asu.edu
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Abstract

The susceptible→exposed→infectious→susceptible (SEIS) model is well known in mathematical epidemiology as a model of infection in which there is a latent period between the moment of infection and the onset of infectiousness. The compartment model is well studied, but the corresponding particle system has so far received no attention. For the particle system model in one spatial dimension, we give upper and lower bounds on the critical values, prove convergence of critical values in the limit of small and large latent time, and identify a limiting process to which the SEIS model converges in the limit of large latent time.

Keywords

SEIS modelcontact processinteracting particle system

MSC classification

Primary: 60J25: Continuous-time Markov processes on general state spaces 92B99: None of the above, but in this section

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 3 , September 2016 , pp. 783 - 801
Copyright
Copyright © Applied Probability Trust 2016 

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