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On the outcome of epidemics with detections

Part of: Markov processes

Published online by Cambridge University Press:  15 September 2017

Claude Lefèvre  and
Philippe Picard
Claude Lefèvre*
Affiliation:
Université Libre de Bruxelles and Université de Lyon
Philippe Picard*
Affiliation:
Université de Lyon
*
* Postal address: Département de Mathématique, Campus de la Plaine C.P. 210, B-1050 Bruxelles, Belgium. Email address: clefevre@ulb.ac.be
** Postal address: Ecole ISFA, 50 Avenue Tony Garnier, F-69007 Lyon, France. Email address: philippe.picard69@free.fr
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Abstract

The classical SIR epidemic model is generalized to incorporate a detection process of infectives in the course of time. Our purpose is to determine the exact distribution of the population state at the first detection instant and the following ones. An extension is also discussed that allows the parameters to change with the number of detected cases. The followed approach relies on simple martingale arguments and uses a special family of Abel–Gontcharoff polynomials.

Keywords

General epidemicdetection of infectiveschange of parametersstopping timeAbel–Gontcharoff polynomial

MSC classification

Primary: 60J28: Applications of continuous-time Markov processes on discrete state spaces 92D30: Epidemiology
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 3 , September 2017 , pp. 890 - 904
Copyright
Copyright © Applied Probability Trust 2017 

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