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Large deviation principle for epidemic models

Part of: Stochastic analysis Limit theorems Physiological, cellular and medical topics Markov processes

Published online by Cambridge University Press:  15 September 2017

Etienne Pardoux  and
Brice Samegni-Kepgnou
Etienne Pardoux*
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France
Brice Samegni-Kepgnou*
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France
*
* Postal address: CNRS UMR 7373 (I2M), Aix-Marseille Université, CMI, 39 rue F. Joliot Curie, F-13453 Marseille, France.
* Postal address: CNRS UMR 7373 (I2M), Aix-Marseille Université, CMI, 39 rue F. Joliot Curie, F-13453 Marseille, France.
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Abstract

We consider a general class of epidemic models obtained by applying the random time changes of Ethier and Kurtz (2005) to a collection of Poisson processes and we show the large deviation principle for such models. We generalise the approach followed by Dolgoarshinnykh (2009) in the case of the SIR epidemic model. Thanks to an additional assumption which is satisfied in many examples, we simplify the recent work of Kratz and Pardoux (2017).

Keywords

Poisson processlarge deviation principlelaw of large numbers

MSC classification

Primary: 60F10: Large deviations 60H10: Stochastic ordinary differential equations 60J75: Jump processes 92C60: Medical epidemiology
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 3 , September 2017 , pp. 905 - 920
Copyright
Copyright © Applied Probability Trust 2017 

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