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| HAL : hal-00320363, version 3 |
| arXiv : 0809.1824 |
| DOI : 10.1239/jap/1294170513 |
| Fiche détaillée |  Récupérer au format |
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| Journal of Applied Probability 47, 4 (2010) 976--996 |
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| Versions disponibles : | v1 (10-09-2008) | v2 (24-10-2008) | v3 (19-02-2010) |
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| A Markov model for the spread of viruses in an open population |
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| Laure Coutin 1Laurent Decreusefond 2, 3 |
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| (12/2010) |
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| We propose a Markov model for the spread of Hepatitis C virus (HCV) among drug users who use injections. We then proceed to an asymptotic analysis (large initial population) and show that the Markov process is close to the solution of a non linear autonomous differential system. We prove both a law of large numbers and functional central limit theorem to precise the speed of convergence towards the limiting system. The deterministic system itself converges, as time goes to infinity, to an equilibrium point. This corroborates the empirical observations about the prevalence of HCV. |
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| 1 : | Institut Mathématiques de Toulouse |
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Institut Mathématiques de Toulouse |
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| 2 : | Laboratoire traitement et communication de l'information (LTCI) |
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CNRS : UMR5141 – Institut Télécom – Télécom ParisTech |
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| 3 : | Institut Télécom - Télécom ParisTech |
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Télécom ParisTech |
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| 4 : | Institut Galilée (IG) |
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Université Paris XIII - Paris Nord |
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| Domaine | : | Mathématiques/Probabilités |
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| Epidemiology – HCV – Markov processes – mean field approximation |
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| hal-00320363, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00320363 | |
| oai:hal.archives-ouvertes.fr:hal-00320363 | |
| Contributeur : Laurent Decreusefond | |
| Soumis le : Vendredi 19 Février 2010, 17:12:00 | |
| Dernière modification le : Vendredi 11 Mars 2011, 10:39:12 | |
