On a temporal model for the Chikungunya disease: Modeling, theory and numerics

Dumont Yves, Chiroleu Frédéric, Domerg Caroline. 2008. On a temporal model for the Chikungunya disease: Modeling, theory and numerics. Mathematical Biosciences, 213 (1) : 80-91.

https://doi.org/10.1016/j.mbs.2008.02.008

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Résumé : Reunion Island faced two episodes of Chikungunya, a vector-borne disease, in 2005 and in 2006. The latter was of unprecedented magnitude: one third of the population was infected. Until the severe episode of 2006, our knowledge of Chikungunya was very limited. The principal aim of our study is to propose a model, including human and mosquito compartments, that is associated to the time course of the first epidemic of Chikungunya. By computing the basic reproduction number R0, we show there exists a disease-free equilibrium that is locally asymptotically stable if the basic reproduction number is less than 1. Moreover, we give a necessary condition for global asymptotic stability of the disease-free equilibrium. Then, we propose a numerical scheme that is qualitatively stable and present several simulations as well as numerical estimates of the basic reproduction number for some cities of Reunion Island. For the episode of 2005, R0 was less than one, which partly explains why no outbreak appeared. Using recent entomological results, we investigate links between the episode of 2005 and the outbreak of 2006. Finally, our work shows that R0 varied from place to place on the island, indicating that quick and focused interventions, like the destruction of breeding sites, may be effective for controlling the disease.

Mots-clés Agrovoc : maladie transmise par vecteur, Alphavirus, modèle de simulation, modèle mathématique, technique de prévision, contrôle de maladies, épidémiologie, virus de chikungunya

Mots-clés géographiques Agrovoc : La Réunion, France

Classification Agris : S50 - Santé humaine
L73 - Maladies des animaux
U10 - Informatique, mathématiques et statistiques

Champ stratégique Cirad : Axe 4 (2005-2013) - Santé animale et maladies émergentes

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