Mathematical modeling and study of dynamical systems in epidemiology. Case of the Chikungunya disease.
Identifieur interne : 000627 ( France/Analysis ); précédent : 000626; suivant : 000628Mathematical modeling and study of dynamical systems in epidemiology. Case of the Chikungunya disease.
Auteurs : Djamila Moulay [France]Source :
Descripteurs français
- mix :
- Wicri :
- topic : épidémiologie.
English descriptors
Abstract
These last years several infectious diseases have appeared or reappeared. These phenomenon are not new and several factors, such as climatic changes, the increase of exchanges and travels, have influenced the increase, the maintenance or the emergence of several infectious diseases. The study of this kind of diseases is recent (introduced in the 1990's by S. Morse). In this work, we consider a tropical disease: Chikungunya. This disease, caused by an arbovirus (arthropode-borne virus), is a vector borne disease transmitted by mosquitoes from \textit{Aedes} genus. For about fifty years, several epidemics have been reported, like in Africa and Asia and more recently in the Réunion Island (2005-2006) and in Italy (2007). It is currently not possible to predict the emergence of such events, that can be geographically localized, sporadic or epidemic. The mathematical modeling then appears to be a useful tool in order to understand their evolution. These models help us taking decisions and direct control efforts. In this work, we first present biological characteristics about the vector and the virus transmission to human population. Then models are proposed and studied (Ordinary differential equations, delay differential equations, optimal control) describing the mosquito population dynamics, based on the biological life cycle (eggs/larvae/pupae/adult) using stage structure models. This model is then integrated in a transmission virus model, described thanks to a SI-SIR epidemiological model. Different scenarios and control strategies, including control technics, that may be applied to limit the number of infection and the vector proliferation, are studied. Then a metapopulation model including human and vector displacements is formulated and studied in the case of the Réunion Island, where the environment is modeled using a network. Finally a comparison and validation of these models are given, based on the real seroprevalence data observed in the Réunion Island and obtained from the INVS (the French institution for public health watching).
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These phenomenon are not new and several factors, such as climatic changes, the increase of exchanges and travels, have influenced the increase, the maintenance or the emergence of several infectious diseases. The study of this kind of diseases is recent (introduced in the 1990's by S. Morse). In this work, we consider a tropical disease: Chikungunya. This disease, caused by an arbovirus (arthropode-borne virus), is a vector borne disease transmitted by mosquitoes from \textit{Aedes} genus. For about fifty years, several epidemics have been reported, like in Africa and Asia and more recently in the Réunion Island (2005-2006) and in Italy (2007). It is currently not possible to predict the emergence of such events, that can be geographically localized, sporadic or epidemic. The mathematical modeling then appears to be a useful tool in order to understand their evolution. These models help us taking decisions and direct control efforts. In this work, we first present biological characteristics about the vector and the virus transmission to human population. Then models are proposed and studied (Ordinary differential equations, delay differential equations, optimal control) describing the mosquito population dynamics, based on the biological life cycle (eggs/larvae/pupae/adult) using stage structure models. This model is then integrated in a transmission virus model, described thanks to a SI-SIR epidemiological model. Different scenarios and control strategies, including control technics, that may be applied to limit the number of infection and the vector proliferation, are studied. Then a metapopulation model including human and vector displacements is formulated and studied in the case of the Réunion Island, where the environment is modeled using a network. Finally a comparison and validation of these models are given, based on the real seroprevalence data observed in the Réunion Island and obtained from the INVS (the French institution for public health watching).</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Haute-Normandie</li><li>Région Normandie</li></region><settlement><li>Le Havre</li></settlement><orgName><li>Université du Havre</li></orgName></list><tree><country name="France"><region name="Région Normandie"><name sortKey="Moulay, Djamila" sort="Moulay, Djamila" uniqKey="Moulay D" first="Djamila" last="Moulay">Djamila Moulay</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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