Optimal control of chikungunya disease: Larvae reduction, treatment and prevention

Djamila Moulay; M. A. Aziz-Alaoui; Hee-Dae Kwon

doi:10.3934/mbe.2012.9.369

Article Contents

2012, Volume 9, Issue 2: 369-392. Doi: 10.3934/mbe.2012.9.369

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Optimal control of chikungunya disease: Larvae reduction, treatment and prevention

1.
LMAH, Université du Havre, 25 rue Philippe Lebon, BP540, 76058 Le Havre Cedex
2.
Department of Mathematics, Inha University, Incheon, 402-751

Received: March 31, 2011

Revised: November 30, 2011

Published: February 2012

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Abstract

Since the 1980s, there has been a worldwide re-emergence of vector-borne diseases including Malaria, Dengue, Yellow fever or, more recently, chikungunya. These viruses are arthropod-borne viruses (arboviruses) transmitted by arthropods like mosquitoes of Aedes genus. The nature of these arboviruses is complex since it conjugates human, environmental, biological and geographical factors. Recent researchs have suggested, in particular during the Réunion Island epidemic in 2006, that the transmission by Aedes albopictus (an Aedes genus specie) has been facilitated by genetic mutations of the virus and the vector capacity to adapt to non tropical regions. In this paper we formulate an optimal control problem, based on biological observations. Three main efforts are considered in order to limit the virus transmission. Indeed, there is no vaccine nor specific treatment against chikungunya, that is why the main measures to limit the impact of such epidemic have to be considered. Therefore, we look at time dependent breeding sites destruction, prevention and treatment efforts, for which optimal control theory is applied. Using analytical and numerical techniques, it is shown that there exist cost effective control efforts.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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