Establishing Traveling Wave in Bistable Reaction-Diffusion System by Feedback

Abstract : Several stains of the intracellular parasitic bacterium Wolbachia limit severely the competence of the mosquitoes Aedes aegypti as a vector of dengue fever and possibly other arboviroses. For this reason, the release of mosquitoes infected by this bacterium in natural populations is presently considered a promising tool in the control of these diseases. Following works by M. Turelli and subsequently M. Strugarek et al., we consider a simple scalar reaction-diffusion model describing the evolution of the proportion of infected mosquitoes, sufficient to reveal the bistable nature of the Wolbachia dynamics. A simple distributed feedback law is proposed, whose application on a compact domain during finite time is shown to be sufficient to invade the whole space. The corresponding stabilization result is established for any space dimension.
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IEEE Control Systems Letters, IEEE, 2017, 1 (1), pp.62 - 67. 〈10.1109/LCSYS.2017.2703303〉
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Pierre-Alexandre Bliman, Nicolas Vauchelet. Establishing Traveling Wave in Bistable Reaction-Diffusion System by Feedback. IEEE Control Systems Letters, IEEE, 2017, 1 (1), pp.62 - 67. 〈10.1109/LCSYS.2017.2703303〉. 〈hal-01558631〉

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