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 [4] and subsequently M. Strugarek et al. [21, 22], 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.
Keywords
Cite
@article{arxiv.1703.00672,
title = {Establishing Traveling Wave in Bistable Reaction-Diffusion System by Feedback},
author = {Pierre-Alexandre Bliman and Nicolas Vauchelet},
journal= {arXiv preprint arXiv:1703.00672},
year = {2017}
}