Math. Model. Nat. Phenom.
Volume 17, 2022
|Number of page(s)||20|
|Published online||01 August 2022|
Wave blocking in a bistable system by local introduction of a population: application to sterile insect techniques on mosquito populations
Sorbonne Université, CNRS, Université de Paris, Inria, Laboratoire Jacques-Louis Lions UMR7598, 75005 Paris, France
2 Laboratoire Analyse, Géométrie et Applications CNRS UMR 7539, Université Sorbonne Paris Nord, Villetaneuse, France
* Corresponding author: firstname.lastname@example.org
Accepted: 8 June 2022
The Sterile Insect Technique (SIT) is a classic vector control method that has been successfully applied to fight against diverse insect plagues since the 1950s. In recent years, this strategy has been used to control mosquito populations, in order to limit the spread of the diseases they transmit. In this paper, we consider a system of reaction-diffusion equations to model the mosquito population and study the effect of the release of sterile mosquito males. Then, we propose to analyze the release in a limited area inside a wider area containing a natural mosquito population. We are interested in protecting a mosquito free region from invasion by mosquitoes from an exterior domain by controlling the population in a release band at the border between the two regions: we construct a barrier blocking the invasion of mosquitoes from the exterior. We adapt the geometric method of Lewis and Keener (see Lewis and Keener [SIAM J. Appl. Math. 61 (2000) 293-316]) in this framework and extend their main result to find relations on the size of the release region and the density of the released sterile males that allow us to block the invasion. Numerical simulations are also performed to illustrate our results.
Mathematics Subject Classification: 35K57 / 35C07 / 35Q92 / 92D45 / 93C20
Key words: Bistable reaction-diffusion systems / sterile insect technique / pest control / propagation failure / stationary solutions
© The authors. Published by EDP Sciences, 2022
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