Issue |
Math. Model. Nat. Phenom.
Volume 17, 2022
|
|
---|---|---|
Article Number | 22 | |
Number of page(s) | 20 | |
DOI | https://doi.org/10.1051/mmnp/2022026 | |
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
1
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: luis.almeida@sorbonne-universite.fr
Received:
13
October
2021
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
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.