Sorbonne Université, Université Paris-Diderot SPC, Inria, CNRS, Laboratoire Jacques-Louis Lions, équipe Mamba, F-75005 Paris
Lugar: NIDTEC de la FPUNA
Fecha y hora: 26/marzo/2019 10:00 hs.
The rapid spread and establishment of mosquitoes population of the genus Aedes have amplified worldwide the risk of Dengue, Chikungunya or Zika epidemics, including in the Northern hemisphere; and the control of these vector-borne diseases is now a major public health issue. Chemical control was the main control method during decades. But with increasing consciousness of the resistance development and of the impact of insecticides on the biodiversity, alternatives have been sought, especially in the form of biological control methods. The Sterile Insect Technique is one of them.
We propose here a sex-structured entomological model and use it to design control strategies capable of eliminating a wild mosquito population in some target locality, through releases of sterile male mosquitoes. Sufficient conditions are provided that achieve this result with periodic impulsive releases of constant value (‘open-loop control’). Also, in the case where periodic measurement of the wild population size is performed, we propose a method to set the release amplitude based on this information (‘closed-loop control’), which serves the same purpose. Last a mixed strategy is proposed, with the advantages of each of the previous ones: exponential decrease of the release amplitudes with respect to time is guaranteed, with a reduced peak-value. Convergence proof is presented for every control law. Comparison is then achieved through numerical simulations, with regard to the whole treatment time, the number of releases and the total amount of released insects.
This is a joint work with Yves Dumont (CIRAD, Montpellier and University of Pretoria, South Africa), Olga Vasilieva (Universidad del Valle, Cali, Colombia) and Daiver Cardona-Salgado (Universidad Autonoma de Occidente, Cali, Colombia).