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Book Sections Year : 2022

Minimal cost-time strategies for mosquito population replacement


Vector control plays a central role in the fight against vector-borne diseases and, in particular, arboviruses. The use of the endosymbiotic bacterium \textit{Wolbachia} has proven effective in preventing the transmission of some of these viruses between mosquitoes and humans, making it a promising control tool. The population replacement technique we consider consists in replacing the wild population by a population carrying the aforementioned bacterium, thereby preventing outbreaks of the associated vector-borne diseases. In this work, we consider a two species model incorporating both Wolbachia infected and wild mosquitoes. Our system can be controlled thanks to a term representing an artificial introduction of Wolbachia-infected mosquitoes. Under the assumption that the birth rate of mosquitoes is high, we may reduce the model to a simpler one regarding the proportion of infected mosquitoes. We investigate minimal cost-time strategies to achieve a population replacement both analytically and numerically for the simplified 1D model and only numerically for the full 2D system.
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Dates and versions

hal-02532677 , version 1 (05-04-2020)
hal-02532677 , version 2 (30-04-2020)
hal-02532677 , version 3 (27-11-2020)


  • HAL Id : hal-02532677 , version 3


Luis Almeida, Jesús Bellver Arnau, Michel Duprez, Yannick Privat. Minimal cost-time strategies for mosquito population replacement. Roland Herzog, Matthias Heinkenschloss, Dante Kalise, Georg Stadler and Emmanuel Trélat. Optimization and Control for Partial Differential Equations, 29, De Gruyter, 2022, Radon Series on Computational and Applied Mathematics, 9783110695984. ⟨hal-02532677v3⟩
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