Sorbonne Université, Université Paris-Diderot SPC, Inria, CNRS, Laboratoire Jacques-Louis Lions, équipe Mamba, Paris, France.
Universidad Autónoma de Occidente, Cali, Colombia.
Math Biosci. 2019 Aug;314:43-60. doi: 10.1016/j.mbs.2019.06.002. Epub 2019 Jun 6.
In this paper, we propose a sex-structured entomological model that serves as a basis for design of control strategies relying on releases of sterile male mosquitoes (Aedes spp) and aiming at elimination of the wild vector population in some target locality. We consider different types of releases (constant and periodic impulsive), providing sufficient conditions to reach elimination. However, the main part of the paper is focused on the study of the periodic impulsive control in different situations. When the size of wild mosquito population cannot be assessed in real time, we propose the so-called open-loop control strategy that relies on periodic impulsive releases of sterile males with constant release size. Under this control mode, global convergence towards the mosquito-free equilibrium is proved on the grounds of sufficient condition that relates the size and frequency of releases. If periodic assessments (either synchronized with the releases or more sparse) of the wild population size are available in real time, we propose the so-called closed-loop control strategy, under which the release size is adjusted in accordance with the wild population size estimate. Finally, we propose a mixed control strategy that combines open-loop and closed-loop strategies. This control mode renders the best result, in terms of overall time needed to reach elimination and the number of releases to be effectively carried out during the whole release campaign, while requiring for a reasonable amount of released sterile insects.
本文提出了一个基于性别的昆虫学模型，作为依赖释放不育雄蚊（Aedes 属）以消除特定目标区域野生传播媒介种群的控制策略的设计基础。我们考虑了不同类型的释放（连续和周期性脉冲），提供了达到消除的充分条件。然而，本文的主要部分侧重于研究不同情况下的周期性脉冲控制。当无法实时评估野生蚊种群的规模时，我们提出了所谓的开环控制策略，该策略依赖于具有恒定释放规模的周期性脉冲释放不育雄蚊。在这种控制模式下，基于与释放规模和频率相关的充分条件，证明了向无蚊平衡点的全局收敛性。如果能够实时进行定期的野生种群规模评估（与释放同步或更稀疏），我们提出了所谓的闭环控制策略，根据野生种群规模的估计来调整释放规模。最后，我们提出了一种混合控制策略，将开环和闭环策略结合起来。这种控制模式在达到消除所需的总时间和整个释放期间需要实际进行的释放次数方面取得了最佳效果，同时要求释放合理数量的不育昆虫。
