消灭入侵物种的“滚动地毯”策略分析
Analysis of the "Rolling carpet" strategy to eradicate an invasive species
摘要：
为了防止由蚊子传播的人类疾病（如登革热或寨卡病毒）的传播，一种可能的解决方案是直接对蚊子种群采取行动。在这项工作中，我们考虑一种入侵物种（蚊子），我们研究了两种策略，通过局部干预消除整个空间的人口。种群的动态是通过一维环境中的非线性反应扩散方程建模的，这两种策略都基于相同的想法：我们作用于移动区间。第一个策略的行动是在这个移动区间内杀死尽可能多的个体。第二种策略的作用是在这个移动间隔中释放不育的雄性。对于这两种策略，我们设法生成相对于自然侵入性行波的方向相反的传播的行波。这些案例相当于成功地消灭了入侵物种。此外，对于第一个策略，我们充分刻画了区间的最小尺寸。所有的结果都通过数值模拟进行了说明。
英文摘要：
In order to prevent the propagation of human diseases transmitted by mosquitoes (such as dengue or zika), one possible solution is to act directly on the mosquito population. In this work, we consider an invasive species (the mosquitoes) and we study two strategies to eradicate the population in the whole space by a local intervention. The dynamics of the population is modeled through a bistable reaction diffusion equation in an one dimensional setting and both strategies are based on the same idea : we act on a moving interval. The action of the first strategy is to kill as many individuals as we can in this moving interval. The action of the second strategy is to release sterile males in this moving interval. For both strategies, we manage to generate traveling waves that propagate in the opposite direction relative to the one of the natural invasive traveling wave. These cases correspond to succeeding in eradicating the invasive species. Furthermore, for the first strategy, we fully characterize the minimal size of the interval. All the results are illustrated by numerical simulations.
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