Slowing the evolution of insecticide resistance in mosquitoes: a mathematical model
Slowing the evolution of insecticide resistance in mosquitoes: a mathematical model
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DOI：
10.1098/rspa.2010.0413
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发表时间：
2011-08-08
影响因子：
3.5
通讯作者：
Wu, Jianhong
中科院分区：
文献类型：
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作者：
Gourley, Stephen A.;Liu, Rongsong;Wu, Jianhong
疟疾控制的一个大问题是蚊子对杀虫剂产生抗药性的速度。因此，创造抗进化杀虫剂的可能性具有相当大的意义。生物学家提出，如果杀虫剂只针对已经产下大部分卵的老蚊子，那么可以实现有效的疟疾控制，只有对杀虫剂的抗药性选择很弱。该策略旨在利用大多数疟疾蚊子的寿命不足以传播疾病的事实。我们推导，分析和比较两个数学模型，一个是一种杀虫剂，杀死暴露，另一种杀虫剂，只针对老年蚊子。这两种模型都预测，随着时间的推移，抗药性蚊子将成为主导，但非常重要的是，这发生在一个非常缓慢的时间尺度上，当杀虫剂只影响老年蚊子。我们提出的非平凡的平衡，其中只有抗性蚊子株的线性和全局稳定性的分析结果，连同定理比较两个模型的收敛速度。数值模拟表明，只针对老蚊子的抗性进化的效果是显着的。
A big problem in malaria control is the rapidity with which mosquitoes can develop resistance to insecticides. The possibility of creating evolution-proof insecticides is therefore of considerable interest. Biologists have suggested that effective malaria control, with only weak selection for insecticide resistance, could be achieved if insecticides target only old mosquitoes that have already laid most of their eggs. The strategy aims to exploit the fact that most malarial mosquitoes do not live long enough to transmit the disease. We derive, analyse and compare two mathematical models, one for an insecticide that kills on exposure, and the other for an insecticide that targets only older mosquitoes. Both models predict that insecticide-resistant mosquitoes will become dominant over time but, very importantly, this occurs on a very much slower time scale when the insecticide only affects older mosquitoes. We present analytical results on linear and global stability of the non-trivial equilibrium in which only the resistant mosquito strain is present, together with a theorem comparing the rates of convergence for the two models. Numerical simulations show that the effect of targeting only old mosquitoes on the evolution of resistance is dramatic.