Department of Mathematics, The University of Ottawa, 585 King Edward Avenue, Ottawa, Ontario, Canada.
Math Biosci Eng. 2011 Oct 1;8(4):889-914. doi: 10.3934/mbe.2011.8.889.
Indoor residual spraying-spraying insecticide inside houses to kill mosquitoes-has been one of the most effective methods of disease control ever devised, being responsible for the near-eradication of malaria from the world in the third quarter of the twentieth century and saving tens of millions of lives. However, with malaria resurgence currently underway, it has received relatively little attention, been applied only in select physical locations and not always at regular intervals. We extend a time-dependent model of malaria spraying to include spatial heterogeneity and address the following research questions: 1. What are the effects of spraying in different geographical areas? 2. How do the results depend upon the regularity of spraying? 3. Can we alter our control strategies to account for asymmetric phenomena such as wind? We use impulsive partial differential equation models to derive thresholds for malaria control when spraying occurs uniformly, within an interior disc or under asymmetric advection effects. Spatial heterogeneity results in an increase in the necessary frequency of spraying, but control is still achievable.
室内滞留喷洒——在室内喷洒杀虫剂以杀死蚊子——是有史以来最有效的疾病控制方法之一，它在 20 世纪第三个四分之一的时间里几乎根除了疟疾，挽救了数以千万计的生命。然而，随着疟疾的死灰复燃，它相对较少受到关注，只在特定的物理地点使用，而且并不总是定期使用。我们扩展了一个疟疾喷洒的时变模型，包括空间异质性，并解决了以下研究问题：1. 在不同地理区域喷洒的效果如何？2. 结果如何取决于喷洒的规律性？3. 我们能否改变我们的控制策略，以考虑到风等不对称现象？我们使用脉冲偏微分方程模型来推导在均匀喷洒、在内部圆盘内喷洒或在不对称平流效应下喷洒时控制疟疾所需的阈值。空间异质性导致喷洒的必要频率增加，但仍可以进行控制。
