a Department of Mathematics, Computer Science and Information Systems , California University of PA , California , PA , USA.
b Infectious and Tropical Disease Institute, Department of Biomedical Sciences , Ohio University , Athens , OH , USA.
J Biol Dyn. 2019 Dec;13(1):518-537. doi: 10.1080/17513758.2019.1640293.
Insecticide spraying of housing units is an important control measure for vector-borne infections such as Chagas disease. However, some vectors may survive treatment, due to imperfect spraying by the operator or because they hide deep in the cracks or other places, and re-emerge in the same unit when the effect of the insecticide wears off. While several mathematical models of this phenomenon have been previously described and studied in the literature, the model presented here is more basic than existing ones. Thus it is more amenable to mathematical analysis, which is carried out here. In particular, we demonstrate that an initially very high spraying rate may push the system into a region of the state space with low endemic levels of infestation that can be maintained in the long run at relatively moderate cost, while in the absence of an aggressive initial intervention the same average cost would only allow a much less significant reduction in long-term infestation levels.
对住房单元进行杀虫剂喷洒是控制恰加斯病等虫媒传染病的重要措施。然而，由于操作人员喷洒不完美或由于它们隐藏在裂缝深处或其他地方，一些载体可能在处理后幸存下来，并在杀虫剂的效果消失后重新出现在同一单元中。尽管以前已经在文献中描述和研究了几种关于这种现象的数学模型，但这里提出的模型比现有的模型更为基础。因此，它更适合于数学分析，我们在这里进行了分析。特别是，我们证明了最初非常高的喷洒率可能会使系统进入一个感染程度较低的状态空间区域，而在相对较低的成本下可以长期维持，而在没有积极的初始干预的情况下，同样的平均成本只会允许长期感染水平的显著降低。
