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J Biol Dyn. 2019 Dec;13(1):518-537. doi: 10.1080/17513758.2019.1640293.

A model of insect control with imperfect treatment.

Author information

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.
c Center for Health Research in Latin America (CISeAL), School of Biological Sciences , Pontifical Catholic University of Ecuador , Quito , Ecuador.
d Quantitative Biology Institute and Infectious and Tropical Disease Institute, Department of Mathematics , Ohio University , Athens , OH , USA.


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.


Chagas disease; Insecticide treatment; cost of insecticide treatment; dual-rate effect; imperfect treatment model; insecticide efficacy

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