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Bull Math Biol. 2018 Apr;80(4):788-824. doi: 10.1007/s11538-018-0401-y. Epub 2018 Feb 5.

Models of Disease Vector Control: When Can Aggressive Initial Intervention Lower Long-Term Cost?

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Department of Mathematics, Ohio University, Athens, OH, 45701, USA.
Department of Biomedical Sciences, Infectious and Tropical Disease Institute, Ohio University, Athens, OH, 45701, USA.
Center for Health Research in Latin America, School of Biological Sciences, Pontifical Catholic University of Ecuador, Quito, Ecuador.
Department of Mathematics, Ohio University, Athens, OH, 45701, USA.


Insecticide spraying of housing units is an important control measure for vector-borne infections such as Chagas disease. As vectors may invade both from other infested houses and sylvatic areas and as the effectiveness of insecticide wears off over time, the dynamics of (re)infestations can be approximated by [Formula: see text]-type models with a reservoir, where housing units are treated as hosts, and insecticide spraying corresponds to removal of hosts. Here, we investigate three ODE-based models of this type. We describe a dual-rate effect where an initially very high spraying rate can 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. We determine some sufficient and some necessary conditions under which this effect occurs and show that it is robust in models that incorporate some heterogeneity in the relevant properties of housing units.


(Re)infestation; Chagas disease; Cost of insecticide treatment; Dual-rate effect; SIRS models

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