Bulletin of Mathematical Biology

, Volume 80, Issue 4, pp 788–824 | Cite as

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

  • Bismark Oduro
  • Mario J. Grijalva
  • Winfried Just
Original Article


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 \({ SIRS}\)-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.


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



We are greatly indebted to former Ohio University student William Clark for helping us with preliminary simulations and pointing out the strange shape of the curves for the cost at equilibrium level that led to this study of the dual-rate effect. We also thank Sofia Ocaña-Mayorga, Anita G. Villacis, and Cesar Yumiseva of the Center for Research on Health in Latin America (CISeAL) for sharing valuable insights on Chagas disease transmission. Special thanks are due to the referees and the editor for valuable comments. They greatly helped us in improving the manuscript and pointed us to promising directions of future research. This work received financial support to MG from Pontifical Catholic University of Ecuador (K13063 and L13254), Children’s Heartlink USA Division of Microbiology and Infectious Diseases, National Institute of Allergy and Infectious Diseases, National Institutes of Health (DMID/NIADID/NIH) [AI077896-01] and Fogarty International Center, Global Infectious Disease Training Grant (TW008261-01A1).


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Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  • Bismark Oduro
    • 1
  • Mario J. Grijalva
    • 2
    • 3
  • Winfried Just
    • 1
  1. 1.Department of MathematicsOhio UniversityAthensUSA
  2. 2.Department of Biomedical Sciences, Infectious and Tropical Disease InstituteOhio UniversityAthensUSA
  3. 3.Center for Health Research in Latin America, School of Biological SciencesPontifical Catholic University of EcuadorQuitoEcuador

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