Journal of Applied Mathematics and Decision Sciences
Volume 2008 (2008), Article ID 745463, 19 pages
Research Article

Determining Effective Spraying Periods to Control Malaria via Indoor Residual Spraying in Sub-Saharan Africa

Robert J. Smith?1,2 and Senelani D. Hove-Musekwa3

1Department of Mathematics, University of Ottawa, 585 King Edward Ave, Ottawa, ON, K1N 6N5, Canada
2Faculty of Medicine, University of Ottawa, 585 King Edward Ave, Ottawa, ON, K1N 6N5, Canada
3Department of Applied Mathematics, National University of Science and Technology, P.O. Box AC939, Ascot, Bulawayo, Zimbabwe

Received 8 March 2008; Revised 3 July 2008; Accepted 28 July 2008

Academic Editor: Graeme Wake

Copyright © 2008 Robert J. Smith? and Senelani D. Hove-Musekwa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Indoor residual spraying—spraying insecticide inside houses to kill mosquitoes—is an important method for controlling malaria vectors in sub-Saharan Africa. We propose a mathematical model for both regular and non-fixed spraying, using impulsive differential equations. First, we determine the stability properties of the nonimpulsive system. Next, we derive minimal effective spraying intervals and the degree of spraying effectiveness required to control mosquitoes when spraying occurs at regular intervals. If spraying is not fixed, then we determine the “next best” spraying times. We also consider the effects of climate change on the prevalence of mosquitoes. We show that both regular and nonfixed spraying will result in a significant reduction in the overall number of mosquitoes, as well as the number of malaria cases in humans. We thus recommend that the use of indoor spraying be re-examined for widespread application in malaria-endemic areas.