Journal of Applied Mathematics and Decision Sciences
Volume 2008 (2008), Article ID 745463, 19 pages
doi:10.1155/2008/745463
Research Article
Determining Effective Spraying Periods to Control Malaria via Indoor
Residual Spraying in Sub-Saharan Africa
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.
Abstract
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.