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.