Determining effective spraying periods to control malaria via indoor residual spraying in Sub-Saharan Africa

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.