# American Institute of Mathematical Sciences

2011, 8(4): 889-914. doi: 10.3934/mbe.2011.8.889

## Controlling malaria with indoor residual spraying in spatially heterogenous environments

 1 Department of Mathematics, The University of Ottawa, 585 King Edward Ave Ottawa, ON K1N 6N5, Canada 2 Department of Mathematics and Faculty of Medicine, The University of Ottawa, 585 King Edward Ave Ottawa, ON K1N 6N5, Canada

Received  December 2010 Revised  March 2011 Published  August 2011

Indoor residual spraying – spraying insecticide inside houses to kill mosquitoes – has been one of the most effective methods of disease control ever devised, being responsible for the near-eradication of malaria from the world in the third quarter of the twentieth century and saving tens of millions of lives. However, with malaria resurgence currently underway, it has received relatively little attention, been applied only in select physical locations and not always at regular intervals. We extend a time-dependent model of malaria spraying to include spatial heterogeneity and address the following research questions: 1. What are the effects of spraying in different geographical areas? 2. How do the results depend upon the regularity of spraying? 3. Can we alter our control strategies to account for asymmetric phenomena such as wind? We use impulsive partial differential equation models to derive thresholds for malaria control when spraying occurs uniformly, within an interior disc or under asymmetric advection effects. Spatial heterogeneity results in an increase in the necessary frequency of spraying, but control is still achievable.
Citation: Mo'tassem Al-Arydah, Robert Smith?. Controlling malaria with indoor residual spraying in spatially heterogenous environments. Mathematical Biosciences & Engineering, 2011, 8 (4) : 889-914. doi: 10.3934/mbe.2011.8.889
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