title: Comparing malaria surveillance with periodic spraying in the presence of insecticide-resistant mosquitoes: Should we spray regularly or based on human infections?
abstract: There is an urgent need for more understanding of the effects of surveillance on malaria control. Indoor residual spraying has had beneficial effects on global malaria reduction, but resistance to the insecticide poses a threat to eradication. We develop a model of impulsive differential equations to account for a resistant strain of mosquitoes that is entirely immune to the insecticide. The impulse is triggered either due to periodic spraying or when a critical number of malaria cases are detected. For small mutation rates, the mosquito-only submodel exhibits either a single mutant-only equilibrium, a mutant-only equilibrium and a single coexistence equilibrium, or a mutant-only equilibrium and a pair of coexistence equilibria. Bistability is a likely outcome, while the effect of impulses is to introduce a saddle-node bifurcation, resulting in persistence of malaria in the form of impulsive periodic orbits. If certain parameters are small, triggering the insecticide based on number of malaria cases is asymptotically equivalent to spraying periodically.
authors.affiliation: Department of Applied Mathematics, The University of Waterloo, Waterloo, ON N2L 3G1, Canada.
authors.forename: Kevin E M
authors.initials: KE
authors.lastname: Church
authors.affiliation: Department of Mathematics and Faculty of Medicine, The University of Ottawa, 585 King Edward Ave, Ottawa, ON K1N 6N5, Canada. Electronic address: rsmith43@uottawa.ca.
authors.forename: Robert J
authors.initials: RJ
authors.lastname: Smith
mesh_terms: D000818:Animals; D004351:Drug Resistance; D062665:Epidemiological Monitoring; D006801:Humans; D007306:Insecticides; D008288:Malaria / Q000517:prevention & control*; D008962:Models, Theoretical; D009032:Mosquito Control
chemical_list: D007306:Insecticides
keywords: Bistability; Impulsive differential equations; Insecticide; Malaria; Resistance; Surveillance