Optimizing insecticide deployment strategies to delay quantitative resistance in mosquito populations.

The large-scale use of insecticides remains a cornerstone of malaria vector control, but its long-term effectiveness is undermined by the evolution of quantitative insecticide resistance (qIR) in mosquito populations. We develop and analyze a mathematical model to identify optimal deployment strategies for two insecticides that differ only in their relative efficacy against target mosquito populations. Resistance is represented as a continuous phenotypic trait influencing mosquito fecundity and mortality, and the model accounts for successive deployment periods. Our results show that when mutational variance is high, the optimal strategy is to deploy the most effective insecticide at full coverage, regardless of its relative efficacy or pre-deployment exposure history. By contrast, when mutational variance is low, optimal deployment requires a transient reduction in coverage during early periods, with a threshold effect driven by both relative efficacy and initial exposure rates. Crucially, we find that, under the hypothesis that the first insecticide is ineffective against mosquitoes, simultaneous use of both insecticides is rarely optimal. Instead, sequential deployment-using one insecticide until resistance reaches a critical threshold, followed by optimal use of the second-delays resistance evolution and improves long-term control. These findings provide a theoretical foundation for adaptive qIR management strategies aimed at prolonging the effectiveness of insecticides in malaria vector control.