Exploring operational requirements of mixtures for insecticide resistance management in public health using a mathematical model assuming polygenic resistance.

Long-lasting insecticide treated nets (LLINs) have been developed which contain two active ingredients. Mixture products for vector control are now an available insecticide resistance management (IRM) strategy. There is a theoretical concern around the use mixtures pertaining to dosing, insecticide decay, initial resistance, and cross resistance. Mixture LLINs all currently have a pyrethroid as one of the partner insecticides. Using previously described mathematical models of polygenic insecticide resistance evolution, which implement selection either by truncation ("polytrucate) or as a probabilistic process ("polysmooth") mixtures are evaluated for their IRM potential. Scenarios are developed to explore the impact of the initial levels of resistance to the pyrethroid insecticide, insecticide decay rates, and insecticide doses, and cross resistance. Results from our simulations indicate that mixtures should be deployed at full doses. As the initial level of resistance to the pyrethroid increases the benefit of mixture decreases. Insecticide decay was found to be less important than might be thought, with other variables having a greater impact. The mechanism of selection demonstrated consistent results, diverging only at very high levels of resistance to the pyrethroid. Our simulations demonstrate that the impact of positive cross resistance is best mitigated using full-dose mixtures. Insecticide decay less important than previously considered, and opens up the opportunity to mix a wider variety of insecticides. However, as mixtures remain a challenge to develop and therefore strategies which could generate an effect of a "temporal" mixture should be evaluated.