Mathematical Methodology for Dynamic Models of Insecticide Selection Assuming a Polygenic Basis of Resistance

Mathematical models for evaluating insecticide resistance management (IRM) have primarily assumed insecticide resistance (IR) is monogenic. Modelling using a quantitative genetics framework to model polygenic IR has less frequently been used. We introduce a complex mathematical model for polygenic IR with a focus on public health insecticide deployments for vector control. Conventional polygenic models assume selection differentials are constant over the course of selection. We instead propose calculating the selection differentials dynamically depending on the level of IR and the amount of insecticide encountered. Dynamically calculating the selection differentials increases biological and operational realism, allowing for the evaluation of strategies of policy relevance, including reduced dose mixtures or the deployment of long-lasting insecticide-treated nets and indoor residual spraying in combination. The dynamic calculations of insecticide selection allow for two methods: 1) Truncation ("polytruncate") - where only the most resistant individuals in the population survive, and 2) Probabilistic ("polysmooth") - where an individuals survival probability is dependent on their own level of IR. We describe in detail the calculation and calibration of these models. The models ("polytruncate" and "polysmooth") are compared against a previous polygenic model ("polyres") and the monogenic literature for the IRM strategies of rotations, sequences and full-dose mixtures. We demonstrate consistency in results of full-dose mixtures remaining the best IRM strategy, with sequences and rotations being similar in their efficacy between the two selection processes, and consistency in "global conclusions" with previous models. Consistency between the "polysmooth", "polytruncate" and previous models helps provide confidence in their predictions, as operational interpretations are not overly impacted by model assumptions. This increases confidence in the application of these dynamic models to investigate more complex IRM strategies and scenarios, and their future applications will investigate more scenario specific evaluations of IRM strategies.