The unplanned and intensified use of insecticides to control mosquito-borne diseases has led to an upsurge of resistance to commonly used insecticides. Aedes aegypti, the main vector of dengue, chikungunya, and Zika virus, is primarily controlled through the application of adulticides (pyrethroid insecticides) and larvicides (temephos). Fine spatial-scale analysis of resistance may reveal important resistance-related patterns, and the application of mathematical models to determine the phenotypic resistance status lessens the cost and usage of resources, thus resulting in an enhanced and successful control program.
The phenotypic resistance for permethrin, deltamethrin, and malathion was monitored in the Ae. aegypti populations using the World Health Organization (WHO) adult bioassay method. Mosquitoes’ resistance to permethrin and deltamethrin was evaluated for the commonly occurring base substitutions in the voltage-gated sodium channel (vgsc) gene. Rational functions were used to determine the relationship between the kdr alleles and the phenotypic resistant percentage of Ae. aegypti in Sri Lanka.
The results of the bioassays revealed highly resistant Ae. aegypti populations for the two pyrethroid insecticides (permethrin and deltamethrin) tested. All populations were susceptible to 5% malathion insecticide. The study also revealed high frequencies of C1534 and G1016 in all the populations studied. The highest haplotype frequency was detected for the haplotype CC/VV, followed by FC/VV and CC/VG. Of the seven models obtained, this study suggests the prediction models using rational approximation considering the C allele frequencies and the total of C, G, and P allele frequencies and phenotypic resistance as the best fits for the area concerned.
This is the first study to our knowledge to provide a model to predict phenotypic resistance using rational functions considering kdr alleles. The flexible nature of the rational functions has revealed the most suitable association among them. Thus, a general evaluation of kdr alleles prior to insecticide applications would unveil the phenotypic resistance percentage of the wild mosquito population. A site-specific strategy is recommended for monitoring resistance with a mathematical approach and management of insecticide applications for the vector population.

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