An evolutionary model propounding Anopheles double resistance against insecticides

Abstract

Continuous usage of insecticide in malaria control has decreased its viability due to the emergence of resistant mosquitoes. Strategic interventions, including the well-known rotation–mixing technique, have been implemented to inhibit (multiple) resistance problems. In this paper, a mathematical model describing the dynamic evolution of Anopheles’s gametes in the gene pool is developed, taking into account double resistance. This model involves three essential factors in producing different genotypes, namely random mating, natural selection, and recombination. Two special cases of the model, the allele and epistasis model, are presented and evaluated for qualitative studies. The allele model admits three equilibria: two monomorphic equilibria corresponding to the competitive exclusion principle and one polymorphic equilibrium describing coexistence of the susceptible and resistant alleles. Meanwhile limit cycles cease to exist around these equilibria, the stability of the latter depends on the threshold measures Ru, Rv and dominance conditions on the fitness levels. The corresponding analysis suggests that overdominance condition for heterozygous gametes combined with Ru,Rv>1 evoke the stability of the polymorphic equilibrium, maintaining the genetic diversity. The epistasis model is divided into two scenarios, namely recessive and dominant epistasis, which mediate different allele expressions in the two loci and recombination. Four monomorphic equilibria with their stability conditions are obtained explicitly. An analysis of the existence and stability of the polymorphic equilibrium is carried out numerically using Monte Carlo method. It is shown that the fitness level of resistant gametes has an essential role in the evolution of double resistance. In addition, parameter sensitivity analysis leads us to conclude that the intrinsic birth rate as well as logistic factors greatly affect the model behavior. This indicates that management of larval sources (habitat manipulation, larvicides) is an important strategy in suppressing double resistance.