PRELIMINARY RESULTS: SIMPLE MODEL OF EVOLUTIONARY DYNAMIC ON INSECTICIDE RESISTANCE IN MOSQUITO

Abstract

The information on insecticide resistance in mosquitoes as diseases vectors is a critical issue for the success of mosquito population control. This is because the resistance can reduce the effectiveness of insecticides. Based on the resistance level to insecticides, the mosquitoes are divided into susceptible and resistant groups. Genetically, the existence of susceptible and resistant mosquitoes are determined by the frequency of alleles. In this paper, a dynamical model is constructed based on the genetic information to observe the effect of selection by exposure to insecticides. The model is a two-dimensional nonlinear differential equation system. In the analysis of this mathematical model, we consider two important factors in the evolution of resistance, i.e., the fitness value and the effectiveness of the insecticide. The condition of coexistence and stability are obtained here. The simulations are performed to illustrate the effect of insecticide usage continuously on mosquito resistance. Based on analysis and simulation, the fitness value of intermediate mosquitoes plays an essential role in maintaining the coexistence of the mosquito population. Furthermore, the resistant mosquitoes increases significantly following the pattern of increasing the dose of exposure to insecticides.