Modelagem bidimensional da dinâmica e espalhamento de mosquitos selvagens e transgênicos

Abstract

In this work, we present the modeling of the dynamics of the interaction between wild and transgenic mosquito populations and their spread in a two-dimensional spatial domain. For this, the subpopulations are classi ed according to their zygosity: wild, heterozygotes and homozygotes transgenic, which interact by mating and competition for resources. The lineages obtained from mating between these three varieties are in agreement with classical Mendelian genetics. This model is represented by a reaction-di usion system, where reaction term is strongly non-linear. To solve this system, we decouple the di usion and reaction operators, using the sequential operator decomposition technique and apply the nite elements method to solve the di usive system, and fourth-order Runge-Kutta to solve the system associated with the reaction. Numerical simulations are presented showing the potential of the model application.