Dinâmica e espalhamento de mosquitos geneticamente modificados via reação em cadeia mutagênica

Abstract

In this work, we present the two-dimensional model of iteration and dynamics between wild and genetically modified mosquito populations. The model classifies subpopulations according to zygosity: wild, heterozygous transgenics and homozygous transgenics. The resulting strains are in accordance with the Mutagenic Chain Reaction (MCR) technique. This model is represented by a system of partial diferential equations of the reaction-difusion type, where the reaction term is non-linear. For the numerical solution of the problem, we applied the technique of Operator Decomposition, which allowed us to solve the difusion problem separately from the reaction problem. To solve the diffusion problem, we used a finite difference method, the Alternate Directions Implicit Method (ADI), and for the reaction term, a fourth order Runge-Kutta method was used. Numerical simulations are presented showing the potential of the MCR technique to combat diseases transmitted by mosquitoes.