Reaction-diffusion Model Applied to the Population Dynamics of Wild and Transgenic Mosquitoes

ABSTRACT

Due to recent advances in genetic manipulation, transgenic mosquitoes can be a viable alternative to reduce some diseases. Viability conditions are obtained by the simulation and analysis of mathematical models that describe the behavior of wild and transgenic mosquitoes population living in the same geographic area. In this work, we present a reaction-diffusion model with a nonlinear reaction term, a function that describes the interaction between wild and transgenic mosquitoes taking into account their zygosity. The diffusive term represents a uniform spatial spread characterized by a fixed diffusion parameter. The system of partial differential equations obtained is solved numerically by combining a implicit Runge-Kutta method and finite elements method, through the sequential operator splitting technique. Several scenarios are analyzed, simulating the spatial release of transgenic mosquitoes, and lead to an understanding of an intrinsic relationship between the transgenic and wild varieties for different initial conditions.

Keywords:
mathematical model; operator splitting; genetically modified mosquito