A Numerical Comparison Between Quasi-Monte Carlo and Sparse Grid Stochastic Collocation Methods - Volume 12 Issue 4 - Juarez dos Santos Azevedo, Saulo Pomponet Oliveira

Due to recent advances in genetic manipulation, transgenic mosquitoes may be a viable alternative to reduce some diseases. Feasibility conditions are obtained by simulating and analyzing mathematical models that describe the behavior of wild and transgenic populations living in the same geographic area. In this paper, we present a reaction–diffusion model in which the reaction term is a nonlinear function that describes the interaction between wild and transgenic mosquitoes, considering the zygosity, and the diffusive term that represents a nonuniform spatial spreading characterized by a random diffusion parameter. The resulting nonlinear system of partial differential equations is numerically solved using the sequential operator splitting technique, combining the finite element method and Runge-Kutta method. This scheme is numerically implemented considering uncertainty in the diffusion parameters of the model. Several scenarios simulating spatial release strategies of transgenic mosquitoes are analyzed, demonstrating an intrinsic association between the transgene frequency in the total population and the strategy adopted.