Modeling spreading and interaction between wild and transgenic mosquitoes with randomic diffusion

Ana Paula Pintado Wyse¹; Antonio José Boness dos Santos¹; Juarez dos Santos Azevedo²

¹ UFPB; ² UFRB

doi:10.20906/CPS/CILAMCE2017-0299

Resumo

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 work, we present a reaction--diffusion model where the reaction term is a nonlinear function that describes the interaction between wild and transgenic mosquitoes taking into account the zygosity. The system of partial differential equations obtained is solved numerically by combining Runge-Kutta's method and finite element method through the sequential operator splitting technique. This scheme is numerically implemented considering uncertainty in the diffusion parameters of the model. Simulations show that it may be possible to reduce or even eradicate the wild mosquitoes only if the heterozygous and homozygous population are better adapted during a certain time interval on uncertainty parameters.

Palavras-chave: Mathematical model; transgenic mosquitoes; reaction-diffusion systems; uncertainty