Mathematical modeling of the performance of wild and transgenic mosquitoes in malaria transmission.

A mathematical model that simulates malaria transmission under the influence of transgenic mosquitoes refractory to malaria is presented in this paper. The zygosity of transgenic mosquitoes is taken into account and, consequently, the total population of mosquitoes is comprised of wild type and heterozygous and homozygous transgenic mosquitoes. These three mosquito varieties interact by mating and competition, and the genetic characteristics of their resulting offspring are in accordance with Mendelian genetics or the mutagenic chain reaction (MCR) technique.

Modeling the spreading and interaction between wild and transgenic mosquitoes with a random dispersal.

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.