To study the impact of releasing transgenic mosquitoes on malaria transmission, we
formulate discrete-time models for interacting wild and transgenic mosquitoes
populations, based on systems of difference equations. We start with models
including all homozygous and heterozygous mosquitoes. We then consider either
dominant or recessive transgenes to reduce the 3-dimensional model systems to
2-dimensional systems. We include density-dependent vital rates and incorporate
Allee effects in the functional mating rates. Dynamics of these models are explored
by investigating the existence and stability of boundary and positive fixed points.
Numerical simulations are provided and brief discussions are given.