Simple mathematical models for interacting wild and transgenic mosquito populations

Two discrete-time models for interacting populations of wild and genetically altered mosquito are presented, where the genetically altered mosquitoes are grouped into a single population without distinguishing their zygosity. The birth and death rates for both populations are density-dependent, and the mating rates between the mosquitoes are assumed to be either constant or proportional to the total populations for the two models, respectively. The existence and stability of the boundary and positive equilibria are investigated. In particular, it is shown that bifurcations from both boundary and positive equilibria can appear for the model with proportional mating rates. Stable equilibria, periodic-doubling bifurcations, aperiodic oscillations, and chaotic behavior are all illustrated by numerical simulations.