UAH > Math > Colloquia > 2/23/2007
Malaria is by far the world's most important tropical parasitic disease, killing more people than any other communicable disease except tuberculosis. A new technique producing genetically-altered (transgenic) mosquitoes that are resistant to malaria infection provides an effective weapon against malaria. To study the impact of releasing transgenic mosquitoes into the field of wild mosquitoes, we formulate both discrete- and continuous-time mathematical models of interacting mosquitoes populations, based on difference and differential equations, respectively. Density-dependent vital rates are considered and, in particular, Allee effects are incorporated in the functional mating rates. Dynamics of these models are explored by investigating existence and stability of boundary and positive equilibria. These models exhibit richer dynamics which are demonstrated by numerical simulations.