American Institute of Mathematical Sciences

Advanced
2010, 7(1): 99-121. doi: 10.3934/mbe.2010.7.99

Modeling of mosquitoes with dominant or recessive Transgenes and Allee effects

Jia Li 1,

1. 

Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899

Received  June 2009 Revised  August 2009 Published  January 2010

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.
Keywords: period-doubling bifurcation., stability, discrete-time population model, malaria transmission, transgenic mosquito.
Mathematics Subject Classification: 39A11, 39A99, 92D25, 92D4.
Citation: Jia Li. Modeling of mosquitoes with dominant or recessive Transgenes and Allee effects. Mathematical Biosciences & Engineering, 2010, 7 (1) : 99-121. doi: 10.3934/mbe.2010.7.99
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