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Mathematical Biosciences and Engineering

2010, Volume 7, Issue 1: 99-121. doi: 10.3934/mbe.2010.7.99
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Modeling of mosquitoes with dominant or recessive Transgenes and Allee effects

  • 1.
    Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899
  • Received: 01 June 2009 Accepted: 29 June 2018 Published: 01 January 2010

  • MSC : 39A11, 39A99, 92D25, 92D40.

  • 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.

    Citation: Jia Li. Modeling of mosquitoes with dominantor recessive Transgenes and Allee effects[J]. Mathematical Biosciences and Engineering, 2010, 7(1): 99-121. doi: 10.3934/mbe.2010.7.99

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  • 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.


  • This article has been cited by:

    1. Jia Li, Shangbing Ai, Impulsive releases of sterile mosquitoes and interactive dynamics with time delay, 2020, 14, 1751-3758, 289, 10.1080/17513758.2020.1748239
    2. Mingzhan Huang, Xinyu Song, Jia Li, Modelling and analysis of impulsive releases of sterile mosquitoes, 2017, 11, 1751-3758, 147, 10.1080/17513758.2016.1254286
    3. Jianshe Yu, Jia Li, Dynamics of interactive wild and sterile mosquitoes with time delay, 2019, 13, 1751-3758, 606, 10.1080/17513758.2019.1682201
    4. Chen Liang, Hai-Feng Huo, Hong Xiang, Modelling mosquito population suppression based on competition system with strong and weak Allee effect, 2024, 21, 1551-0018, 5227, 10.3934/mbe.2024231
    5. 可 张, Two Release Strategies of Sterile Mosquitoes under Weak Allee Effect, 2025, 14, 2324-7991, 303, 10.12677/aam.2025.141031
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  • © 2010 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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