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Mathematical Biosciences and Engineering

2011, Volume 8, Issue 3: 753-768. doi: 10.3934/mbe.2011.8.753
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Malaria model with stage-structured mosquitoes

  • 1.
    Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899
  • Received: 01 November 2010 Accepted: 29 June 2018 Published: 01 June 2011

  • MSC : 39A11, 39A99, 92D25, 92D40.

  • A simple SEIR model for malaria transmission dynamics is formulated as our baseline model. The metamorphic stages in the mosquito population are then included and a simple stage-structured mosquito population model is introduced, where the mosquito population is divided into two classes, with all three aquatic stages in one class and all adults in the other class, to keep the model tractable in mathematical analysis. After a brief investigation of this simple stage-structured mosquito model, it is incorporated into the baseline model to formulate a stage-structured malaria model. A basic analysis for the stage-structured malaria model is provided and it is shown that a theoretical framework can be built up for further studies on the impact of environmental or climate change on the malaria transmission. It is also shown that both the baseline and the stage-structured malaria models undergo backward bifurcations.

    Citation: Jia Li. Malaria model with stage-structured mosquitoes[J]. Mathematical Biosciences and Engineering, 2011, 8(3): 753-768. doi: 10.3934/mbe.2011.8.753

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  • A simple SEIR model for malaria transmission dynamics is formulated as our baseline model. The metamorphic stages in the mosquito population are then included and a simple stage-structured mosquito population model is introduced, where the mosquito population is divided into two classes, with all three aquatic stages in one class and all adults in the other class, to keep the model tractable in mathematical analysis. After a brief investigation of this simple stage-structured mosquito model, it is incorporated into the baseline model to formulate a stage-structured malaria model. A basic analysis for the stage-structured malaria model is provided and it is shown that a theoretical framework can be built up for further studies on the impact of environmental or climate change on the malaria transmission. It is also shown that both the baseline and the stage-structured malaria models undergo backward bifurcations.


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  • © 2011 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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