Mathematical Biosciences and Engineering (MBE)

Malaria model with stage-structured mosquitoes

Pages: 753 - 768, Volume 8, Issue 3, July 2011      doi:10.3934/mbe.2011.8.753

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Jia Li - Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899, United States (email)

Abstract: 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.

Keywords:  Malaria transmission, mosquito metamorphic stages, stage-structured model, reproductive number, climate change, backward bifurcation.
Mathematics Subject Classification:  39A11, 39A99, 92D25, 92D40.

Received: November 2010;      Accepted: November 2010;      Available Online: June 2011.