Mathematical Biosciences and Engineering, 2011, 8(3): 753-768. doi: 10.3934/mbe.2011.8.753.

39A11, 39A99, 92D25, 92D40.

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Malaria model with stage-structured mosquitoes

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

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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Keywords backward bifurcation.; mosquito metamorphic stages; reproductive number; climate change; Malaria transmission; stage-structured model

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


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