Malaria model with stage-structured mosquitoes

Jia Li

doi:10.3934/mbe.2011.8.753

Article Contents

2011, Volume 8, Issue 3: 753-768. Doi: 10.3934/mbe.2011.8.753

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Malaria model with stage-structured mosquitoes

Jia Li^1,

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

Received: October 31, 2010

Revised: October 31, 2010

Published: May 2011

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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.

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Mathematics Subject Classification: 39A11, 39A99, 92D25, 92D40.

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