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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 378968, 8 pages
http://dx.doi.org/10.1155/2014/378968
Research Article

Behaviors and Numerical Simulations of Malaria Dynamic Models with Transgenic Mosquitoes

1College of Science, National University of Defense Technology, Changsha, Hunan 410073, China
2Xichang Satellite Launch Center, Xichang, Sichuan 615000, China

Received 21 November 2013; Accepted 4 January 2014; Published 20 February 2014

Academic Editor: Bingwen Liu

Copyright © 2014 Xiongwei Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The release of transgenic mosquitoes to interact with wild ones is a promising method for controlling malaria. How to effectively release transgenic mosquitoes to prevent malaria is always a concern for researchers. This paper investigates two methods of releasing transgenic mosquitoes and proposes two epidemic models involving malaria patients, anopheles, wild mosquitoes, and transgenic mosquitoes based on system of continuous differential equations. A basic reproduction number is defined for the models and it serves as a threshold parameter that predicts whether malaria will spread. By theoretical analysis of the dynamic behaviors of the models and numerical simulations, it is verified that malaria can be effectively controlled by the opportune release of transgenic mosquitoes; that is, when , malaria will disappear; when , malaria will become an endemic disease in the target field.