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Journal of Applied Mathematics
Volume 2014, Article ID 139046, 15 pages
Research Article

Permanence and Extinction for a Nonautonomous Malaria Transmission Model with Distributed Time Delay

1School of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi 041004, China
2Department of Mathematics, Xinyang Normal University, Xinyang, Henan 464000, China

Received 5 January 2014; Revised 8 April 2014; Accepted 8 April 2014; Published 8 May 2014

Academic Editor: Junjie Wei

Copyright © 2014 Xiaohong Zhang 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.


We study the permanence, extinction, and global asymptotic stability for a nonautonomous malaria transmission model with distributed time delay. We establish some sufficient conditions on the permanence and extinction of the disease by using inequality analytical techniques. By a Lyapunov functional method, we also obtain some sufficient conditions for global asymptotic stability of this model. A numerical analysis is given to explain the analytical findings.