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Abstract and Applied Analysis
Volume 2014, Article ID 853960, 8 pages
Research Article

Mathematical Analysis of HIV Models with Switching Nonlinear Incidence Functions and Pulse Control

1Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, China
2Department of Applied Mathematics, Shandong University of Science and Technology, Qingdao, Shandong 266510, China
3School of Mathematics Science, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China

Received 24 June 2014; Accepted 23 July 2014; Published 16 October 2014

Academic Editor: Xinzhu Meng

Copyright © 2014 Xiying Wang 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.


This paper aims to study the dynamics of new HIV (the human immunodeficiency virus) models with switching nonlinear incidence functions and pulse control. Nonlinear incidence functions are first assumed to be time-varying functions and switching functional forms in time, which have more realistic significance to model infectious disease models. New threshold conditions with the periodic switching term are obtained to guarantee eradication of the disease, by using the novel type of common Lyapunov function. Furthermore, pulse vaccination is applied to the above model, and new sufficient conditions for the eradication of the disease are presented in terms of the pulse effect and the switching effect. Finally, several numerical examples are given to show the effectiveness of the proposed results, and future directions are put forward.