Abstract and Applied Analysis

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

Xiying Wang, Wei Xu, Yujun Cui, and Xiaomei Wang

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Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 853960, 8 pages.

Dates
First available in Project Euclid: 27 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1425047995

Digital Object Identifier
doi:10.1155/2014/853960

Mathematical Reviews number (MathSciNet)
MR3272219

Zentralblatt MATH identifier
07023202

Citation

Wang, Xiying; Xu, Wei; Cui, Yujun; Wang, Xiaomei. Mathematical Analysis of HIV Models with Switching Nonlinear Incidence Functions and Pulse Control. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 853960, 8 pages. doi:10.1155/2014/853960. https://projecteuclid.org/euclid.aaa/1425047995


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