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Abstract and Applied Analysis
Volume 2014, Article ID 414383, 12 pages
http://dx.doi.org/10.1155/2014/414383
Research Article

Modeling Saturated Diagnosis and Vaccination in Reducing HIV/AIDS Infection

Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049, China

Received 18 January 2014; Accepted 26 February 2014; Published 30 March 2014

Academic Editor: Kaifa Wang

Copyright © 2014 Can Chen and Yanni Xiao. 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

A mathematical model is proposed to consider the effects of saturated diagnosis and vaccination on HIV/AIDS infection. By employing center manifold theory, we prove that there exists a backward bifurcation which suggests that the disease cannot be eradicated even if the basic reproduction number is less than unity. Global stability of the disease-free equilibrium is investigated for appropriate conditions. When the basic reproduction number is greater than unity, the system is uniformly persistent. The proposed model is applied to describe HIV infection among injecting drug users (IDUs) in Yunnan province, China. Numerical studies indicate that new cases and prevalence are sensitive to transmission rate, vaccination rate, and vaccine efficacy. The findings suggest that increasing vaccination rate and vaccine efficacy and enhancing interventions like reducing share injectors can greatly reduce the transmission of HIV among IDUs in Yunnan province, China.