Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 758745, 12 pages
Research Article

A Class Age-Structured HIV/AIDS Model with Impulsive Drug-Treatment Strategy

College of Mathematics and Information, Xinyang Normal University, Henan 464000, China

Received 28 September 2009; Accepted 28 January 2010

Academic Editor: Antonia Vecchio

Copyright © 2010 Helong Liu and Lianbing Li. 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 formulate an HIV/AIDS transmission model that considers the dependence of HIV/AIDS progress on infection age (the time since infection), disease age (the time elapsed since the onset), and impulsive antiretroviral treatment. Since no effective vaccine is available for HIV/AIDS, our impulsive disease-control strategy is targeted at infected individuals (I control). Thus the model only includes infective class and AIDS class: infected population is the state at birth, and AIDS population is not the state at birth. Assuming the theoretical strategy can provide HIV testing for risk population groups every T years and immediate antiretroviral treatment for HIV-positive people. The action is approximated by impulsive differential equations. We demonstrate the effect of the impulsive drug treatment and show that there exists a globally stable infection-free state when the impulsive period Tand drug-treatment proportion p satisfy R(p,T)<1. This result shows that the prevention effects can drive HIV/AIDS epidemic towards to elimination.