College of Mathematics and Information, Xinyang Normal University, Henan 464000, China
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 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 and drug-treatment proportion satisfy . This result shows that the prevention effects can drive HIV/AIDS epidemic towards to elimination.