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

Abstract

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.