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

Helong Liu,Lianbing Li

doi:10.1155/2010/758745

Helong Liu, Lianbing Li

Open Access

https://doi.org/10.1155/2010/758745

Copy DOI

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 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.

Highlights

Human immunodeficiency virus HIV disease has become one of the major public health problems in the world
AIDS population transmission rate depends on disease-age i.e., the time elapsed since the onset
Few people are aware of their HIV status; HIV testing for risk population groups is an important prevention approach for HIV/AIDS; where we use impulsive HIV testing scheme for risk population groups, and apply drug treatment scheme to infected individuals who are not on treatment

Summary

Introduction

Human immunodeficiency virus HIV disease has become one of the major public health problems in the world. A handful of age-structured or class age-structured models has been developed for HIV/AIDS 3–6 The dynamics of these models tend to generally be completely determined by a threshold quantity called the basic reproduction number denoted by R0 , which measures the expected number of secondary infections from a single individual during his or her entire infectious period, in a population of susceptibles. Impulsive equations have been recently introduced into some HIV transmission models in relation to impulsive drug behaviour 1, 14, 15 From those authors mentioned above, in order to reflect the dependence of HIV/AIDS progress on the infection age, disease age and impulsive antiretroviral treatment, we formulate a class age-structured population model of HIV/AIDS infection with impulsive effects, and discuss the role of impulsive proportion and impulsive period in controlling HIV/AIDS transmission.

The Model

This can be formulated as

Global Stability of the Infection-Free State

Discussion