Analysis of a nonautonomous HIV/AIDS epidemic model with distributed time delay

Abstract

In this paper, we have considered a nonautonomous stage‐structured HIV/AIDS epidemic model through vertical and horizontal transmissions of infections, having two stages of the period of infection according to the developing progress of infection before AIDS defined would be detected, with varying total population size and distributed time delay to become infectious (through horizontal transmission) due to intracellular delay between initial infection of a cell by HIV and the release of new virions. The infected people in the different stages have different ability of transmitting disease. We have established some sufficient conditions on the permanence and extinction of the disease by using inequality analytical technique. We have obtained the explicit formula of the eventual lower bounds of infected people. We have introduced some new threshold values _Ro and R* and further obtained that the disease will be permanent when _Ro > 1 and the disease will be going to extinct when R* < 1. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. Computer simulations are carried out to explain the analytical findings. First published online: 09 Jun 2011

Keywords

• HIV/AIDS
• time delay
• permanence, extinction
• Lyapunov functional
• global stability