Analysis of HIV models with two time delays. (17th March 2017)

• Record Type: Journal Article
• Authors: Alshorman, Areej; Wang, Xia; Joseph Meyer, M.; Rong, Libin
• Is Part Of: Journal of biological dynamics. Volume 11(2017)supplement 1
• Page Start: 40
• Page End: 64
• Publication Date: 2017-03-17
• Subjects: HIV infection -- latency -- immune response -- characteristic quasipolynomial -- stability -- stability crossing curve; 92B05 -- 92D25 -- 92C37 -- 34D23; Biology -- Mathematical models -- Periodicals; 570.15118
• DOI: 10.1080/17513758.2016.1148202
• Languages: English
• ISSNs: 1751-3758

Abstract

ABSTRACT: Time delays can affect the dynamics of HIV infection predicted by mathematical models. In this paper, we studied two mathematical models each with two time delays. In the first model with HIV latency, one delay is the time between viral entry into a cell and the establishment of HIV latency, and the other delay is the time between cell infection and viral production. We defined the basic reproductive number and showed the local and global stability of the steady states. Numerical simulations were performed to evaluate the influence of time delays on the dynamics. In the second model with HIV immune response, one delay is the time between cell infection and viral production, and the other delay is the time needed for the adaptive immune response to emerge to control viral replication. With two positive delays, we obtained the stability crossing curves for the model, which were shown to be a series of open-ended curves.