title: Analysis of HIV models with two time delays.
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.
authors.affiliation: a Department of Mathematics and Statistics , Oakland University , Rochester , MI , USA.
authors.forename: Areej
authors.initials: A
authors.lastname: Alshorman
authors.affiliation: b College of Mathematics and Information Science , Xinyang Normal University , Xinyang , People's Republic of China.
authors.forename: Xia
authors.initials: X
authors.lastname: Wang
authors.affiliation: a Department of Mathematics and Statistics , Oakland University , Rochester , MI , USA.
authors.forename: M
authors.initials: M
authors.lastname: Joseph Meyer
authors.affiliation: a Department of Mathematics and Statistics , Oakland University , Rochester , MI , USA.
authors.forename: Libin
authors.initials: L
authors.lastname: Rong
mesh_terms: D050936:Basic Reproduction Number; D015658:HIV Infections / Q000821:virology*; D015497:HIV-1 / Q000502:physiology*; D006801:Humans; D008954:Models, Biological; D008962:Models, Theoretical; D013997:Time Factors; D017735:Virus Latency; D014779:Virus Replication
keywords: 34D23; 92B05; 92C37; 92D25; HIV infection; characteristic quasipolynomial; immune response; latency; stability; stability crossing curve