title: Mathematical analysis of delay differential equation models of HIV-1 infection.
abstract: Models of HIV-1 infection that include intracellular delays are more accurate representations of the biology and change the estimated values of kinetic parameters when compared to models without delays. We develop and analyze a set of models that include intracellular delays, combination antiretroviral therapy, and the dynamics of both infected and uninfected T cells. We show that when the drug efficacy is less than perfect the estimated value of the loss rate of productively infected T cells, delta, is increased when data is fit with delay models compared to the values estimated with a non-delay model. We provide a mathematical justification for this increased value of delta. We also provide some general results on the stability of non-linear delay differential equation infection models.
authors.affiliation: Department of Mathematics, The University of Michigan, 525 E. University, 3071 E. Hall, Ann Arbor, MI 48109-1109, USA. pwn@math.lsa.umich.edu
authors.forename: Patrick W
authors.initials: PW
authors.lastname: Nelson
authors.forename: Alan S
authors.initials: AS
authors.lastname: Perelson
mesh_terms: D000998:Antiviral Agents / Q000627:therapeutic use; D015658:HIV Infections / Q000188:drug therapy / Q000276:immunology / Q000821:virology*; D015497:HIV-1; D006801:Humans; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted; D013601:T-Lymphocytes / Q000187:drug effects / Q000276:immunology; D019562:Viral Load
chemical_list: D000998:Antiviral Agents