Mathematical analysis of delay differential equation models of HIV-1 infection

Math Biosci. 2002 Jul-Aug;179(1):73-94. doi: 10.1016/s0025-5564(02)00099-8.

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.

Publication types

  • Comparative Study
  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.
  • Research Support, U.S. Gov't, P.H.S.

MeSH terms

  • Antiviral Agents / therapeutic use
  • HIV Infections / drug therapy
  • HIV Infections / immunology
  • HIV Infections / virology*
  • HIV-1*
  • Humans
  • Models, Biological*
  • Numerical Analysis, Computer-Assisted
  • T-Lymphocytes / drug effects
  • T-Lymphocytes / immunology
  • Viral Load

Substances

  • Antiviral Agents