A delay-differential equation model of HIV infection of CD4+ T-cells

Rebecca V. Culshaw, Shigui Ruan

Research output: Contribution to journalArticlepeer-review

446 Scopus citations


A.S. Perelson, D.E. Kirschner and R. De Boer (Math. Biosci. 114 (1993) 81) proposed an ODE model of cell-free viral spread of human immunodeficiency virus (HIV) in a well-mixed compartment such as the bloodstream. Their model consists of four components: uninfected healthy CD4+ T-cells, latently infected CD4+ T-cells, actively infected CD4+ T-cells, and free virus. This model has been important in the field of mathematical modeling of HIV infection and many other models have been proposed which take the model of Perelson, Kirschner and De Boer as their inspiration, so to speak (see a recent survey paper by A.S. Perelson and P.W. Nelson (SIAM Rev. 41 (1999) 3- 44)). We first simplify their model into one consisting of only three components: the healthy CD4+ T-cells, infected CD4+ T-cells, and free virus and discuss the existence and stability of the infected steady state. Then, we introduce a discrete time delay to the model to describe the time between infection of a CD4+ T-cell and the emission of viral particles on a cellular level (see A.V.M. Herz, S. Bonhoeffer, R.M. Anderson, R.M. May, M.A. Nowak [Proc. Nat. Acad. Sci. USA 93 (1996) 7247]). We study the effect of the time delay on the stability of the endemically infected equilibrium, criteria are given to ensure that the infected equilibrium is asymptotically stable for all delay. Numerical simulations are presented to illustrate the results. (C) 2000 Elsevier Science Inc.

Original languageEnglish (US)
Pages (from-to)27-39
Number of pages13
JournalMathematical Biosciences
Issue number1
StatePublished - May 2000
Externally publishedYes


  • Characteristic equation
  • HIV infection
  • Intercellular delay
  • Stability
  • Steady state

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics


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