Threshold virus dynamics with impulsive antiretroviral drug effects

Jie Lou, Yijun Lou, Jianhong Wu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

49 Citations (Scopus)


The purposes of this paper are twofold: to develop a rigorous approach to analyze the threshold behaviors of nonlinear virus dynamics models with impulsive drug effects and to examine the feasibility of virus clearance following the Manuals of National AIDS Free Antiviral Treatment in China. An impulsive system of differential equations is developed to describe the within-host virus dynamics of both wild-type and drug-resistant strains when a combination of antiretroviral drugs is used to induce instantaneous drug effects at a sequence of dosing times equally spaced while drug concentrations decay exponentially after the dosing time. Threshold parameters are derived using the basic reproduction number of periodic epidemic models, and are used to depict virus clearance/persistence scenarios using the theory of asymptotic periodic systems and the persistence theory of discrete dynamical systems. Numerical simulations using model systems parametrized in terms of the antiretroviral therapy recommended in the aforementioned Manuals illustrate the theoretical threshold virus dynamics, and examine conditions under which the impulsive antiretroviral therapy leads to treatment success. In particular, our results show that only the drug-resistant strain can dominate (the first-line treatment program guided by the Manuals) or both strains may be rapidly eliminated (the second-line treatment program), thus the work indicates the importance of implementing the second-line treatment program as soon as possible.
Original languageEnglish
Pages (from-to)623-652
Number of pages30
JournalJournal of Mathematical Biology
Issue number4
Publication statusPublished - 1 Sept 2012
Externally publishedYes


  • Antiretroviral therapy
  • Disease persistence
  • Drug kinetics
  • HIV
  • Impulsive dynamics
  • Periodic virus dynamics model

ASJC Scopus subject areas

  • Modelling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics


Dive into the research topics of 'Threshold virus dynamics with impulsive antiretroviral drug effects'. Together they form a unique fingerprint.

Cite this