Bulletin of Mathematical Biology

, Volume 70, Issue 6, pp 1749–1771 | Cite as

Modeling and Estimation of Kinetic Parameters and Replicative Fitness of HIV-1 from Flow-Cytometry-Based Growth Competition Experiments

  • Hongyu Miao
  • Carrie Dykes
  • Lisa M. Demeter
  • James Cavenaugh
  • Sung Yong Park
  • Alan S. Perelson
  • Hulin Wu
Original Article


Growth competition assays have been developed to quantify the relative fitness of HIV-1 mutants. In this article, we develop mathematical models to describe viral/cellular dynamic interactions in the assay system from which the competitive fitness indices or parameters are defined. In our previous HIV-viral fitness experiments, the concentration of uninfected target cells was assumed to be constant (Wu et al. 2006). But this may not be true in some experiments. In addition, dual infection may frequently occur in viral fitness experiments and may not be ignorable. Here, we relax these two assumptions and extend our earlier viral fitness model (Wu et al. 2006). The resulting models then become nonlinear ODE systems for which closed-form solutions are not achievable. In the new model, the viral relative fitness is a function of time since it depends on the target cell concentration. First, we studied the structure identifiability of the nonlinear ODE models. The identifiability analysis showed that all parameters in the proposed models are identifiable from the flow-cytometry-based experimental data that we collected. We then employed a global optimization approach (the differential evolution algorithm) to directly estimate the kinetic parameters as well as the relative fitness index in the nonlinear ODE models using nonlinear least square regression based on the experimental data. Practical identifiability was investigated via Monte Carlo simulations.


Differential evolution Global optimization HIV/AIDS Model identifiability Ordinary differential equation (ODE) Statistical inverse problem Viral fitness 


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Copyright information

© Society for Mathematical Biology 2008

Authors and Affiliations

  • Hongyu Miao
    • 1
  • Carrie Dykes
    • 2
  • Lisa M. Demeter
    • 2
  • James Cavenaugh
    • 1
  • Sung Yong Park
    • 1
  • Alan S. Perelson
    • 3
  • Hulin Wu
    • 1
  1. 1.Department of Biostatistics and Computational BiologyUniversity of Rochester School of Medicine and DentistryRochesterUSA
  2. 2.Department of MedicineUniversity of Rochester School of Medicine and DentistryRochesterUSA
  3. 3.Theoretical Biology & Biophysics Group, MS-K710, T-10Los Alamos National LaboratoryLos AlamosUSA

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