A differential equation model for functional mapping of a virus-cell dynamic system

Jiangtao Luo, William W. Hager, Rongling Wu

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


The dynamic pattern of viral load in a patient's body critically depends on the host's genes. For this reason, the identification of those genes responsible for virus dynamics, although difficult, is of fundamental importance to design an optimal drug therapy based on patients' genetic makeup. Here, we present a differential equation (DE) model for characterizing specific genes or quantitative trait loci (QTLs) that affect viral load trajectories within the framework of a dynamic system. The model is formulated with the principle of functional mapping, originally derived to map dynamic QTLs, and implemented with a Markov chain process. The DE-integrated model enhances the mathematical robustness of functional mapping, its quantitative prediction about the temporal pattern of genetic expression, and therefore its practical utilization and effectiveness for gene discovery in clinical settings. The model was used to analyze simulated data for viral dynamics, aimed to investigate its statistical properties and validate its usefulness. With an increasing availability of genetic polymorphic data, the model will have great implications for probing the molecular genetic mechanism of virus dynamics and disease progression.

Original languageEnglish (US)
Pages (from-to)1-15
Number of pages15
JournalJournal of Mathematical Biology
Issue number1
StatePublished - 2010


  • Differential equation
  • Functional mapping
  • Quantitative trait loci
  • Viral dynamics

ASJC Scopus subject areas

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


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