Mathematical Analysis of a Transformed ODE from a PDE Multiscale Model of Hepatitis C Virus Infection

Kosaku Kitagawa, Toshikazu Kuniya, Shinji Nakaoka, Yusuke Asai, Koichi Watashi, Shingo Iwami

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


Mathematical modeling has revealed the quantitative dynamics during the process of viral infection and evolved into an important tool in modern virology. Coupled with analyses of clinical and experimental data, the widely used basic model of viral dynamics described by ordinary differential equations (ODEs) has been well parameterized. In recent years, age-structured models, called “multiscale model,” formulated by partial differential equations (PDEs) have also been developed and become useful tools for more detailed data analysis. However, in general, PDE models are considerably more difficult to subject to mathematical and numerical analyses. In our recently reported study, we successfully derived a mathematically identical ODE model from a PDE model, which helps to overcome the limitations of the PDE model with regard to clinical data analysis. Here, we derive the basic reproduction number from the identical ODE model and provide insight into the global stability of all possible steady states of the ODE model.

Original languageEnglish
Pages (from-to)1427-1441
Number of pages15
JournalBulletin of Mathematical Biology
Issue number5
Publication statusPublished - May 15 2019

All Science Journal Classification (ASJC) codes

  • Neuroscience(all)
  • Immunology
  • Mathematics(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Environmental Science(all)
  • Pharmacology
  • Agricultural and Biological Sciences(all)
  • Computational Theory and Mathematics


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