A PDE multiscale model of hepatitis C virus infection can be transformed to a system of ODEs

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

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Direct-acting antivirals (DAAs) treat hepatitis C virus (HCV) by targeting its intracellular viral replication. DAAs are effective and deliver high clinical performance against HCV infection, but optimization of the DAA treatment regimen is ongoing. Different classes of DAAs are currently under development, and HCV treatments that combine two or three DAAs with different action mechanisms are being improved. To accurately quantify the antiviral effect of these DAA treatments and optimize multi-drug combinations, we must describe the intracellular viral replication processes corresponding to the action mechanisms by multiscale mathematical models. Previous multiscale models of HCV treatment have been formulated by partial differential equations (PDEs). However, estimating the parameters from clinical datasets requires comprehensive numerical PDE computations that are time consuming and often converge poorly. Here, we propose a user-friendly approach that transforms a standard PDE multiscale model of HCV infection (Guedj J et al., Proc. Natl. Acad. Sci. USA 2013; 110(10):3991–6) to mathematically identical ordinary differential equations (ODEs) without any assumptions. We also confirm consistency between the numerical solutions of our transformed ODE model and the original PDE model. This relationship between a detailed structured model and a simple model is called “model aggregation problem” and a fundamental important in theoretical biology. In particular, as the parameters of ODEs can be estimated by already established methods, our transformed ODE model and its modified version avoid the time-consuming computations and are broadly available for further data analysis.

Original languageEnglish
Pages (from-to)80-85
Number of pages6
JournalJournal of Theoretical Biology
Volume448
DOIs
Publication statusPublished - Jul 7 2018

Fingerprint

Multiscale Model
Hepatitis C virus
Virus Diseases
Viruses
System of Ordinary Differential Equations
Ordinary differential equations
Hepacivirus
Virus
Partial differential equations
Antiviral Agents
Infection
Partial differential equation
Ordinary differential equation
infection
Replication
virus replication
Model
mechanism of action
combination drug therapy
Drug Combinations

All Science Journal Classification (ASJC) codes

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

Cite this

A PDE multiscale model of hepatitis C virus infection can be transformed to a system of ODEs. / Kitagawa, Kosaku; Nakaoka, Shinji; Asai, Yusuke; Watashi, Koichi; Iwami, Shingo.

In: Journal of Theoretical Biology, Vol. 448, 07.07.2018, p. 80-85.

Research output: Contribution to journalArticle

Kitagawa, Kosaku ; Nakaoka, Shinji ; Asai, Yusuke ; Watashi, Koichi ; Iwami, Shingo. / A PDE multiscale model of hepatitis C virus infection can be transformed to a system of ODEs. In: Journal of Theoretical Biology. 2018 ; Vol. 448. pp. 80-85.
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