A Parameter Estimation Method for Multiscale Models of Hepatitis C Virus Dynamics

  • Vladimir Reinharz
  • Alexander Churkin
  • Stephanie Lewkiewicz
  • Harel Dahari
  • Danny BarashEmail author
Research Methods Article


Mathematical models that are based on differential equations require detailed knowledge about the parameters that are included in the equations. Some of the parameters can be measured experimentally while others need to be estimated. When the models become more sophisticated, such as in the case of multiscale models of hepatitis C virus dynamics that deal with partial differential equations (PDEs), several strategies can be tried. It is possible to use parameter estimation on an analytical approximation of the solution to the multiscale model equations, namely the long-term approximation, but this limits the scope of the parameter estimation method used and a long-term approximation needs to be derived for each model. It is possible to transform the PDE multiscale model to a system of ODEs, but this has an effect on the model parameters themselves and the transformation can become problematic for some models. Finally, it is possible to use numerical solutions for the multiscale model and then use canned methods for the parameter estimation, but the latter is making the user dependent on a black box without having full control over the method. The strategy developed here is to start by working directly on the multiscale model equations for preparing them toward the parameter estimation method that is fully coded and controlled by the user. It can also be adapted to multiscale models of other viruses. The new method is described, and illustrations are provided using a user-friendly simulator that incorporates the method.


Parameter estimation Multiscale models Differential equations Hepatitis C virus 



Funding was provided by National Institutes of Health Grant Nos. R01-AI078881, R01-AI144112, and R01-GM121600, Azrieli Foundation and Fonds Québécois de la Recherche sur la Nature et les Technologies.


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Copyright information

© Society for Mathematical Biology 2019

Authors and Affiliations

  1. 1.Department of Computer ScienceBen-Gurion UniversityBeershebaIsrael
  2. 2.Department of Software EngineeringSami Shamoon College of EngineeringBeershebaIsrael
  3. 3.Department of MathematicsUniversity of California at Los AngelesLos AngelesUSA
  4. 4.Program for Experimental and Theoretical Modeling, Division of Hepatology, Department of MedicineLoyola University Medical CenterMaywooodUSA

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