Bulletin of Mathematical Biology

 July 2019

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[Full Text, Pubmed]

Abstract

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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.