HCvmultiscalefit: A simulator for parameter estimation in multiscale models of hepatitis C virus dynamics

Alexander Churkin, Vladimir Reinharz, Stephanie Lewkiewicz, Harel Dahari, Danny Barash

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Calibration in mathematical models that are based on differential equations is known to be of fundamental importance. For sophisticated models such as age-structured models that simulate biological agents, parameter estimation or fitting (callibration) that solves all cases of data points available presents a formidable challenge, as efficiency considerations need to be employed in order for the method to become practical. In the case of multiscale models of hepatitis C virus dynamics that deal with partial differential equations (PDEs), a fully numerical parameter estimation method was developed that does not require an analytical approximation of the solution to the multiscale model equations, avoiding the necessity to derive the long-term approximation for each model. However, the method is considerably slow because of precision problems in estimating derivatives with respect to the parameters near their boundary values, making it almost impractical for general use. In order to overcome this limitation, two steps have been taken that significantly reduce the running time by orders of magnitude and thereby lead to a practical method. First, constrained optimization is used, letting the user add constraints relating to the boundary values of each parameter before the method is executed. Second, optimization is performed by derivative-free methods, eliminating the need to evaluate expensive numerical derviative approximations. These steps that were successful in significantly speeding up a highly non-efficient approach, rendering it practical, can also be adapted to multiscale models of other viruses and other sophisticated differential equation models. The newly efficient methods that were developed as a result of the above approach are described. Illustrations are provided using a user-friendly simulator that incorporates the efficient methods for multiscale models. We provide a simulator called HCVMultiscaleFit with a Graphical User Interface that applies these methods and is useful to perform parameter estimation for simulating viral dynamics during antiviral treatment.

Original languageEnglish
Title of host publicationInternational Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019
EditorsTheodore E. Simos, Theodore E. Simos, Theodore E. Simos, Theodore E. Simos, Theodore E. Simos, Charalambos Tsitouras
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735440258
DOIs
StatePublished - 24 Nov 2020
EventInternational Conference on Numerical Analysis and Applied Mathematics 2019, ICNAAM 2019 - Rhodes, Greece
Duration: 23 Sep 201928 Sep 2019

Publication series

NameAIP Conference Proceedings
Volume2293
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

ConferenceInternational Conference on Numerical Analysis and Applied Mathematics 2019, ICNAAM 2019
Country/TerritoryGreece
CityRhodes
Period23/09/1928/09/19

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