A Parameter Estimation Method for Multiscale Models of Hepatitis C Virus Dynamics
- 44 Downloads
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.
KeywordsParameter 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.
- AASLD/IDSA HCV Guidance Panel (2015) Hepatitis C guidance: AASLD-IDSA recommendations for testing, managing, and treating adults infected with hepatitis C virus. Hepatology 62(3):932–954Google Scholar
- Barash D, Israeli M, Kimmel R (2001) An accurate operator splitting scheme for nonlinear diffusion filtering. In: Proceedings of the 3rd international conference on scalespace and morphology. LNCS Series. Springer, pp 281–289Google Scholar
- Dahari H, Shteingart S, Gafanovich I, Cotler SJ, D’Amato M, Pohl RT, Weiss G, Ashkenazi YJ, Tichler T, Goldin E et al (2015) Sustained virological response with intravenous silibinin: individualized IFN-free therapy via real-time modelling of HCV kinetics. Liver Int 35(2):289–294CrossRefGoogle Scholar
- Dahari H, Canini L, Graw F, Uprichard SL, Araújo ES, Pénaranda G, Coquet E, Chiche L, Riso A, Renou C, Bourliere M, Cotler S, Halfon P (2016) HCV kinetic and modeling analyses indicate similar time to cure among sofosbuvir combination regimens with daclatasvir, simeprevir or ledipasvir. J Hepatol 64:1232–1239CrossRefGoogle Scholar
- Etzion O, Dahari H, Yardeni D, Issachar A, Nevo-Shor A, Cohen-Naftaly M, Uprichard S, Sneh Arbib O, Munteanu D, Braun M, Cotler S, Abufreha N, Mor O, Shlomai A (2018) Response-guided therapy with DAA shortens treatment duration in 50% of HCV treated patients. Hepatology 68:1468A–1469AGoogle Scholar
- Gambato M, Canini L, Lens S, Graw F, Londoño M-C, Uprichard SL, Mariño Z, Reverter E, Bartres C, González P, Pla A, Costa J, Burra P, Cotler SJ, Forns X, Dahari H (2019) Modeling early HCV kinetics to individualize treatment in patients with advanced liver cirrhosis. Liver Int 39(5):826–834CrossRefGoogle Scholar
- Guedj J, Dahari H, Rong L, Sansone ND, Nettles RE, Cotler SJ, Layden TJ, Uprichard SL, Perelson AS (2013a) Modeling shows that the NS5A inhibitor daclatasvir has two modes of action and yields a shorter estimate of the hepatitis C virus half-life. Proc Natl Acad Sci USA 110:3991–3996CrossRefGoogle Scholar
- Guedj J, Rotman Y, Cotler SJ, Koh C, Schmid P, Albrecht J, Haynes-Williams V, Liang TJ, Hoofnagle JH, Heller T et al (2014) Understanding early serum hepatitis D virus and hepatitis B surface antigen kinetics during pegylated interferon-alpha therapy via mathematical modeling. Hepatology 60(6):1902–1910CrossRefGoogle Scholar
- Koh C, Canini L, Dahari H, Zhao X, Uprichard SL, Haynes-Williams V, Winters MA, Subramanya G, Cooper SL, Pinto P et al (2015) Oral prenylation inhibition with lonafarnib in chronic hepatitis D infection: a proof-of-concept randomised, double-blind, placebo-controlled phase 2A trial. Lancet Infect Dis 15(10):1167–1174CrossRefGoogle Scholar
- Rohatgi A (2018) Webplotdigitizer: web based tool to extract data from plots, images, and maps. V 4.1. https://automeris.io/WebPlotDigitizer
- World Health Organization (2014) Guidelines for the screening, care and treatment of persons with hepatitis C infection. World Health Organization, GenevaGoogle Scholar