Skip to main content
SpringerLink
Log in

Parameter Estimation in Mathematical Models of Viral Infections Using R

  • Protocol
  • First Online:
Influenza Virus

Part of the book series: Methods in Molecular Biology ((MIMB,volume 1836))

Abstract

In recent years, mathematical modeling approaches have played a central role in understanding and quantifying mechanisms in different viral infectious diseases. In this approach, biology-based hypotheses are expressed via mathematical relations and then tested based on empirical data. The simulation results can be used to either identify underlying mechanisms and provide predictions of infection outcomes or to evaluate the efficacy of a treatment.

Conducting parameter estimation for mathematical models is not an easy task. Here we detail an approach to conduct parameter estimation and to evaluate the results using the free software R. The method is applicable to influenza virus dynamics at different complexity levels, widening experimentalists’ capabilities in understanding their data. The parameter estimation approach presented here can be also applied to other viral infections or biological applications.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Protocol
USD 49.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. World Health Organization (2009) Global Surveillance during an Influenza Pandemic

    Google Scholar 

  2. Potter CW (2001) A history of influenza. J Appl Microbiol 91:572–579. https://doi.org/10.1046/j.1365-2672.2001.01492.x

    Article  PubMed  CAS  Google Scholar 

  3. World Health Organization (2011) WHO global technical consultation: global standards and tools for influenza surveillance, Geneva, Switzerland, 8–10 March 2011

    Google Scholar 

  4. Boianelli A, Nguyen VK, Ebensen T et al (2015) Modeling influenza virus infection: a roadmap for influenza research. Viruses 7:5274–5304. https://doi.org/10.3390/v7102875

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  5. Smith AM, Perelson AS (2010) Influenza A virus infection kinetics: quantitative data and models. WIREs Syst Biol Med 3:429–445. https://doi.org/10.1002/wsbm.129

    Article  CAS  Google Scholar 

  6. Canini L, Perelson AS (2014) Viral kinetic modeling: state of the art. J Pharmacokinet Pharmacodyn 41:431–443. https://doi.org/10.1007/s10928-014-9363-3

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  7. Beauchemin CA, Handel A (2011) A review of mathematical models of influenza A infections within a host or cell culture: lessons learned and challenges ahead. BMC Public Health 11:S7. https://doi.org/10.1186/1471-2458-11-S1-S7

    Article  PubMed  PubMed Central  Google Scholar 

  8. Duvigneau S, Sharma-Chawla N, Boianelli A et al (2016) Hierarchical effects of pro-inflammatory cytokines on the post-influenza susceptibility to pneumococcal coinfection. Sci Rep 6:643. https://doi.org/10.1038/srep37045

    Article  CAS  Google Scholar 

  9. Hernandez-Vargas EA, Wilk E, Canini L et al (2014) Effects of aging on influenza virus infection dynamics. J Virol 88:4123–4131. https://doi.org/10.1128/JVI.03644-13

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  10. Baccam P, Beauchemin CA, Macken CA et al (2006) Kinetics of influenza A virus infection in humans. J Virol 80:7590–7599. https://doi.org/10.1128/JVI.01623-05

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  11. Nowak MA, May RM (2000) Virus dynamics: mathematical principles of immunology and virology: mathematical principles of immunology and virology. Oxford University Press, Oxford

    Google Scholar 

  12. Pawelek KA, Huynh GT, Quinlivan M et al (2012) Modeling within-host dynamics of influenza virus infection including immune responses. PLoS Comput Biol 8:e1002588–e1002513. https://doi.org/10.1371/journal.pcbi.1002588

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  13. Soetaert K, Cash J, Mazzia F (2012) Solving differential equations in R. https://doi.org/10.1007/978-3-642-28070-2

  14. Nguyen VK, Binder SC, Boianelli A et al (2015) Ebola virus infection modeling and identifiability problems. Front Microbiol 6:7590. https://doi.org/10.3389/fmicb.2015.00257

    Article  Google Scholar 

  15. R Core Team (2015) R: A language and environment for statistical computing. R Core Team, Vienna

    Google Scholar 

  16. Storn R, Price K (1997) Differential evolution -- a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359. https://doi.org/10.1023/A:1008202821328

    Article  Google Scholar 

  17. Toapanta FR, Ross TM (2009) Impaired immune responses in the lungs of aged mice following influenza infection. Respir Res 10:340–319. https://doi.org/10.1186/1465-9921-10-112

    Article  CAS  Google Scholar 

  18. Mullen K, Ardia D, Gil D et al (2011) DEoptim: an RPackage for global optimization by differential evolution. J Stat Softw 40:1–26. https://doi.org/10.18637/jss.v040.i06

    Article  Google Scholar 

  19. Sakamoto Y, Ishiguro M, Kitagawa G (1986) Akaike information criterion statistics. D. Reidel Publishing Company, Tokyo

    Google Scholar 

  20. Gelman A, Hwang J, Vehtari A (2014) Understanding predictive information criteria for Bayesian models. Stat Comput 24:997–1016. https://doi.org/10.1007/s11222-013-9416-2

    Article  Google Scholar 

  21. Burnham KP, Anderson DR (2013) Model selection and inference. Springer Science & Business Media, New York

    Google Scholar 

  22. Nguyen VK, Klawonn F, Mikolajczyk R, Hernandez-Vargas EA (2016) Analysis of practical identifiability of a viral infection model. PLoS One 11:e0167568. https://doi.org/10.1371/journal.pone.0167568

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  23. Raue A, Kreutz C, Theis FJ, Timmer J (2013) Joining forces of Bayesian and frequentist methodology: a study for inference in the presence of non-identifiability. Philos Trans R Soc A Math Phys Eng Sci 371:20110544. https://doi.org/10.1098/rsta.2011.0544

    Article  Google Scholar 

  24. Hastie T, Tibshirani R, Friedman J (2009) The elements of statistical learning. Springer, New York, NY. https://doi.org/10.1007/978-0-387-84858-7

    Book  Google Scholar 

  25. Mammen E (2012) When does bootstrap work? Springer Science & Business Media, New York, NY

    Google Scholar 

  26. Liepe J, Kirk P, Filippi S et al (2014) A framework for parameter estimation and model selection from experimental data in systems biology using approximate Bayesian computation. Nat Protoc 9:439–456. https://doi.org/10.1038/nprot.2014.025

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  27. Raue A, Becker V, Klingmüller U, Timmer J (2010) Identifiability and observability analysis for experimental design in nonlinear dynamical models. Chaos 20:045105–045109. https://doi.org/10.1063/1.3528102

    Article  PubMed  CAS  Google Scholar 

  28. Pinilla LT, Holder BP, Abed Y et al (2012) The H275Y neuraminidase mutation of the pandemic a/H1N1 influenza virus lengthens the eclipse phase and reduces viral output of infected cells, potentially compromising fitness in ferrets. J Virol 86:10651–10660. https://doi.org/10.1128/JVI.07244-11

    Article  PubMed  PubMed Central  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Frankfurt Institute for Advanced Studies, Frankfurt am Main, Germany

    Van Kinh Nguyen & Esteban A. Hernandez-Vargas

Authors
  1. Van Kinh Nguyen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Esteban A. Hernandez-Vargas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Van Kinh Nguyen or Esteban A. Hernandez-Vargas .

Editor information

Editors and Affiliations

  1. School of Cellular and Molecular Medicine, University of Bristol, Bristol, UK

    Yohei Yamauchi

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Science+Business Media, LLC, part of Springer Nature

About this protocol

Check for updates. Verify currency and authenticity via CrossMark

Cite this protocol

Nguyen, V.K., Hernandez-Vargas, E.A. (2018). Parameter Estimation in Mathematical Models of Viral Infections Using R. In: Yamauchi, Y. (eds) Influenza Virus. Methods in Molecular Biology, vol 1836. Humana Press, New York, NY. https://doi.org/10.1007/978-1-4939-8678-1_25

Download citation

  • DOI: https://doi.org/10.1007/978-1-4939-8678-1_25

  • Published:

  • Publisher Name: Humana Press, New York, NY

  • Print ISBN: 978-1-4939-8677-4

  • Online ISBN: 978-1-4939-8678-1

  • eBook Packages: Springer Protocols

Publish with us

Policies and ethics

Search

Navigation