Startseite Mathematik Identifiability of basic models and parameters in mathematical immunology
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Identifiability of basic models and parameters in mathematical immunology

  • Dmitry S. Grebennikov , Rostislav S. Savinkov und Gennady A. Bocharov EMAIL logo
Veröffentlicht/Copyright: 12. Juni 2025

Abstract

We analyzed the fundamental issues related to the development of mathematical models in immunology, i.e., the structural and practical identifiability of the models in mathematical immunology. To this end, the differential algebraic techniques and Bayesian approach implemented in StructuralIdentifiability.jl and DynamicHMC.jl Julia-based packages, respectively, are used. The experimental data on kinetics of viral load and cytotoxic T lymphocyte (CTL) response characterizing an acute lymphocytic choriomeningitis virus (LCMV) infection in mice were considered. Although the models differ in terms of one to three parameters, the structural identifiability strongly depends on details of observability and initial determination of the state variables. The estimated via a Bayesian approach posterior distributions for model parameter characterize the rates of interactions underlying the acute infection development. The results of the data assimilation on LCMV-CTL kinetics suggest that a bilinear-type description of the virus-induced CTL expansion and the CTL-driven virus elimination need to be refined to a bounded-rate (e.g., Michaelis–Menten) type parameterizations.

MSC 2010: 92-10

Funding statement: The reported study was funded by the Russian Science Foundation, grant No. 23-11-00116.

References

[1] C. T. H. Baker, G. A. Bocharov, J. M. Ford, P. M. Lumb, S. J. Norton, C. A. H. Paul, T. Junt, P. Krebs, and B. Ludewig, Computational approaches to parameter estimation and model selection in immunology. Journal of Computational and Applied Mathematics 184 (2005), No. 1, 50–76.10.1016/j.cam.2005.02.003Suche in Google Scholar

[2] R. X. Barreiro and A. F. Villaverde, Benchmarking tools for a priori identifiability analysis. Bioinformatics 39 (2023), No. 2, btad065.10.1093/bioinformatics/btad065Suche in Google Scholar PubMed PubMed Central

[3] G. I. Bell, Predator-prey equations simulating an immune response. Mathematical Biosciences 16 (1973), No. 3–4, 291–314.10.1016/0025-5564(73)90036-9Suche in Google Scholar

[4] M. Betancourt, A conceptual introduction to Hamiltonian Monte Carlo. arXiv preprint arXiv:1701.02434, 2017.Suche in Google Scholar

[5] R. Blanco-Rodríguez, X. Du, and E. Hernández-Vargas, Computational simulations to dissect the cell immune response dynamics for severe and critical cases of SARS-CoV-2 infection. Comput. Methods Programs Biomed. 211 (2021), 106412.10.1016/j.cmpb.2021.106412Suche in Google Scholar PubMed PubMed Central

[6] G. A. Bocharov, Modelling the dynamics of LCMV infection in mice: conventional and exhaustive CTL responses. Journal of Theoretical Biology 193 (1998), No. 3, 283–308.10.1006/jtbi.1997.0612Suche in Google Scholar PubMed

[7] G. Bocharov, J. Argilaguet, and A. Meyerhans, Understanding experimental LCMV infection of mice: the role of mathematical models. Journal of Immunology Research (2015), No. 1, 739706.10.1155/2015/739706Suche in Google Scholar PubMed PubMed Central

[8] G. Bocharov, B. Ludewig, A. Meyerhans, and V. Volpert, Mathematical Immunology of Virus Infections. Springer, 2018.10.1007/978-3-319-72317-4Suche in Google Scholar

[9] G. A. Bocharov, D. S. Grebennikov, and R. S. Savinkov, Mathematical immunology: From phenomenological to multiphysics modelling. Russian Journal of Numerical Analysis and Mathematical Modelling 35 (2021), No. 4, 203–213.10.1515/rnam-2020-0017Suche in Google Scholar

[10] G. A. Bocharov, D. S. Grebennikov, and R. S. Savinkov, Multiphysics modelling of immune processes using distributed parameter systems. Russian Journal of Numerical Analysis and Mathematical Modelling 38 (2023), No. 5, 279–292.10.1515/rnam-2023-0021Suche in Google Scholar

[11] O. T. Chis, J. R. Banga, and E. Balsa-Canto, Structural identifiability of systems biology models: a critical comparison of methods. PLoS One 6 (2011), No. 11, e27755.10.1371/journal.pone.0027755Suche in Google Scholar PubMed PubMed Central

[12] F. Curion and F. J. Theis, Machine learning integrative approaches to advance computational immunology. Genome Med. 16 (2024), No. 1, 80.10.1186/s13073-024-01350-3Suche in Google Scholar PubMed PubMed Central

[13] R. Dong, C. Goodbrake, H. Harrington, and G. Pogudin, Differential elimination for dynamical models via projections with applications to structural identifiability. SIAM J. Appl. Algebra Geom., 7 (2023), 194–235.10.1137/22M1469067Suche in Google Scholar

[14] D. S. Grebennikov and G. A. Bocharov, Spatially resolved modelling of immune responses following a multiscale approach: From computational implementation to quantitative predictions. Russian Journal of Numerical Analysis and Mathematical Modelling 34 (2019), No. 5, 253–260.10.1515/rnam-2019-0021Suche in Google Scholar

[15] D. Grebennikov, A. Karsonova, M. Loguinova, V. Casella, A. Meyerhans, and G. Bocharov, Predicting the kinetic coordination of immune response dynamics in SARS-CoV-2 infection: Implications for disease pathogenesis. Mathematics 10 (2022), No. 17, 3154.10.3390/math10173154Suche in Google Scholar

[16] D. S. Grebennikov, V. V. Zheltkova, and G. A. Bocharov, Application of minimum description length criterion to assess the complexity of models in mathematical immunology. Russian Journal of Numerical Analysis and Mathematical Modelling 37 (2022), No. 5, 253–261.10.1515/rnam-2022-0022Suche in Google Scholar

[17] M. D. Hoffman and A. Gelman, The No-U-Turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo. J. Mach. Learn. Res. 15 (2014), No. 1, 1593–1623.Suche in Google Scholar

[18] H. Hong, A. Ovchinnikov, G. Pogudin, and C. Yap, SIAN: Software for structural identifiability analysis of ODE models. Bioinformatics 35 (2019), 2873–2874.10.1093/bioinformatics/bty1069Suche in Google Scholar PubMed

[19] H. Y. Kueh, A. Handel, A. Hoffmann, D. Chowell, R. A. Gottschalk, H. Singh, R. N. Germain, M. Meier-Schellersheim, K. Miller-Jensen, and G. Altan-Bonnet, What unique insights can modeling approaches capture about the immune system? Cell Syst. 15 (2024), No. 12, 1148–1152.10.1016/j.cels.2024.11.016Suche in Google Scholar PubMed

[20] Y. R. Liyanage, N. Heitzman-Breen, N. Tuncer, and S. M. Ciupe, Identifiability investigation of within-host models of acute virus infection. Math. Biosci. Engrg. 21 (2024), No. 10, 7394–7420.10.3934/mbe.2024325Suche in Google Scholar PubMed PubMed Central

[21] T. Luzyanina and G. Bocharov, Stochastic modeling of the impact of random forcing on persistent hepatitis B virus infection. Mathematics and Computers in Simulation 96 (2014), 54–65.10.1016/j.matcom.2011.10.002Suche in Google Scholar

[22] G. I. Marchuk, Mathematical Models in Immunology. Optimization Software, Inc., New York, 1983.Suche in Google Scholar

[23] G. I. Marchuk, Mathematical Modelling of Immune Response in Infectious Diseases. Mathematics and Its Applications. Vol. 395, Springer Science & Business Media, 1997.10.1007/978-94-015-8798-3Suche in Google Scholar

[24] H. Miao, X. Xia, A. S. Perelson, and H. Wu, On identifiability of nonlinear ode models and applications in viral dynamics. SIAM Rev. Soc. Ind. Appl. Math. 53 (2011), No. 1, 3–39.10.1137/090757009Suche in Google Scholar PubMed PubMed Central

[25] R. M. Neal, MCMC using Hamiltonian dynamics. In: Handbook of Markov Chain Monte Carlo (Eds. S. Brooks, A. Gelman, G. L. Jones, X.-L. Meng). Chapman and Hall/CRC, 2011.10.1201/b10905-6Suche in Google Scholar

[26] M. Ostaszewski et al., COVID-19 Disease Map Community. COVID-19 Disease Map, a computational knowledge repository of virus-host interaction mechanisms. Mol. Syst. Biol. (2021); 17(12):e10851. DOI: 10.15252/msb.202110851. Erratum for: Mol. Syst. Biol. (2021); 17(10):e10387. DOI: 10.15252/msb.202110387.10.15252/msb.202110851Suche in Google Scholar PubMed PubMed Central

[27] A. S. Perelson and R. Ke, Mechanistic modeling of SARS-CoV-2 and other infectious diseases and the effects of therapeutics. Clin. Pharmacol. Ther. 109 (2021). No. 4, 829–840.10.1002/cpt.2160Suche in Google Scholar PubMed PubMed Central

[28] C. Voutouri, M. R. Nikmaneshi, C. C. Hardin, A. B. Patel, A. Verma, M. J. Khandekar, S. Dutta, T. Stylianopoulos, L. L. Munn, and R. K. Jain, In silico dynamics of COVID-19 phenotypes for optimizing clinical management. Proc. Natl. Acad. Sci. USA 118 (2021), No. 3, e2021642118.10.1073/pnas.2021642118Suche in Google Scholar PubMed PubMed Central

[29] B. Whipple, T. A. Miura, and E. A. Hernandez-Vargas, Modeling the CD8 + T cell immune response to influenza infection in adult and aged mice. J. Theor. Biol. 593 (2024), 111898.10.1016/j.jtbi.2024.111898Suche in Google Scholar PubMed PubMed Central

[30] H. Wu, H. Miao, H. Xue, D. J. Topham, and M. Zand, Quantifying immune response to influenza virus infection via multivariate nonlinear ODE models with partially observed state variables and time-varying parameters. Stat. Biosci. 7 (2015), No. 1, 147–166.10.1007/s12561-014-9108-2Suche in Google Scholar PubMed PubMed Central

Received: 2025-03-19
Accepted: 2025-03-25
Published Online: 2025-06-12
Published in Print: 2025-06-26

© 2025 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 15.1.2026 von https://www.degruyterbrill.com/document/doi/10.1515/rnam-2025-0015/pdf
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