{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T21:10:09Z","timestamp":1778533809300,"version":"3.51.4"},"reference-count":33,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T00:00:00Z","timestamp":1778198400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>We analyze parameter identifiability in a Marchuk-type immune-response model using longitudinal whole-blood transcriptomic signatures from the influenza challenge. Latent states are extracted from curated gene signatures derived from nine symptomatic and eight asymptomatic subjects. The governing delay differential equations are cast in a linear-in-parameters form; derivatives are estimated by smoothing splines, coefficients are fit by ridge regression, and the delay \u03c4 is selected by grid search. We find that the parameters governing viral and innate dynamics are consistently identifiable, with low relative error, and are highly determined, whereas adaptive-immunity and tissue-damage parameters are poorly constrained by transcriptomics alone. Introducing a small additive background term and tissue dependence markedly reduces residual variance and stabilizes estimates. Symptomatic patients exhibit a characteristic regulatory delay near 21 h. These results show that aggregated transcriptomic time series can reliably identify some subsystems of classical immune models, but that adaptive immunity and damage dynamics require explicit structural extensions or additional data modalities. The study provides a practical identification pipeline and concrete guidance on model extensions needed for transcriptomic-driven mechanistic inference.<\/jats:p>","DOI":"10.3390\/computation14050108","type":"journal-article","created":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T20:14:16Z","timestamp":1778530456000},"page":"108","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Limits of Classical Immune Response Models"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7310-7333","authenticated-orcid":false,"given":"Marina","family":"Bershadsky","sequence":"first","affiliation":[{"name":"Department of Computer Science, Shamoon College of Engineering, Beer Sheva 8410802, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-2974-1547","authenticated-orcid":false,"given":"Genady","family":"Kogan","sequence":"additional","affiliation":[{"name":"Department of Software Engineering, Shamoon College of Engineering, Beer Sheva 8410802, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,5,8]]},"reference":[{"key":"ref_1","unstructured":"Zuev, S.M. (1988). Statistical Evaluation of Parameters of Mathematical Models of Diseases, Nauka."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Huang, Y., Zaas, A.K., Rao, A., Dobigeon, N., Woolf, P.J., Veldman, T., Ien, N.C., McClain, M.T., Varkey, J.B., and Nicholson, B. (2011). Temporal dynamics of host molecular responses differentiate symptomatic and asymptomatic influenza a infection. PLoS Genet., 7, Available online: https:\/\/www.ncbi.nlm.nih.gov\/geo\/query\/acc.cgi?acc=GSE30550.","DOI":"10.1371\/journal.pgen.1002234"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1038\/nri3642","article-title":"Democratizing systems immunology with modular transcriptional repertoire analyses","volume":"14","author":"Chaussabel","year":"2014","journal-title":"Nat. Rev. Immunol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"579","DOI":"10.15593\/RJBiomech\/2019.4.08","article-title":"Distributed control in stabilization of a model of infection diseases","volume":"23","author":"Domoshnitsky","year":"2019","journal-title":"Russ. J. Biomech."},{"key":"ref_5","first-page":"85","article-title":"Marchuk\u2019s model of immune system dynamics with application to tumour growth","volume":"4","year":"2002","journal-title":"J. Theor. Med."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"15545","DOI":"10.1073\/pnas.0506580102","article-title":"Gene set enrichment analysis: A knowledgebased approach for interpreting genome-wide expression profiles","volume":"102","author":"Subramanian","year":"2005","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"e2024681118","DOI":"10.1073\/pnas.2024681118","article-title":"Influenza A viruses balance ER stress with host protein synthesis shutoff","volume":"118","author":"Iwaszkiewicz","year":"2021","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1255","DOI":"10.1016\/j.cell.2009.12.018","article-title":"A physical and regulatory map of host-influenza interactions reveals pathways in H1N1 infection","volume":"139","author":"Shapira","year":"2009","journal-title":"Cell"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1038\/nri3787","article-title":"Type I interferons in infectious disease","volume":"15","author":"McNab","year":"2015","journal-title":"Nat. Rev. Immunol."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Huang, M., Xu, R., Triffon, C., Mifsud, N., and Chen, W. (2021). Broad-Based Influenza-Specific CD8+ T Cell Response without the Typical Immunodominance Hierarchy and Its Potential Implication. Viruses, 13.","DOI":"10.3390\/v13061080"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3422","DOI":"10.1038\/s41467-019-11249-y","article-title":"Neutrophils-related host factors associated with severe disease and fatality in patients with influenza infection","volume":"10","author":"Tang","year":"2019","journal-title":"Nat. Commun."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"e99022","DOI":"10.1172\/jci.insight.99022","article-title":"Matrix metalloproteinase-9 deficiency protects mice from severe influenza A viral infection","volume":"3","author":"Wang","year":"2018","journal-title":"JCI Insight"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3507","DOI":"10.1073\/pnas.1222878110","article-title":"Genomic responses in mouse models poorly mimic human inflammatory diseases","volume":"110","author":"Seok","year":"2013","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Marchuk, G.I. (1997). Mathematical Modelling of Immune Response in Infectious Diseases, Springer Science.","DOI":"10.1007\/978-94-015-8798-3"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0022-5193(05)80142-0","article-title":"Mathematical model of antiviral immune response. I. Data analysis, generalized picture construction and parameters evaluation for hepatitis B","volume":"151","author":"Marchuk","year":"1997","journal-title":"J. Theor. Biol."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Volinsky, I., Domoshnitsky, A., Bershadsky, M., and Shklyar, R. (2020). Marchuk\u2019s models of infection diseases: New developments in Functional Differential Equations and Applications. International Workshop on Functional Differential Equations and Applications, Springer.","DOI":"10.1007\/978-981-16-6297-3_10"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"5234854","DOI":"10.1155\/2019\/5234854","article-title":"Distributed control and the Lyapunov characteristic exponents in the model of infectious diseases","volume":"2019","author":"Bershadsky","year":"2019","journal-title":"Complexity"},{"key":"ref_18","first-page":"85","article-title":"Numerical Solution of Marchuk Model of Infection Diseases","volume":"28","author":"Volinsky","year":"2021","journal-title":"Funct. Differ. Equ."},{"key":"ref_19","first-page":"289","article-title":"A brief look at the mathematical modelling of the immune response","volume":"66","year":"2020","journal-title":"Analele \u015eTiin\u0163ifice Ale Univ. Cuza\u2019Din Ia\u015fi. Mat. (New Ser.)"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3932","DOI":"10.1073\/pnas.1517384113","article-title":"Discovering governing equations from data by sparse identification of nonlinear dynamical systems","volume":"113","author":"Brunton","year":"2016","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Bellen, A., and Zennaro, M. (2003). Numerical Methods for Delay Differential Equations, OUP.","DOI":"10.1093\/acprof:oso\/9780198506546.001.0001"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"803","DOI":"10.1016\/0270-0255(86)90136-3","article-title":"Solution of the Marchuk Model of Infectious Disease and Immune Response","volume":"7","author":"Adomian","year":"1986","journal-title":"Math. Model."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"741","DOI":"10.1111\/j.1467-9868.2007.00610.x","article-title":"Parameter estimation for differential equations: A generalized smoothing approach","volume":"69","author":"Ramsay","year":"2007","journal-title":"J. R. Stat. Soc. Ser. Stat. Methodol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1242","DOI":"10.1214\/07-EJS132","article-title":"Parameter estimation of ODE\u2019s via nonparametric estimators","volume":"2","author":"Brunel","year":"2008","journal-title":"Electron. J. Stat."},{"key":"ref_25","unstructured":"Gugushvili, S., and Klaassen, C.A.J. (2010). n-consistent parameter estimation for systems of ordinary differential equations: Bypassing numerical integration via smoothing. arXiv."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1515\/1569398054308630","article-title":"Computational Aspects of Time-Lag Models of Marchuk Type That Arise in Immunology","volume":"20","author":"Baker","year":"2005","journal-title":"Russ. J. Numer. Anal. Math. Model."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Villaverde, A.F., Barreiro, A., and Papachristodoulou, A. (2016). Structural identifiability of dynamic systems biology models. PLoS Comput. Biol., 12.","DOI":"10.1371\/journal.pcbi.1005153"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.ygeno.2012.11.008","article-title":"Neutrophils infected with highly virulent influenza H3N2 virus exhibit augmented early cell death and rapid induction of type I interferon signaling pathways","volume":"101","author":"Ivan","year":"2013","journal-title":"Genomics"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"7590","DOI":"10.1128\/JVI.01623-05","article-title":"Kinetics of influenza A virus infection in humans","volume":"80","author":"Baccam","year":"2006","journal-title":"J. Virol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1002\/wsbm.129","article-title":"Influenza A virus infection kinetics: Quantitative data and models","volume":"3","author":"Smith","year":"2011","journal-title":"Wiley Interdiscip. Rev. Syst. Biol. Med."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"4627","DOI":"10.4049\/jimmunol.166.7.4627","article-title":"Diversity of epitope and cytokine profiles for primary and secondary influenza a virus-specific CD8+ T cell responses","volume":"166","author":"Belz","year":"2001","journal-title":"J. Immunol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1109\/MRA.2012.2192817","article-title":"System identification: Theory for the user, (ljung, l.; 1999) [on the shelf]","volume":"19","author":"Simpkins","year":"2012","journal-title":"IEEE Robot. Autom. Mag."},{"key":"ref_33","unstructured":"(2025, December 31). Python 3 version. Available online: https:\/\/www.google.com\/search?q=Python+3.10.12&oq=Python+3.10.12&gs_lcrp=EgZjaHJvbWUqBggAEEUYOzIGCAAQRRg."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/14\/5\/108\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T20:33:13Z","timestamp":1778531593000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/14\/5\/108"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,8]]},"references-count":33,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2026,5]]}},"alternative-id":["computation14050108"],"URL":"https:\/\/doi.org\/10.3390\/computation14050108","relation":{},"ISSN":["2079-3197"],"issn-type":[{"value":"2079-3197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,8]]}}}