{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:41:21Z","timestamp":1760146881558,"version":"build-2065373602"},"reference-count":59,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,12,31]],"date-time":"2024-12-31T00:00:00Z","timestamp":1735603200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NIAID","award":["1R21-AI169170-01A1"],"award-info":[{"award-number":["1R21-AI169170-01A1"]}]},{"name":"Duke Transplant Center Fund","award":["1R21-AI169170-01A1"],"award-info":[{"award-number":["1R21-AI169170-01A1"]}]},{"name":"Center for Research in Scientific Computation at North Carolina State University","award":["1R21-AI169170-01A1"],"award-info":[{"award-number":["1R21-AI169170-01A1"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Viruses"],"abstract":"<jats:p>Kidney transplant recipients require a lifelong protocol of immunosuppressive therapy to prevent graft rejection. However, these same medications leave them susceptible to opportunistic infections. One pathogen of particular concern is human polyomavirus 1, also known as BK virus (BKPyV). This virus attacks kidney tubule epithelial cells and is a direct threat to the health of the graft. Current standard of care in BK virus-infected transplant recipients is reduction in immunosuppressant therapy, to allow the patient\u2019s immune system to control the virus. This requires a delicate balance; immune suppression must be strong enough to prevent rejection, yet weak enough to allow viral clearance. We seek to model viral and immune dynamics with the ultimate goal of applying optimal control methods to this problem. In this paper, we begin with a previously published model and make simplifying assumptions that reduce the number of parameters from 20 to 14. We calibrate our model using newly available patient data and a detailed sensitivity analysis. Numerical results for multiple patients are given to show that the newer model reflects observed dynamics well.<\/jats:p>","DOI":"10.3390\/v17010050","type":"journal-article","created":{"date-parts":[[2024,12,31]],"date-time":"2024-12-31T14:21:12Z","timestamp":1735654872000},"page":"50","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Modeling BK Virus Infection in Renal Transplant Recipients"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-6522-4947","authenticated-orcid":false,"given":"Nicholas","family":"Myers","sequence":"first","affiliation":[{"name":"Center for Research in Scientific Computation, Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dana","family":"Droz","sequence":"additional","affiliation":[{"name":"Center for Research in Scientific Computation, Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bruce W.","family":"Rogers","sequence":"additional","affiliation":[{"name":"Department of Surgery, Duke University, Durham, NC 27710, USA"},{"name":"Duke Center for Human Systems Immunology, Duke University, Durham, NC 27701, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2348-746X","authenticated-orcid":false,"given":"Hien","family":"Tran","sequence":"additional","affiliation":[{"name":"Center for Research in Scientific Computation, Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kevin B.","family":"Flores","sequence":"additional","affiliation":[{"name":"Center for Research in Scientific Computation, Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5901-6806","authenticated-orcid":false,"given":"Cliburn","family":"Chan","sequence":"additional","affiliation":[{"name":"Duke Center for Human Systems Immunology, Duke University, Durham, NC 27701, USA"},{"name":"Department of Biostatistics and Bioinformatics, Duke University, Durham, NC 27710, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stuart J.","family":"Knechtle","sequence":"additional","affiliation":[{"name":"Department of Surgery, Duke University, Durham, NC 27710, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2648-2944","authenticated-orcid":false,"given":"Annette M.","family":"Jackson","sequence":"additional","affiliation":[{"name":"Department of Surgery, Duke University, Durham, NC 27710, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xunrong","family":"Luo","sequence":"additional","affiliation":[{"name":"Department of Medicine, Duke University, Durham, NC 27710, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eileen T.","family":"Chambers","sequence":"additional","affiliation":[{"name":"Department of Surgery, Duke University, Durham, NC 27710, USA"},{"name":"Department of Pediatrics, Duke University, Durham, NC 27710, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Janice M.","family":"McCarthy","sequence":"additional","affiliation":[{"name":"Duke Center for Human Systems Immunology, Duke University, Durham, NC 27701, USA"},{"name":"Department of Biostatistics and Bioinformatics, Duke University, Durham, NC 27710, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"51","DOI":"10.5500\/wjt.v2.i4.51","article-title":"Current state of renal transplant immunosuppression: Present and future","volume":"2","author":"Kalluri","year":"2012","journal-title":"World J. Transplant."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Kant, S., Dasgupta, A., Bagnasco, S., and Brennan, D.C. (2022). BK Virus Nephropathy in Kidney Transplantation: A State-of-the-Art Review. Viruses, 14.","DOI":"10.3390\/v14081616"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1111\/j.1600-6143.2011.03840.x","article-title":"Understanding the causes of kidney transplant failure: The dominant role of antibody-mediated rejection and nonadherence","volume":"12","author":"Sellares","year":"2012","journal-title":"Am. J. Transplant."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2368","DOI":"10.1111\/j.1600-6143.2008.02402.x","article-title":"Polyomavirus BK replication dynamics in vivo and in silico to predict cytopathology and viral clearance in kidney trans-plants","volume":"8","author":"Funk","year":"2008","journal-title":"Am. J. Transplant."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1582","DOI":"10.1126\/science.271.5255.1582","article-title":"HIV-1 Dynamics In Vivo: Virion Clearance Rate, Infected Cell Life-Span, and Viral Generation Time","volume":"271","author":"Perelson","year":"1996","journal-title":"Science"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"5274","DOI":"10.3390\/v7102875","article-title":"Modeling Influenza Virus Infection: A Roadmap for Influenza Research","volume":"7","author":"Boianelli","year":"2015","journal-title":"Viruses"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1615\/CritRevImmunol.v30.i2.30","article-title":"Treatment of hepatitis C virus infection with interferon and small molecule direct antivirals: Viral kinetics and modeling","volume":"30","author":"Rong","year":"2010","journal-title":"Crit. Rev. Immunol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1038\/nrgastro.2015.97","article-title":"Modelling hepatitis C therapy\u2014Predicting effects of treatment","volume":"12","author":"Perelson","year":"2015","journal-title":"Nat. Rev. Gastroenterol. Hepatol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1137\/S0036144598335107","article-title":"Mathematical Analysis of HIV-1 Dynamics In Vivo","volume":"41","author":"Perelson","year":"1999","journal-title":"SIAM Rev."},{"key":"ref_10","first-page":"149","article-title":"A mathematical model of an integrated haemodialysis and renal transplantation programme","volume":"28","author":"West","year":"1974","journal-title":"Br. J."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3177","DOI":"10.1002\/sim.1876","article-title":"Parametric accelerated failure time models with random effects and an application to kidney transplant survival","volume":"23","author":"Labert","year":"2004","journal-title":"Stat. Med."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.dss.2017.12.004","article-title":"Predicting graft survival among kidney transplant recipients: A Bayesian decision support model","volume":"106","author":"Topuz","year":"2018","journal-title":"Decis. Support Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"167","DOI":"10.4285\/kjt.2020.34.3.167","article-title":"Mathematical model for early functional recovery pattern of kidney transplant recipients using serum creatinine","volume":"34","author":"Bang","year":"2020","journal-title":"Korean J. Transplant."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Blazquez-Navarro, A., Schachtner, T., Stervbo, U., Sefrin, A., Stein, M., Westhoff, T.H., Reinke, P., Klipp, E., Babel, N., and Neumann, A.U. (2018). Differential T cell response against BK virus regulatory and structural antigens: A viral dynamics modelling approach. PLoS Comput. Biol., 14.","DOI":"10.1371\/journal.pcbi.1005998"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Mahato, H., Ahlstrom, C., Jansson-L\u00f6fmark, R., Johansson, U., Helminger, G., and Hallow, K. (2018). Mathematical model of hemodynamic mechanisms and consequences of glomerular hyper-tension in diabetic mice. NPJ Syst. Biol. Appl., 4.","DOI":"10.1038\/s41540-018-0077-9"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1080\/17415977.2015.1017484","article-title":"Modelling immune response to BK virus infection and donor kidney in renal transplant recipients","volume":"24","author":"Banks","year":"2016","journal-title":"Inverse Probl. Sci. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1002\/oca.2478","article-title":"Optimal control of immunosuppressants in renal transplant recipients susceptible to BKV infection","volume":"40","author":"Murad","year":"2019","journal-title":"Optim. Control. Appl. Methods"},{"key":"ref_18","unstructured":"Murad, N., Tran, H.T., Banks, H., Everett, R.A., and Rosenberg, E. (2018). Immunosuppressant treatment dynamics in renal transplant recipients: An iterative modeling approach. Discret. Contin. Dyn. Syst. B, 223\u2013241."},{"key":"ref_19","unstructured":"Murad, N. (2018). Quantitative Modeling and Optimal Control of Immunosuppressant Treatment Dynamics in Renal Transplant Recipients. [Ph.D. Thesis, North Carolina State University]."},{"key":"ref_20","unstructured":"Myers, N.J. (2021). Applications of Mathematical Modeling in Ecology and Health Care. [Ph.D. Thesis, North Carolina State University]."},{"key":"ref_21","unstructured":"Newell, K. (2009). SDY1433: Optimization of NULOJIX\u00ae (Belatacept) Usage as a Means of Minimizing CNI Exposure in Simultaneous Pancreas and Kidney Transplantation (CTOT-15), NCT01790594."},{"key":"ref_22","unstructured":"Heeger, P. (2023). SDY2400: Effects of Inhibiting Early Inflammation in Kidney Transplant Patients (CTOT-19), NCT02495077."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"e13528","DOI":"10.1111\/ctr.13528","article-title":"BK polyomavirus in solid organ transplantation: Guidelines from the American Society of Transplantation Infectious Diseases Community of Practice","volume":"33","author":"Hirsch","year":"2019","journal-title":"Clin. Transplant."},{"key":"ref_24","unstructured":"Haldeman-Englert, C., Cunningham Turley, R., and Novick, T. (2024, October 15). Creatinine (Blood)\u2014University of Rochester Medical Center. Available online: https:\/\/www.urmc.rochester.edu\/encyclopedia\/content.aspx?ContentTypeID=167&ContentID=creatinine_serum."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"604","DOI":"10.7326\/0003-4819-150-9-200905050-00006","article-title":"A new equation to estimate glomerular filtration rate","volume":"150","author":"Levey","year":"2009","journal-title":"Ann. Intern. Med."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"180015","DOI":"10.1038\/sdata.2018.15","article-title":"ImmPort, toward repurposing of open access immunological assay data for translational and clinical research","volume":"5","author":"Bhattacharya","year":"2018","journal-title":"Sci. data"},{"key":"ref_27","first-page":"203","article-title":"The effect of statistical error model formulation on the fit and selection of mathematical models of tumor growth for small sample sizes","volume":"117","author":"Banks","year":"2017","journal-title":"Int. J. Pure Appl. Math."},{"key":"ref_28","unstructured":"The MathWorks Inc. (2022). MATLAB Version: 9.13.0 (R2022b), The MathWorks Inc."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"937","DOI":"10.3934\/mbe.2015.12.937","article-title":"Uncertainty quantification in modeling HIV viral mechanics","volume":"12","author":"Banks","year":"2015","journal-title":"MBE"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Smith, R.C. (2014). Uncertainty Quantification: Theory, Implementation, and Applications, Siam.","DOI":"10.1137\/1.9781611973228"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1515\/jiip-2014-0048","article-title":"Feasibility of parameter estimation in hepatitis C viral dynamics models","volume":"25","author":"Arthur","year":"2017","journal-title":"J. Inverse Ill-Posed Probl."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"978","DOI":"10.1016\/j.cpc.2010.12.039","article-title":"From screening to quantitative sensitivity analysis. A unified approach","volume":"182","author":"Campolongo","year":"2011","journal-title":"Comput. Phys. Commun."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Brady, R., Frank-Ito, D., Tran, H., Janum, S., M\u00f8ller, K., Brix, S., Ottensen, J., Mehlsen, J., and Olufsen, M. (2018). Personalized mathematical model of endotoxin-induced inflammatory responses in young men and associated changes in heart rate variability. Math. Model. Nat. Phenom., 13.","DOI":"10.1051\/mmnp\/2018031"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1137\/15M1008245","article-title":"Parameter Selection and Verification Techniques Based on Global Sensitivity Analysis Illustrated for an HIV Model","volume":"4","author":"Wentworth","year":"2016","journal-title":"SIAM\/ASA J. Uncertain. Quantif."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., and Tarantola, S. (2007). Introduction to Sensitivity Analysis. Global Sensitivity Analysis. The Primer, John Wiley & Sons, Ltd.. chapter 1.","DOI":"10.1002\/9780470725184"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Otto, S., and Day, T. (2007). A Biologist\u2019s Guide to Mathematical Modeling in Ecology and Evolution, Princeton University Press.","DOI":"10.1515\/9781400840915"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1529","DOI":"10.1007\/s00467-011-1843-8","article-title":"Human nephron number: Implications for health and disease","volume":"26","author":"Bertram","year":"2011","journal-title":"Pediatr. Nephrol."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Borriello, M., Ingrosso, D., Perna, A., Lombardi, A., Maggi, P., Altucci, L., and Caraglia, M. (2019). BK Virus Infection and BK-Virus-Associated Nephropathy in Renal Transplant Recipients. Genes, 13.","DOI":"10.3390\/genes13071290"},{"key":"ref_39","unstructured":"Farlow, J., Hall, J.E., McDill, J.M., and West, B.H. (2007). Differential Equations and Linear Algebra, Pearson."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1080\/17513758.2012.655328","article-title":"Modelling and optimal control of immune response of renal transplant recipients","volume":"6","author":"Banks","year":"2012","journal-title":"J. Biol. Dyn."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"113159","DOI":"10.1016\/j.jim.2021.113159","article-title":"A flow cytometry-based proliferation assay for clinical evaluation of T-cell memory against SARS-CoV-2","volume":"499","author":"Enoksson","year":"2021","journal-title":"J. Immunol. Methods"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1111\/ajt.15623","article-title":"A case for the reuse and adaptation of mechanistic computational models to study transplant immunology","volume":"20","author":"Fribourg","year":"2020","journal-title":"Am. J. Transplant."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"103957","DOI":"10.1016\/j.ijmedinf.2019.103957","article-title":"Machine learning in predicting graft failure following kidney transplantation: A systematic review of published predictive models","volume":"130","author":"Senanayake","year":"2019","journal-title":"Int. J. Med. Inform."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"456","DOI":"10.1016\/j.bspc.2017.01.012","article-title":"Decision tree and random forest models for outcome prediction in antibody incompatible kidney transplantation","volume":"52","author":"Shaikhina","year":"2019","journal-title":"Biomed. Signal Process. Control"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1048","DOI":"10.1097\/TP.0000000000002918","article-title":"The first Asian kidney transplantation prediction models for long-term patient and allograft survival","volume":"104","author":"Udomkarnjananun","year":"2020","journal-title":"Transplantation"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1095","DOI":"10.1097\/TP.0000000000002922","article-title":"Patient survival after kidney transplantation: Important role of graft-sustaining factors as determined by predictive modeling using random survival forest analysis","volume":"104","author":"Scheffner","year":"2020","journal-title":"Transplantation"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Alcendor, D.J. (2019). BK polyomavirus virus glomerular tropism: Implications for virus reactivation from latency and amplification during immunosuppression. J. Clin. Med., 8.","DOI":"10.3390\/jcm8091477"},{"key":"ref_48","unstructured":"Janeway, C.A., Travers, P., Walport, M., and Shlomchik, M.J. (2001). Immunobiology: The Immune System in Health and Disease, Garland Science. [5th ed.]."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1038\/nri1550","article-title":"The role of models in understanding CD8 + T-cell memory","volume":"5","author":"Antia","year":"2005","journal-title":"Nat. Rev. Immunol."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"15572","DOI":"10.1073\/pnas.242358099","article-title":"In vivo Dynamics of T Cell Activation, Proliferation, and Death in HIV-1 Infection: Why Are CD4+but Not CD8+T Cells Depleted?","volume":"99","author":"Ribeiro","year":"2002","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/s00285-011-0459-8","article-title":"Mathematical model of the primary CD8 T cell immune response: Stability analysis of a nonlinear age-structured system","volume":"65","author":"Terry","year":"2012","journal-title":"J. Math. Biol."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/j.smim.2004.02.007","article-title":"Lessons from the study of T-cell differentiation in persistent human virus infection","volume":"16","author":"Appay","year":"2004","journal-title":"Semin. Immunol."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"2240","DOI":"10.4049\/jimmunol.180.4.2240","article-title":"Comprehensive Assessment and Mathematical Modeling of T Cell Population Dynamics and Homeostasis1","volume":"180","author":"Altes","year":"2008","journal-title":"J. Immunol."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"1509","DOI":"10.1016\/j.envsoft.2006.10.004","article-title":"An effective screening design for sensitivity analysis of large models","volume":"22","author":"Campolongo","year":"2007","journal-title":"Environ. Model. Softw."},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Dennis, J.E., and Schnabel, R.B. (1996). Numerical Methods for Unconstrained Optimization and Nonlinear Equations, SIAM.","DOI":"10.1137\/1.9781611971200"},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Quaiser, T., and M\u00f6nnigmann, M. (2009). Systematic identifiability testing for unambiguous mechanistic modeling\u2013application to JAK-STAT, MAP kinase, and NF-\u03ba B signaling pathway models. BMC Syst. Biol., 3.","DOI":"10.1186\/1752-0509-3-50"},{"key":"ref_57","first-page":"545","article-title":"A sensitivity matrix based methodology for inverse problem formulation","volume":"17","author":"Banks","year":"2009","journal-title":"J. Inverse Ill-Posed Probl."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/978-3-642-32882-4_3","article-title":"Parameter selection methods in inverse problem formulation","volume":"Volume 2064","author":"Batzel","year":"2013","journal-title":"Mathematical Modeling and Validation in Physiology"},{"key":"ref_59","unstructured":"Bohl, D.L., and Brennan, D.C. (2021). Matrix Methods: Applied Linear Algebra and Sabermetrics, Academic Press. [4th ed.]."}],"container-title":["Viruses"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4915\/17\/1\/50\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:57:48Z","timestamp":1760115468000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4915\/17\/1\/50"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,31]]},"references-count":59,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,1]]}},"alternative-id":["v17010050"],"URL":"https:\/\/doi.org\/10.3390\/v17010050","relation":{},"ISSN":["1999-4915"],"issn-type":[{"type":"electronic","value":"1999-4915"}],"subject":[],"published":{"date-parts":[[2024,12,31]]}}}