{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T16:26:13Z","timestamp":1780676773189,"version":"3.54.1"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1011437","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2024,4,26]],"date-time":"2024-04-26T00:00:00Z","timestamp":1714089600000}}],"reference-count":127,"publisher":"Public Library of Science (PLoS)","issue":"4","license":[{"start":{"date-parts":[[2024,4,16]],"date-time":"2024-04-16T00:00:00Z","timestamp":1713225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/publicdomain\/zero\/1.0\/"}],"funder":[{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["89233218CNA000001"],"award-info":[{"award-number":["89233218CNA000001"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000009","name":"Foundation for the National Institutes of Health","doi-asserted-by":"publisher","award":["R01-AI152703 and U54-HL143541"],"award-info":[{"award-number":["R01-AI152703 and U54-HL143541"]}],"id":[{"id":"10.13039\/100000009","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000009","name":"Foundation for the National Institutes of Health","doi-asserted-by":"publisher","award":["R01-AI078881"],"award-info":[{"award-number":["R01-AI078881"]}],"id":[{"id":"10.13039\/100000009","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100008902","name":"Los Alamos National Laboratory","doi-asserted-by":"publisher","award":["20200743ER"],"award-info":[{"award-number":["20200743ER"]}],"id":[{"id":"10.13039\/100008902","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100008902","name":"Los Alamos National Laboratory","doi-asserted-by":"publisher","award":["20200695ER"],"award-info":[{"award-number":["20200695ER"]}],"id":[{"id":"10.13039\/100008902","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Mathematical models of viral infection have been developed, fitted to data, and provide insight into disease pathogenesis for multiple agents that cause chronic infection, including HIV, hepatitis C, and B virus. However, for agents that cause acute infections or during the acute stage of agents that cause chronic infections, viral load data are often collected after symptoms develop, usually around or after the peak viral load. Consequently, we frequently lack data in the initial phase of viral growth, i.e., when pre-symptomatic transmission events occur. Missing data may make estimating the time of infection, the infectious period, and parameters in viral dynamic models, such as the cell infection rate, difficult. However, having extra information, such as the average time to peak viral load, may improve the robustness of the estimation. Here, we evaluated the robustness of estimates of key model parameters when viral load data prior to the viral load peak is missing, when we know the values of some parameters and\/or the time from infection to peak viral load. Although estimates of the time of infection are sensitive to the quality and amount of available data, particularly pre-peak, other parameters important in understanding disease pathogenesis, such as the loss rate of infected cells, are less sensitive. Viral infectivity and the viral production rate are key parameters affecting the robustness of data fits. Fixing their values to literature values can help estimate the remaining model parameters when pre-peak data is missing or limited. We find a lack of data in the pre-peak growth phase underestimates the time to peak viral load by several days, leading to a shorter predicted growth phase. On the other hand, knowing the time of infection (e.g., from epidemiological data) and fixing it results in good estimates of dynamical parameters even in the absence of early data. While we provide ways to approximate model parameters in the absence of early viral load data, our results also suggest that these data, when available, are needed to estimate model parameters more precisely.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1011437","type":"journal-article","created":{"date-parts":[[2024,4,16]],"date-time":"2024-04-16T18:29:05Z","timestamp":1713292145000},"page":"e1011437","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":27,"title":["How robust are estimates of key parameters in standard viral dynamic models?"],"prefix":"10.1371","volume":"20","author":[{"given":"Carolin","family":"Zitzmann","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ruian","family":"Ke","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ruy M.","family":"Ribeiro","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2455-0002","authenticated-orcid":true,"given":"Alan S.","family":"Perelson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2024,4,16]]},"reference":[{"key":"pcbi.1011437.ref001","article-title":"In vivo kinetics of SARS-CoV-2 infection and its relationship with a person\u2019s infectiousness","volume":"118","author":"R Ke","year":"2021","journal-title":"Proc Natl Acad Sci Royal"},{"key":"pcbi.1011437.ref002","doi-asserted-by":"crossref","DOI":"10.7554\/eLife.69302","article-title":"Quantifying the relationship between sars-cov-2 viral load and infectiousness.","volume":"10","author":"A Marc","year":"2021","journal-title":"Elife"},{"key":"pcbi.1011437.ref003","first-page":"465","article-title":"Virological assessment of hospitalized patients with COVID-2019","volume":"581","author":"R W\u00f6lfel","year":"2020","journal-title":"Nature 2020 581:7809."},{"key":"pcbi.1011437.ref004","doi-asserted-by":"crossref","first-page":"775","DOI":"10.1093\/aje\/kwm375","article-title":"Time lines of infection and disease in human influenza: A review of volunteer challenge studies","volume":"167","author":"F Carrat","year":"2008","journal-title":"Am J Epidemiol"},{"key":"pcbi.1011437.ref005","doi-asserted-by":"crossref","first-page":"1420","DOI":"10.1093\/infdis\/jiv225","article-title":"Influenza A virus shedding and infectivity in households","volume":"212","author":"TK Tsang","year":"2015","journal-title":"J Infect Dis"},{"key":"pcbi.1011437.ref006","doi-asserted-by":"crossref","first-page":"e1010797","DOI":"10.1371\/journal.pcbi.1010797","article-title":"Novel modelling approaches to predict the role of antivirals in reducing influenza transmission.","volume":"19","author":"J Asher","year":"2023","journal-title":"PLoS Comput Biol"},{"key":"pcbi.1011437.ref007","doi-asserted-by":"crossref","first-page":"e1008785","DOI":"10.1371\/journal.pcbi.1008785","article-title":"SARS-CoV-2 viral dynamics in non-human primates.","volume":"17","author":"A Gon\u00e7alves","year":"2021","journal-title":"PLoS Comput Biol"},{"key":"pcbi.1011437.ref008","doi-asserted-by":"crossref","first-page":"e1009997","DOI":"10.1371\/journal.pcbi.1009997","article-title":"Modeling within-host and aerosol dynamics of SARS-CoV-2: The relationship with infectiousness.","volume":"18","author":"N Heitzman-Breen","year":"2022","journal-title":"PLoS Comput Biol"},{"key":"pcbi.1011437.ref009","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1001\/jama.2018.21167","article-title":"HIV viral load and transmissibility of HIV infection: Undetectable equals untransmittable","volume":"321","author":"RW Eisinger","year":"2019","journal-title":"JAMA"},{"key":"pcbi.1011437.ref010","doi-asserted-by":"crossref","DOI":"10.1126\/science.1243727","article-title":"Virulence and pathogenesis of HIV-1 infection: an evolutionary perspective","volume":"343","author":"C Fraser","year":"2014","journal-title":"Science"},{"key":"pcbi.1011437.ref011","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1016\/S0140-6736(08)61115-0","article-title":"Relation between HIV viral load and infectiousness: a model-based analysis","volume":"372","author":"DP Wilson","year":"2008","journal-title":"The Lancet"},{"key":"pcbi.1011437.ref012","first-page":"640","article-title":"Daily longitudinal sampling of SARS-CoV-2 infection reveals substantial heterogeneity in infectiousness","volume":"7","author":"R Ke","year":"2022","journal-title":"Nature Microbiology 2022 7:5."},{"key":"pcbi.1011437.ref013","doi-asserted-by":"crossref","first-page":"e3001333","DOI":"10.1371\/journal.pbio.3001333","article-title":"Viral dynamics of acute SARS-CoV-2 infection and applications to diagnostic and public health strategies","volume":"19","author":"SM Kissler","year":"2021","journal-title":"PLoS Biol"},{"key":"pcbi.1011437.ref014","doi-asserted-by":"crossref","first-page":"2489","DOI":"10.1056\/NEJMc2102507","article-title":"Viral dynamics of SARS-CoV-2 variants in vaccinated and unvaccinated persons","volume":"385","author":"SM Kissler","year":"2021","journal-title":"New England Journal of Medicine"},{"key":"pcbi.1011437.ref015","doi-asserted-by":"crossref","article-title":"Trajectory of viral RNA load among persons with incident SARS-CoV-2 G614 infection (wuhan strain) in association with COVID-19 symptom onset and severity.","author":"HC Stankiewicz Karita","DOI":"10.1001\/jamanetworkopen.2021.42796"},{"key":"pcbi.1011437.ref016","doi-asserted-by":"crossref","DOI":"10.1186\/s12916-021-02220-0","article-title":"Modelling upper respiratory viral load dynamics of SARS-CoV-2.","volume":"20","author":"JD Challenger","year":"2022","journal-title":"BMC Med."},{"key":"pcbi.1011437.ref017","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1056\/NEJMoa2108903","article-title":"EDP-938, a respiratory syncytial virus inhibitor, in a human virus challenge","volume":"386","author":"A Ahmad","year":"2022","journal-title":"N Engl J Med"},{"key":"pcbi.1011437.ref018","unstructured":"CDC. Key Facts About Influenza (Flu). Available: https:\/\/www.cdc.gov\/flu\/about\/keyfacts.htm"},{"key":"pcbi.1011437.ref019","doi-asserted-by":"crossref","first-page":"e240","DOI":"10.1371\/journal.pcbi.0030240","article-title":"Neuraminidase inhibitor resistance in influenza: Assessing the danger of its generation and spread.","volume":"3","author":"A Handel","year":"2007","journal-title":"PLoS Comput Biol"},{"key":"pcbi.1011437.ref020","article-title":"Modeling mitigation of influenza epidemics by baloxavir.","volume":"11","author":"Z Du","year":"2020","journal-title":"Nat Commun."},{"key":"pcbi.1011437.ref021","first-page":"2023.05.30.23290747.","article-title":"An explanation for SARS-CoV-2 rebound after Paxlovid treatment.","author":"AS Perelson","year":"2023","journal-title":"medRxiv"},{"key":"pcbi.1011437.ref022","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1002\/psp4.12543","article-title":"Timing of antiviral treatment initiation is critical to reduce SARS-CoV-2 viral load.","volume":"9","author":"A Gon\u00e7alves","year":"2020","journal-title":"CPT Pharmacometrics Syst Pharmacol"},{"key":"pcbi.1011437.ref023","doi-asserted-by":"crossref","DOI":"10.1126\/sciadv.abc7112","article-title":"Potency and timing of antiviral therapy as determinants of duration of SARS-CoV-2 shedding and intensity of inflammatory response.","volume":"6","author":"A Goyal","year":"2020","journal-title":"Sci Adv."},{"key":"pcbi.1011437.ref024","doi-asserted-by":"crossref","first-page":"e3001128","DOI":"10.1371\/journal.pbio.3001128","article-title":"A quantitative model used to compare within-host SARS-CoV-2, MERS-CoV, and SARS-CoV dynamics provides insights into the pathogenesis and treatment of SARS-CoV-2","volume":"19","author":"KS Kim","year":"2021","journal-title":"PLoS Biol"},{"key":"pcbi.1011437.ref025","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":"P Baccam","year":"2006","journal-title":"J Virol"},{"key":"pcbi.1011437.ref026","doi-asserted-by":"crossref","DOI":"10.1016\/S1473-3099(20)30314-5","article-title":"Investigation of a COVID-19 outbreak in Germany resulting from a single travel-associated primary case: a case series","author":"MM B\u00f6hmer","year":"2020"},{"key":"pcbi.1011437.ref027","doi-asserted-by":"crossref","DOI":"10.1098\/rsif.2016.0130","article-title":"Estimating biologically relevant parameters under uncertainty for experimental within-host murine West Nile virus infection.","volume":"13","author":"S Banerjee","year":"2016","journal-title":"J R Soc Interface."},{"key":"pcbi.1011437.ref028","doi-asserted-by":"crossref","first-page":"20140886","DOI":"10.1098\/rsif.2014.0886","article-title":"Minimal within-host dengue models highlight the specific roles of the immune response in primary and secondary dengue infections.","volume":"12","author":"R Ben-Shachar","year":"2014","journal-title":"J R Soc Interface"},{"key":"pcbi.1011437.ref029","doi-asserted-by":"crossref","first-page":"e1005194","DOI":"10.1371\/journal.pcbi.1005194","article-title":"Drivers of inter-individual variation in dengue viral load dynamics.","volume":"12","author":"R Ben-Shachar","year":"2016","journal-title":"PLoS Comput Biol"},{"key":"pcbi.1011437.ref030","doi-asserted-by":"crossref","DOI":"10.1038\/s41467-018-04595-w","article-title":"Transmission-clearance trade-offs indicate that dengue virulence evolution depends on epidemiological context","volume":"9","author":"R Ben-Shachar","year":"2018","journal-title":"Nat Commun"},{"key":"pcbi.1011437.ref031","doi-asserted-by":"crossref","first-page":"504","DOI":"10.1098\/rsif.2014.0094","article-title":"Within-host viral dynamics of dengue serotype 1 infection.","volume":"11","author":"HE Clapham","year":"2014","journal-title":"J R Soc, Interface."},{"key":"pcbi.1011437.ref032","doi-asserted-by":"crossref","first-page":"e1004951","DOI":"10.1371\/journal.pcbi.1004951","article-title":"Modelling virus and antibody dynamics during dengue virus infection suggests a role for antibody in virus clearance.","volume":"12","author":"HE Clapham","year":"2016","journal-title":"PLoS Comput Biol"},{"key":"pcbi.1011437.ref033","doi-asserted-by":"crossref","first-page":"610","DOI":"10.1016\/j.cell.2017.04.008","article-title":"Zika virus persistence in the central nervous system and lymph nodes of rhesus monkeys","volume":"169","author":"M Aid","year":"2017","journal-title":"Cell"},{"key":"pcbi.1011437.ref034","doi-asserted-by":"crossref","first-page":"1448","DOI":"10.1038\/nm.4206","article-title":"Zika viral dynamics and shedding in rhesus and cynomolgus macaques","volume":"22","author":"CE Osuna","year":"2016","journal-title":"Nat Med"},{"key":"pcbi.1011437.ref035","doi-asserted-by":"crossref","first-page":"8847","DOI":"10.1073\/pnas.1704011114","article-title":"Zika plasma viral dynamics in nonhuman primates provides insights into early infection and antiviral strategies","volume":"114","author":"K Best","year":"2017","journal-title":"Proc Natl Acad Sci U S A"},{"key":"pcbi.1011437.ref036","doi-asserted-by":"crossref","first-page":"442","DOI":"10.1093\/jac\/dky415","article-title":"Respiratory syncytial virus-A dynamics and the effects of lumicitabine, a nucleoside viral replication inhibitor, in experimentally infected humans","volume":"74","author":"K Patel","year":"2019","journal-title":"Journal of Antimicrobial Chemotherapy"},{"key":"pcbi.1011437.ref037","doi-asserted-by":"crossref","DOI":"10.1098\/rsif.2019.0389","article-title":"Mathematical modelling identifies the role of adaptive immunity as a key controller of respiratory syncytial virus in cotton rats","volume":"16","author":"D Wethington","year":"2019","journal-title":"J R Soc Interface"},{"key":"pcbi.1011437.ref038","doi-asserted-by":"crossref","first-page":"e1002588","DOI":"10.1371\/journal.pcbi.1002588","article-title":"Modeling within-host dynamics of influenza virus infection including immune responses.","volume":"8","author":"KA Pawelek","year":"2012","journal-title":"PLoS Comput Biol"},{"key":"pcbi.1011437.ref039","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1098\/rsif.2016.0289","article-title":"Understanding the within-host dynamics of influenza A virus: from theory to clinical implications.","volume":"13","author":"C Hadjichrysanthou","year":"2016","journal-title":"J R Soc Interface"},{"key":"pcbi.1011437.ref040","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1111\/imr.12692","article-title":"Host-pathogen kinetics during influenza infection and coinfection: insights from predictive modeling","volume":"285","author":"AM Smith","year":"2018","journal-title":"Immunol Rev"},{"key":"pcbi.1011437.ref041","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":"AM Smith","year":"2011","journal-title":"Wiley Interdiscip Rev Syst Biol Med"},{"key":"pcbi.1011437.ref042","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1093\/ve\/vez018","article-title":"Within-host infectious disease models accommodating cellular coinfection, with an application to influenza \u2020.","volume":"5","author":"K Koelle","year":"2019","journal-title":"Virus Evol"},{"key":"pcbi.1011437.ref043","article-title":"Mechanistic modelling of SARS-CoV-2 and other infectious diseases and the effects of therapeutics","author":"AS Perelson","year":"2021","journal-title":"Clin Pharmacol Ther"},{"key":"pcbi.1011437.ref044","doi-asserted-by":"crossref","first-page":"100454","DOI":"10.1016\/j.epidem.2021.100454","article-title":"Estimation of the incubation period of COVID-19 using viral load data.","volume":"35","author":"K Ejima","year":"2021","journal-title":"Epidemics"},{"key":"pcbi.1011437.ref045","doi-asserted-by":"crossref","first-page":"e2017962118","DOI":"10.1073\/pnas.2017962118","article-title":"Modeling SARS-CoV-2 viral kinetics and association with mortality in hospitalized patients from the French COVID cohort","volume":"118","author":"N N\u00e9ant","year":"2021","journal-title":"Proc Natl Acad Sci U S A"},{"key":"pcbi.1011437.ref046","doi-asserted-by":"crossref","first-page":"e632","DOI":"10.1016\/S2666-5247(23)00139-8","article-title":"Viral and antibody dynamics of acute infection with SARS-CoV-2 omicron variant (B.1.1.529): a prospective cohort study from Shenzhen, China.","volume":"4","author":"Y Yang","year":"2023","journal-title":"Lancet Microbe"},{"key":"pcbi.1011437.ref047","doi-asserted-by":"crossref","first-page":"672","DOI":"10.1038\/s41591-020-0869-5","article-title":"Temporal dynamics in viral shedding and transmissibility of COVID-19","volume":"26","author":"X He","year":"2020","journal-title":"Nat Med"},{"key":"pcbi.1011437.ref048","first-page":"1141","article-title":"Modeling within-host SARS-CoV-2 infection dynamics and potential treatments.","volume":"13","author":"M Sadria","year":"2021","journal-title":"Viruses 2021, Vol 13, Page 1141."},{"key":"pcbi.1011437.ref049","doi-asserted-by":"crossref","first-page":"108438","DOI":"10.1016\/j.mbs.2020.108438","article-title":"Modeling the viral dynamics of SARS-CoV-2 infection","volume":"328","author":"S Wang","year":"2020","journal-title":"Math Biosci"},{"key":"pcbi.1011437.ref050","doi-asserted-by":"crossref","DOI":"10.1016\/j.cmpb.2021.106412","article-title":"Computational simulations to dissect the cell immune response dynamics for severe and critical cases of SARS-CoV-2 infection.","volume":"211","author":"R Blanco-Rodr\u00edguez","year":"2021","journal-title":"Comput Methods Programs Biomed."},{"key":"pcbi.1011437.ref051","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1517\/17425250902787616","article-title":"Modeling HCV kinetics under therapy using PK and PD information.","volume":"5","author":"E Shudo","year":"2009","journal-title":"Expert Opin Drug Metab Toxicol"},{"key":"pcbi.1011437.ref052","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/j.jtbi.2007.03.006","article-title":"Modeling hepatitis C virus dynamics: Liver regeneration and critical drug efficacy","volume":"247","author":"H Dahari","year":"2007","journal-title":"J Theor Biol"},{"key":"pcbi.1011437.ref053","doi-asserted-by":"crossref","first-page":"e1008421","DOI":"10.1371\/journal.pcbi.1008421","article-title":"Mathematical modeling of hepatitis C RNA replication, exosome secretion and virus release.","volume":"16","author":"C Zitzmann","year":"2020","journal-title":"PLoS Comput Biol."},{"key":"pcbi.1011437.ref054","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1517\/17425250902787616","article-title":"Modeling hepatitis C virus kinetics under therapy using pharmacokinetic and pharmacodynamic information.","volume":"5","author":"A Perelson","year":"2009","journal-title":"Expert Opin Drug Metab Toxicol"},{"key":"pcbi.1011437.ref055","doi-asserted-by":"crossref","first-page":"1056","DOI":"10.1053\/j.gastro.2005.01.049","article-title":"Mathematical modeling of primary hepatitis C infection: Noncytolytic clearance and early blockage of virion production","volume":"128","author":"H Dahari","year":"2005","journal-title":"Gastroenterology"},{"key":"pcbi.1011437.ref056","doi-asserted-by":"crossref","first-page":"3991","DOI":"10.1073\/pnas.1203110110","article-title":"Modeling shows that the NS5A inhibitor daclatasvir has two modes of action and yields a shorter estimate of the hepatitis C virus half-life","volume":"110","author":"J Guedj","year":"2013","journal-title":"Proc Natl Acad Sci U S A"},{"key":"pcbi.1011437.ref057","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":"L Rong","year":"2010","journal-title":"Crit Rev Immunol"},{"key":"pcbi.1011437.ref058","doi-asserted-by":"crossref","first-page":"1546","DOI":"10.3389\/fmicb.2018.01546","article-title":"Mathematical analysis of viral replication dynamics and antiviral treatment strategies: From basic models to age-based multi-scale modeling.","author":"C Zitzmann","year":"2018","journal-title":"Front Microbiol. Frontiers"},{"key":"pcbi.1011437.ref059","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1016\/S1286-4579(02)01603-9","article-title":"Dynamics of hepatitis B virus infection","volume":"4","author":"RM Ribeiro","year":"2002","journal-title":"Microbes Infect"},{"key":"pcbi.1011437.ref060","doi-asserted-by":"crossref","first-page":"e1011309","DOI":"10.1371\/journal.pcbi.1011309","article-title":"Modeling suggests that virion production cycles within individual cells is key to understanding acute hepatitis B virus infection kinetics.","volume":"19","author":"A Hailegiorgis","year":"2023","journal-title":"PLoS Comput Biol"},{"key":"pcbi.1011437.ref061","doi-asserted-by":"crossref","first-page":"4398","DOI":"10.1073\/pnas.93.9.4398","article-title":"Viral dynamics in hepatitis B virus infection","volume":"93","author":"MA Nowak","year":"1996","journal-title":"Proc Natl Acad Sci U S A"},{"key":"pcbi.1011437.ref062","doi-asserted-by":"crossref","DOI":"10.3390\/v9110350","article-title":"The role of infected cell proliferation in the clearance of acute HBV infection in humans","volume":"9","author":"A Goyal","year":"2017","journal-title":"Viruses"},{"key":"pcbi.1011437.ref063","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1002\/hep.22586","article-title":"Modeling complex decay profiles of hepatitis B virus during antiviral therapy","volume":"49","author":"H Dahari","year":"2009","journal-title":"Hepatology"},{"key":"pcbi.1011437.ref064","doi-asserted-by":"crossref","first-page":"e1003730","DOI":"10.1371\/journal.pcbi.1003730","article-title":"Antibody responses during hepatitis B viral infection.","volume":"10","author":"SM Ciupe","year":"2014","journal-title":"PLoS Comput Biol"},{"key":"pcbi.1011437.ref065","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.jtbi.2007.02.017","article-title":"Modeling the mechanisms of acute hepatitis B virus infection","volume":"247","author":"SM Ciupe","year":"2007","journal-title":"J Theor Biol"},{"key":"pcbi.1011437.ref066","doi-asserted-by":"crossref","first-page":"5050","DOI":"10.1073\/pnas.0603626104","article-title":"The role of cells refractory to productive infection in acute hepatitis B viral dynamics","volume":"104","author":"SM Ciupe","year":"2007","journal-title":"Proc Natl Acad Sci U S A"},{"key":"pcbi.1011437.ref067","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1038\/387188a0","article-title":"Decay characteristics of HIV-1-infected compartments during combination therapy","volume":"387","author":"AS Perelson","year":"1997","journal-title":"Nature"},{"key":"pcbi.1011437.ref068","first-page":"1232","article-title":"Viral and latent reservoir persistence in HIV-1-infected patients on therapy.","volume":"2","author":"H Kim","year":"2006","journal-title":"PLoS Comput Biol"},{"key":"pcbi.1011437.ref069","first-page":"76","article-title":"HIV-1 dynamics in vivo","volume":"9","author":"DD Ho","year":"1995","journal-title":"J Biol Regul Homeost Agents"},{"key":"pcbi.1011437.ref070","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1177\/135965350400900216","article-title":"Estimates of intracellular delay and average drug efficacy from viral load data of HIV-infected individuals under antiretroviral therapy.","volume":"9","author":"NM Dixit","year":"2004","journal-title":"Antivir Ther."},{"key":"pcbi.1011437.ref071","doi-asserted-by":"crossref","first-page":"e1000533","DOI":"10.1371\/journal.pcbi.1000533","article-title":"Modeling latently infected cell activation: Viral and latent reservoir persistence, and viral blips in HIV-infected patients on potent therapy.","volume":"5","author":"L Rong","year":"2009","journal-title":"PLoS Comput Biol."},{"key":"pcbi.1011437.ref072","doi-asserted-by":"crossref","first-page":"2027","DOI":"10.1007\/s11538-007-9203-3","article-title":"Emergence of HIV-1 drug resistance during antiretroviral treatment.","volume":"69","author":"L Rong","year":"2007","journal-title":"Bull Math Biol."},{"key":"pcbi.1011437.ref073","doi-asserted-by":"crossref","DOI":"10.1371\/journal.ppat.1002881","article-title":"Quantifying the Diversification of Hepatitis C Virus (HCV) during Primary Infection: Estimates of the In Vivo Mutation Rate.","volume":"8","author":"RM Ribeiro","year":"2012","journal-title":"PLoS Pathog"},{"key":"pcbi.1011437.ref074","author":"RM Ribeiro","year":"2004","journal-title":"The analysis of HIV dynamics using mathematical models"},{"key":"pcbi.1011437.ref075","doi-asserted-by":"crossref","DOI":"10.1186\/1741-7007-11-96","article-title":"Modeling the within-host dynamics of HIV infection.","volume":"11","author":"AS Perelson","year":"2013","journal-title":"BMC Biol."},{"key":"pcbi.1011437.ref076","doi-asserted-by":"crossref","first-page":"4647","DOI":"10.1002\/sim.3116","article-title":"Estimating drug efficacy and viral dynamic parameters: HIV and HCV.","volume":"27","author":"AS Perelson","year":"2008","journal-title":"Stat Med"},{"key":"pcbi.1011437.ref077","doi-asserted-by":"crossref","DOI":"10.1136\/bmj-2022-070615","article-title":"Role of mathematical modelling in future pandemic response policy","author":"C Pagel","year":"2022"},{"key":"pcbi.1011437.ref078","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/j.jhin.2023.07.028","article-title":"How have mathematical models contributed to understanding the transmission and control of SARS-CoV-2 in healthcare settings? A systematic search and review","volume":"141","author":"DRM Smith","year":"2023","journal-title":"Journal of Hospital Infection"},{"key":"pcbi.1011437.ref079","author":"J Panovska-Griffiths","year":"2021","journal-title":"Mathematical modeling as a tool for policy decision making: Applications to the COVID-19 pandemic"},{"key":"pcbi.1011437.ref080","doi-asserted-by":"crossref","article-title":"Mathematical models for COVID-19: applications, limitations, and potentials","author":"J. Wang","DOI":"10.21037\/jphe-2020-05"},{"key":"pcbi.1011437.ref081","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1177\/0272989X21990391","article-title":"The use and misuse of mathematical modeling for infectious disease policymaking: Lessons for the COVID-19 pandemic.","volume":"41","author":"LP James","year":"2021","journal-title":"Review Medical Decision Making."},{"key":"pcbi.1011437.ref082","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1371\/journal.pone.0167568","article-title":"Analysis of practical identifiability of a viral infection model.","volume":"11","author":"VK Nguyen","year":"2016","journal-title":"PLoS One."},{"key":"pcbi.1011437.ref083","first-page":"271","article-title":"Why is it difficult to accurately predict the COVID-19 epidemic?","volume":"5","author":"WC Roda","year":"2020","journal-title":"Infect Dis Model."},{"key":"pcbi.1011437.ref084","doi-asserted-by":"crossref","first-page":"5234","DOI":"10.1126\/sciadv.abg5234","article-title":"Lack of practical identifiability may hamper reliable predictions in COVID-19 epidemic models.","volume":"8","author":"L Gallo","year":"2022","journal-title":"Sci Adv."},{"key":"pcbi.1011437.ref085","first-page":"1","article-title":"A review of mathematical models of influenza A infections within a host or cell culture: Lessons learned and challenges ahead","volume":"11","author":"CAA Beauchemin","year":"2011","journal-title":"BMC Public Health"},{"key":"pcbi.1011437.ref086","first-page":"1","article-title":"Identifiability of parameters in mathematical models of SARS-CoV-2 infections in humans.","volume":"12","author":"SM Ciupe","year":"2022","journal-title":"Scientific Reports 2022 12:1."},{"key":"pcbi.1011437.ref087","first-page":"3","article-title":"On identifiability of nonlinear ODE models and applications in viral dynamics","volume":"53","author":"H Miao","year":"2011","journal-title":"SIAM Rev Soc Ind Appl Math"},{"key":"pcbi.1011437.ref088","doi-asserted-by":"crossref","first-page":"430","DOI":"10.1080\/17513758.2021.1970261","article-title":"Determining reliable parameter estimates for within-host and within-vector models of Zika virus.","volume":"15","author":"N Tuncer","year":"2021","journal-title":"J Biol Dyn"},{"key":"pcbi.1011437.ref089","doi-asserted-by":"crossref","DOI":"10.1098\/rsif.2021.0314","article-title":"Timing HIV infection with a simple and accurate population viral dynamics model.","volume":"18","author":"DB Reeves","year":"2021","journal-title":"J R Soc Interface."},{"key":"pcbi.1011437.ref090","doi-asserted-by":"crossref","first-page":"785","DOI":"10.1007\/s11538-007-9279-9","article-title":"Parameter identifiability and estimation of HIV\/AIDS dynamic models","volume":"70","author":"H Wu","year":"2008","journal-title":"Bull Math Biol"},{"key":"pcbi.1011437.ref091","doi-asserted-by":"crossref","first-page":"1199","DOI":"10.1056\/NEJMoa2001316","article-title":"Early transmission dynamics in Wuhan, China, of novel coronavirus\u2013infected pneumonia","volume":"382","author":"Q Li","year":"2020","journal-title":"New England Journal of Medicine"},{"key":"pcbi.1011437.ref092","first-page":"538","article-title":"Incubation period and other epidemiological characteristics of 2019 novel coronavirus infections with right truncation: A Statistical analysis of publicly available case data","volume":"9","author":"NM Linton","year":"2020","journal-title":"Journal of Clinical Medicine 2020, Vol 9, Page 538."},{"key":"pcbi.1011437.ref093","doi-asserted-by":"crossref","first-page":"1708","DOI":"10.1056\/NEJMoa2002032","article-title":"Clinical characteristics of coronavirus disease 2019 in China","volume":"382","author":"W Guan","year":"2020","journal-title":"N Engl J Med"},{"key":"pcbi.1011437.ref094","first-page":"20","article-title":"Incubation period of 2019 novel coronavirus (2019-nCoV) infections among travellers from Wuhan, China.","volume":"25","author":"A Backer Jantien","year":"2020","journal-title":"Euro Surveill"},{"key":"pcbi.1011437.ref095","doi-asserted-by":"crossref","first-page":"911","DOI":"10.1016\/S1473-3099(20)30287-5","article-title":"Epidemiology and transmission of COVID-19 in 391 cases and 1286 of their close contacts in Shenzhen, China: a retrospective cohort study","volume":"20","author":"Q Bi","year":"2020","journal-title":"Lancet Infect Dis"},{"key":"pcbi.1011437.ref096","doi-asserted-by":"crossref","first-page":"577","DOI":"10.7326\/M20-0504","article-title":"The incubation period of coronavirus disease 2019 (CoVID-19) from publicly reported confirmed cases: Estimation and application.","volume":"172","author":"SA Lauer","year":"2020","journal-title":"Ann Intern Med"},{"key":"pcbi.1011437.ref097","article-title":"Challenges in control of COVID-19: short doubling time and long delay to effect of interventions.","author":"J Curran-Sebastian","year":"2021"},{"key":"pcbi.1011437.ref098","article-title":"Epidemiologic characteristics of early cases with 2019 novel coronavirus (2019-nCoV) disease in Korea.","volume":"42","author":"M Ki","year":"2020","journal-title":"Epidemiol Health."},{"key":"pcbi.1011437.ref099","doi-asserted-by":"crossref","first-page":"e201","DOI":"10.1016\/S2589-7500(20)30026-1","article-title":"Early epidemiological analysis of the coronavirus disease 2019 outbreak based on crowdsourced data: a population-level observational study","volume":"2","author":"K Sun","year":"2020","journal-title":"Lancet Digit Health"},{"key":"pcbi.1011437.ref100","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1126\/science.abb4218","article-title":"The effect of human mobility and control measures on the COVID-19 epidemic in China.","volume":"368","author":"MUG Kraemer","year":"2020","journal-title":"Science"},{"key":"pcbi.1011437.ref101","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1002\/jmv.25708","article-title":"Does SARS-CoV-2 has a longer incubation period than SARS and MERS?","volume":"92","author":"X Jiang","year":"2020","journal-title":"J Med Virol"},{"key":"pcbi.1011437.ref102","doi-asserted-by":"crossref","first-page":"113555","DOI":"10.1016\/j.ijheh.2020.113555","article-title":"Estimation of the time-varying reproduction number of COVID-19 outbreak in China.","volume":"228","author":"C You","year":"2020","journal-title":"Int J Hyg Environ Health"},{"key":"pcbi.1011437.ref103","doi-asserted-by":"crossref","first-page":"2027","DOI":"10.1002\/jmv.25975","article-title":"Transmission and clinical characteristics of coronavirus disease 2019 in 104 outside-Wuhan patients, China","volume":"92","author":"C Qiu","year":"2020","journal-title":"J Med Virol"},{"key":"pcbi.1011437.ref104","doi-asserted-by":"crossref","first-page":"1470","DOI":"10.3201\/eid2607.200282","article-title":"High contagiousness and rapid spread of severe acute respiratory syndrome coronavirus 2","volume":"26","author":"S Sanche","year":"2020","journal-title":"Emerg Infect Dis"},{"key":"pcbi.1011437.ref105","first-page":"778","volume-title":"Clinical Microbiology Reviews","author":"CE Samuel","year":"2001"},{"key":"pcbi.1011437.ref106","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/S1359-6101(00)00027-7","article-title":"The virus battles: IFN induction of the antiviral state and mechanisms of viral evasion","volume":"12","author":"DE Levy","year":"2001","journal-title":"Cytokine Growth Factor Rev"},{"key":"pcbi.1011437.ref107","first-page":"879","article-title":"Type 1 interferons and the virus-host relationship: A Lesson in d\u00e9tente","volume":"312","author":"A Garc\u00eda-Sastre","year":"2006","journal-title":"Science (1979)."},{"key":"pcbi.1011437.ref108","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1016\/j.cell.2020.05.042","article-title":"SARS-CoV-2 reverse genetics reveals a variable infection gradient in the respiratory tract","volume":"182","author":"YJ Hou","year":"2020","journal-title":"Cell"},{"key":"pcbi.1011437.ref109","doi-asserted-by":"crossref","first-page":"111491","DOI":"10.1016\/j.jtbi.2023.111491","article-title":"A target-cell limited model can reproduce influenza infection dynamics in hosts with differing immune responses","volume":"567","author":"R Sachak-Patwa","year":"2023","journal-title":"J Theor Biol"},{"key":"pcbi.1011437.ref110","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1098\/rsif.2009.0067","article-title":"Towards a quantitative understanding of the within-host dynamics of influenza A infections.","volume":"7","author":"A Handel","year":"2010","journal-title":"J R Soc Interface"},{"key":"pcbi.1011437.ref111","doi-asserted-by":"crossref","DOI":"10.3389\/fmicb.2018.01554","article-title":"Influenza virus infection model with density dependence supports biphasic viral decay.","volume":"9","author":"AP Smith","year":"2018","journal-title":"Front Microbiol."},{"key":"pcbi.1011437.ref112","doi-asserted-by":"crossref","DOI":"10.1016\/j.jtbi.2023.111449","article-title":"Multiple cohort study of hospitalized SARS-CoV-2 in-host infection dynamics: Parameter estimates, identifiability, sensitivity and the eclipse phase profile","volume":"564","author":"CS Korosec","year":"2023","journal-title":"J Theor Biol"},{"key":"pcbi.1011437.ref113","unstructured":"Package Rsmlx. [cited 13 Nov 2023]. Available: https:\/\/cran.r-project.org\/web\/packages\/Rsmlx\/index.html"},{"key":"pcbi.1011437.ref114","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pone.0162366","article-title":"Driving the model to its limit: Profile likelihood based model reduction","author":"T Maiwald","year":"2016"},{"key":"pcbi.1011437.ref115","doi-asserted-by":"crossref","first-page":"2564","DOI":"10.1111\/febs.12276","article-title":"Profile likelihood in systems biology","author":"C Kreutz","year":"2013","journal-title":"FEBS Journal"},{"key":"pcbi.1011437.ref116","doi-asserted-by":"crossref","first-page":"1923","DOI":"10.1093\/bioinformatics\/btp358","article-title":"Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood","volume":"25","author":"A Raue","year":"2009","journal-title":"Bioinformatics"},{"key":"pcbi.1011437.ref117","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.coisb.2021.03.005","article-title":"On structural and practical identifiability","volume":"25","author":"FG Wieland","year":"2021","journal-title":"Curr Opin Syst Biol"},{"key":"pcbi.1011437.ref118","doi-asserted-by":"crossref","article-title":"Safety, tolerability and viral kinetics during SARS-CoV-2 human challenge in young adults.","author":"B Killingley","DOI":"10.1038\/s41591-022-01780-9"},{"key":"pcbi.1011437.ref119","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1016\/j.ifacol.2015.12.135","article-title":"Identifiability Challenges in Mathematical Models of Viral Infectious Diseases.","volume":"48","author":"VK Nguyen","year":"2015","journal-title":"IFAC-PapersOnLine."},{"key":"pcbi.1011437.ref120","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1016\/j.arcontrol.2020.09.006","article-title":"In-host Mathematical Modelling of COVID-19 in Humans.","volume":"50","author":"EA Hernandez-Vargas","year":"2020","journal-title":"Annu Rev Control."},{"key":"pcbi.1011437.ref121","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1099\/jgv.0.001453","article-title":"SARS-coronavirus-2 replication in Vero E6 cells: replication kinetics, rapid adaptation and cytopathology","volume":"101","author":"NS Ogando","year":"2020","journal-title":"J Gen Virol"},{"key":"pcbi.1011437.ref122","doi-asserted-by":"crossref","first-page":"1","DOI":"10.7554\/eLife.63537","article-title":"Viral load and contact heterogeneity predict sars-cov-2 transmission and super-spreading events.","volume":"10","author":"A Goyal","year":"2021","journal-title":"Elife"},{"key":"pcbi.1011437.ref123","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1002\/psp4.12005","article-title":"Modeling suggests a mechanism of synergy between hepatitis C virus entry inhibitors and drugs of other classes.","volume":"4","author":"P Padmanabhan","year":"2015","journal-title":"CPT Pharmacometrics Syst Pharmacol"},{"key":"pcbi.1011437.ref124","article-title":"Testing structural identifiability by a simple scaling method","author":"M Castroid","year":"2020"},{"key":"pcbi.1011437.ref125","first-page":"87","article-title":"Type I interferons in infectious disease.","volume-title":"Nature Reviews Immunology","author":"F McNab","year":"2015"},{"key":"pcbi.1011437.ref126","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1002\/biof.6","article-title":"Interferons and viral infections","volume":"35","author":"V Fensterl","year":"2009","journal-title":"BioFactors"},{"key":"pcbi.1011437.ref127","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1006\/jtbi.2000.1076","article-title":"Modeling plasma virus concentration during primary HIV infection","volume":"203","author":"MA Stafford","year":"2000","journal-title":"J Theor Biol"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1011437","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2024,4,26]],"date-time":"2024-04-26T00:00:00Z","timestamp":1714089600000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1011437","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,26]],"date-time":"2024-04-26T17:44:07Z","timestamp":1714153447000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1011437"}},"subtitle":[],"editor":[{"given":"Roger Dimitri","family":"Kouyos","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2024,4,16]]},"references-count":127,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,4,16]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1011437","relation":{"new_version":[{"id-type":"doi","id":"10.1371\/journal.pcbi.1011437","asserted-by":"object"}]},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4,16]]}}}