Skip to main content
Top
Published in: BMC Public Health 1/2011

Open Access 01-12-2011 | Review

A review of mathematical models of influenza A infections within a host or cell culture: lessons learned and challenges ahead

Authors: Catherine AA Beauchemin, Andreas Handel

Published in: BMC Public Health | Special Issue 1/2011

Login to get access

Abstract

Most mathematical models used to study the dynamics of influenza A have thus far focused on the between-host population level, with the aim to inform public health decisions regarding issues such as drug and social distancing intervention strategies, antiviral stockpiling or vaccine distribution. Here, we investigate mathematical modeling of influenza infection spread at a different scale; namely that occurring within an individual host or a cell culture. We review the models that have been developed in the last decades and discuss their contributions to our understanding of the dynamics of influenza infections. We review kinetic parameters (e.g., viral clearance rate, lifespan of infected cells) and values obtained through fitting mathematical models, and contrast them with values obtained directly from experiments. We explore the symbiotic role of mathematical models and experimental assays in improving our quantitative understanding of influenza infection dynamics. We also discuss the challenges in developing better, more comprehensive models for the course of influenza infections within a host or cell culture. Finally, we explain the contributions of such modeling efforts to important public health issues, and suggest future modeling studies that can help to address additional questions relevant to public health.
Literature
1.
go back to reference Nicholson KG, Wood JM, Zambon M: Influenza. The Lancet. 2003, 362: 1733-1745. 10.1016/S0140-6736(03)14854-4. Nicholson KG, Wood JM, Zambon M: Influenza. The Lancet. 2003, 362: 1733-1745. 10.1016/S0140-6736(03)14854-4.
3.
go back to reference Cheung TKW, Poon LLM: Biology of influenza A virus. Ann. N.Y. Acad. Sci. 2007, 1102: 1-25. 10.1196/annals.1408.001.PubMed Cheung TKW, Poon LLM: Biology of influenza A virus. Ann. N.Y. Acad. Sci. 2007, 1102: 1-25. 10.1196/annals.1408.001.PubMed
5.
go back to reference van Riel D, Munster VJ, de Wit E, Rimmelzwaan GF, Fouchier RA, Osterhaus AD, Kuiken T: H5N1 virus attachment to lower respiratory tract. Science. 2006, 312 (5772): 399-10.1126/science.1125548. Originally published in Science Express on 23 March 2006PubMed van Riel D, Munster VJ, de Wit E, Rimmelzwaan GF, Fouchier RA, Osterhaus AD, Kuiken T: H5N1 virus attachment to lower respiratory tract. Science. 2006, 312 (5772): 399-10.1126/science.1125548. Originally published in Science Express on 23 March 2006PubMed
6.
go back to reference Nicholls J, Chan M, Chan W, Wong H, Cheung C, Kwong D, Wong M, Chui W, Poon LLM, Tsao S, Guan Y, Peiris J: Tropism of avian influenza A H5N1 in the upper and lower respiratory tract. Nature Medicine. 2007, 13 (2): 147-149. 10.1038/nm1529.PubMed Nicholls J, Chan M, Chan W, Wong H, Cheung C, Kwong D, Wong M, Chui W, Poon LLM, Tsao S, Guan Y, Peiris J: Tropism of avian influenza A H5N1 in the upper and lower respiratory tract. Nature Medicine. 2007, 13 (2): 147-149. 10.1038/nm1529.PubMed
7.
go back to reference Potter CW: Influenza. Principles and Practice of Clinical Virology. Edited by: Zuckerman AJ, Banatvala JE, Pattison JR, Griffiths PD, Schoub BD, John Wiley & Sons, Ltd. 2004, 271-297. full_text. 5th Potter CW: Influenza. Principles and Practice of Clinical Virology. Edited by: Zuckerman AJ, Banatvala JE, Pattison JR, Griffiths PD, Schoub BD, John Wiley & Sons, Ltd. 2004, 271-297. full_text. 5th
8.
go back to reference Patton JS: Mechanisms of macromolecule absorption by the lungs. Adv. Drug Deliver. Rev. 1996, 19: 3-36. 10.1016/0169-409X(95)00113-L. Patton JS: Mechanisms of macromolecule absorption by the lungs. Adv. Drug Deliver. Rev. 1996, 19: 3-36. 10.1016/0169-409X(95)00113-L.
9.
go back to reference Matrosovich MN, Matrosovich TY, Gray T, Roberts NA, Klenk HD: Human and avian influenza viruses target different cell types in cultures of human airway epithelium. P. Natl. Acad. Sci. USA. 2004, 101 (13): 4620-4624. 10.1073/pnas.0308001101. Matrosovich MN, Matrosovich TY, Gray T, Roberts NA, Klenk HD: Human and avian influenza viruses target different cell types in cultures of human airway epithelium. P. Natl. Acad. Sci. USA. 2004, 101 (13): 4620-4624. 10.1073/pnas.0308001101.
10.
go back to reference Matrosovich MN, Matrosovich TY, Uhlendorff J, Garten W, Klenk HD: Avian-virus-like receptor specificity of the hemagglutinin impedes influenza virus replication in cultures of human airway epithelium. Virology. 2007, 361 (2): 384-390. 10.1016/j.virol.2006.11.030.PubMed Matrosovich MN, Matrosovich TY, Uhlendorff J, Garten W, Klenk HD: Avian-virus-like receptor specificity of the hemagglutinin impedes influenza virus replication in cultures of human airway epithelium. Virology. 2007, 361 (2): 384-390. 10.1016/j.virol.2006.11.030.PubMed
11.
go back to reference Shinya K, Ebina M, Yamada S, Ono M, Kasai N, Kawaoka Y: Influenza virus receptors in the human airway. Nature. 2006, 440 (7083): 435-436. 10.1038/440435a.PubMed Shinya K, Ebina M, Yamada S, Ono M, Kasai N, Kawaoka Y: Influenza virus receptors in the human airway. Nature. 2006, 440 (7083): 435-436. 10.1038/440435a.PubMed
13.
go back to reference Mora R, Rodriguez-Boulan E, Palese P, Garía-Sastre A: Apical budding of a recombinant influenza A virus expressing a hemagglutinin protein with a basolateral localization signal. J. Virol. 2002, 76 (7): 3544-3553. 10.1128/JVI.76.7.3544-3553.2002.PubMedCentralPubMed Mora R, Rodriguez-Boulan E, Palese P, Garía-Sastre A: Apical budding of a recombinant influenza A virus expressing a hemagglutinin protein with a basolateral localization signal. J. Virol. 2002, 76 (7): 3544-3553. 10.1128/JVI.76.7.3544-3553.2002.PubMedCentralPubMed
14.
go back to reference Tamura S, Kurata T: Defense mechanisms against influenza virus infection in the respiratory tract mucosa. Jpn. J. Infect. Dis. 2004, 57 (6): 236-247.PubMed Tamura S, Kurata T: Defense mechanisms against influenza virus infection in the respiratory tract mucosa. Jpn. J. Infect. Dis. 2004, 57 (6): 236-247.PubMed
15.
go back to reference Baccam P, Beauchemin C, Macken CA, Hayden FG, Perelson AS: Kinetics of influenza A virus infection in humans. J. Virol. 2006, 80 (15): 7590-7599. 10.1128/JVI.01623-05.PubMedCentralPubMed Baccam P, Beauchemin C, Macken CA, Hayden FG, Perelson AS: Kinetics of influenza A virus infection in humans. J. Virol. 2006, 80 (15): 7590-7599. 10.1128/JVI.01623-05.PubMedCentralPubMed
16.
go back to reference Basler CF, Aguilar PV: Progress in identifying virulence determinants of the 1918 H1N1 and the Southeast Asian H5N1 influenza A viruses. Antiviral Res. 2008, 79 (3): 166-178. 10.1016/j.antiviral.2008.04.006.PubMedCentralPubMed Basler CF, Aguilar PV: Progress in identifying virulence determinants of the 1918 H1N1 and the Southeast Asian H5N1 influenza A viruses. Antiviral Res. 2008, 79 (3): 166-178. 10.1016/j.antiviral.2008.04.006.PubMedCentralPubMed
17.
go back to reference Guarner J, Falcón-Escobedo R: Comparison of the pathology caused by H1N1, H5N1, and H3N2 influenza viruses. Arch Med Res. 2009, 40 (8): 655-661. 10.1016/j.arcmed.2009.10.001.PubMed Guarner J, Falcón-Escobedo R: Comparison of the pathology caused by H1N1, H5N1, and H3N2 influenza viruses. Arch Med Res. 2009, 40 (8): 655-661. 10.1016/j.arcmed.2009.10.001.PubMed
18.
go back to reference Ferguson NM, Cummings DAT, Fraser C, Cajka JC, Cooley PC, Burke DS: Strategies for mitigating an influenza pandemic. Nature. 2006, 442 (7101): 448-452. 10.1038/nature04795.PubMed Ferguson NM, Cummings DAT, Fraser C, Cajka JC, Cooley PC, Burke DS: Strategies for mitigating an influenza pandemic. Nature. 2006, 442 (7101): 448-452. 10.1038/nature04795.PubMed
19.
go back to reference Germann TC, Kadau K, Longini IM, Macken CA: Mitigation strategies for pandemic influenza in the United States. Proc. Natl. Acad. Sci. U.S.A. 2006, 103 (15): 5935-5940. 10.1073/pnas.0601266103.PubMedCentralPubMed Germann TC, Kadau K, Longini IM, Macken CA: Mitigation strategies for pandemic influenza in the United States. Proc. Natl. Acad. Sci. U.S.A. 2006, 103 (15): 5935-5940. 10.1073/pnas.0601266103.PubMedCentralPubMed
20.
go back to reference Halloran ME, Ferguson NM, Eubank S, Longini IM, Cummings DAT, Lewis B, Xu S, Fraser C, Vullikanti A, Germann TC, Wagener D, Beckman R, Kadau K, Barrett C, Macken CA, Burke DS, Cooley P: Modeling targeted layered containment of an influenza pandemic in the United States. Proc. Natl. Acad. Sci. U.S.A. 2008, 105 (12): 4639-4644. 10.1073/pnas.0706849105.PubMedCentralPubMed Halloran ME, Ferguson NM, Eubank S, Longini IM, Cummings DAT, Lewis B, Xu S, Fraser C, Vullikanti A, Germann TC, Wagener D, Beckman R, Kadau K, Barrett C, Macken CA, Burke DS, Cooley P: Modeling targeted layered containment of an influenza pandemic in the United States. Proc. Natl. Acad. Sci. U.S.A. 2008, 105 (12): 4639-4644. 10.1073/pnas.0706849105.PubMedCentralPubMed
21.
go back to reference McVernon J, McCaw CT, Mathews JD: Model answers or trivial pursuits? The role of mathematical models in influenza pandemic preparedness planning. Influenza Other Respi Viruses. 2007, 1 (2): 43-54. 10.1111/j.1750-2659.2007.00008.x. McVernon J, McCaw CT, Mathews JD: Model answers or trivial pursuits? The role of mathematical models in influenza pandemic preparedness planning. Influenza Other Respi Viruses. 2007, 1 (2): 43-54. 10.1111/j.1750-2659.2007.00008.x.
22.
go back to reference Hatchett RJ, Mecher CE, Lipsitch M: Public health interventions and epidemic intensity during the 1918 influenza pandemic. Proc. Natl. Acad. Sci. U.S.A. 2007, 104 (18): 7582-7587. 10.1073/pnas.0610941104.PubMedCentralPubMed Hatchett RJ, Mecher CE, Lipsitch M: Public health interventions and epidemic intensity during the 1918 influenza pandemic. Proc. Natl. Acad. Sci. U.S.A. 2007, 104 (18): 7582-7587. 10.1073/pnas.0610941104.PubMedCentralPubMed
23.
go back to reference Kim SY, Goldie SJ: Cost-effectiveness analyses of vaccination programmes: A focused review of modelling approaches. Pharmacoeconomics. 2008, 26 (3): 191-215. 10.2165/00019053-200826030-00004.PubMed Kim SY, Goldie SJ: Cost-effectiveness analyses of vaccination programmes: A focused review of modelling approaches. Pharmacoeconomics. 2008, 26 (3): 191-215. 10.2165/00019053-200826030-00004.PubMed
24.
go back to reference Wu JT, Leung GM, Lipsitch M, Cooper BS, Riley S: Hedging against antiviral resistance during the next influenza pandemic using small stockpiles of an alternative chemotherapy. PLoS Med. 2009, 6 (5): e1000085-10.1371/journal.pmed.1000085.PubMedCentralPubMed Wu JT, Leung GM, Lipsitch M, Cooper BS, Riley S: Hedging against antiviral resistance during the next influenza pandemic using small stockpiles of an alternative chemotherapy. PLoS Med. 2009, 6 (5): e1000085-10.1371/journal.pmed.1000085.PubMedCentralPubMed
25.
go back to reference Coburn BJ, Wagner BG, Blower S: Modeling influenza epidemics and pandemics: Insights into the future of swine flu (H1N1). BMC Med. 2009, 7: 30-10.1186/1741-7015-7-30.PubMedCentralPubMed Coburn BJ, Wagner BG, Blower S: Modeling influenza epidemics and pandemics: Insights into the future of swine flu (H1N1). BMC Med. 2009, 7: 30-10.1186/1741-7015-7-30.PubMedCentralPubMed
26.
go back to reference Kerkhove MDV, Asikainen T, Becker NG, Bjorge S, Desenclos JC, dos Santos T, Fraser C, Leung GM, Lipsitch M, Longini IM, McBryde ES, Roth CE, Shay DK, Smith DJ, Wallinga J, White PJ, Ferguson NM, Riley S, W H O Informal Network for Mathematical Modelling for Pandemic Influenza H1N1 2009 (WorkingGroup on Data Needs): Studies needed to address public health challenges of the 2009 H1N1 influenza pandemic: insights from modeling. PLoS Med. 2010, 7 (6): e1000275-10.1371/journal.pmed.1000275.PubMedCentralPubMed Kerkhove MDV, Asikainen T, Becker NG, Bjorge S, Desenclos JC, dos Santos T, Fraser C, Leung GM, Lipsitch M, Longini IM, McBryde ES, Roth CE, Shay DK, Smith DJ, Wallinga J, White PJ, Ferguson NM, Riley S, W H O Informal Network for Mathematical Modelling for Pandemic Influenza H1N1 2009 (WorkingGroup on Data Needs): Studies needed to address public health challenges of the 2009 H1N1 influenza pandemic: insights from modeling. PLoS Med. 2010, 7 (6): e1000275-10.1371/journal.pmed.1000275.PubMedCentralPubMed
27.
go back to reference Smith AM, Ribeiro RM: Modeling the viral dynamics of influenza A virus infection. Crit. Rev. Immunol. 2010, 30 (3): 291-298.PubMed Smith AM, Ribeiro RM: Modeling the viral dynamics of influenza A virus infection. Crit. Rev. Immunol. 2010, 30 (3): 291-298.PubMed
28.
go back to reference Lloyd AL: The dependence of viral parameter estimates on the assumed viral life cycle: Limitations of studies of viral load data. Proc Biol Sci. 2001, 268 (1469): 847-854. 10.1098/rspb.2000.1572.PubMedCentralPubMed Lloyd AL: The dependence of viral parameter estimates on the assumed viral life cycle: Limitations of studies of viral load data. Proc Biol Sci. 2001, 268 (1469): 847-854. 10.1098/rspb.2000.1572.PubMedCentralPubMed
29.
go back to reference Wearing HJ, Rohani P, Keeling MJ: Appropriate models for the management of infectious diseases. PLoS Med. 2005, 2 (7): e174-10.1371/journal.pmed.0020174.PubMedCentralPubMed Wearing HJ, Rohani P, Keeling MJ: Appropriate models for the management of infectious diseases. PLoS Med. 2005, 2 (7): e174-10.1371/journal.pmed.0020174.PubMedCentralPubMed
30.
go back to reference Holder BP, Beauchemin CAA: Exploring the effect of implementing different biological delays in constructing kinetic models of influenza infection within a host or cell culture. BMC Public Health. 2011, 11 ((Suppl 1)): S10-10.1186/1471-2458-11-S1-S10. submittedPubMedCentralPubMed Holder BP, Beauchemin CAA: Exploring the effect of implementing different biological delays in constructing kinetic models of influenza infection within a host or cell culture. BMC Public Health. 2011, 11 ((Suppl 1)): S10-10.1186/1471-2458-11-S1-S10. submittedPubMedCentralPubMed
31.
go back to reference Miao H, Hollenbaugh JA, Zand MS, Holden-Wiltse J, Mosmann TR, Perelson AS, Wu H, Topham DJ: Quantifying the early immune response and adaptive immune response kinetics in mice infected with influenza A virus. J. Virol. 2010, 84 (13): 6687-6698. 10.1128/JVI.00266-10.PubMedCentralPubMed Miao H, Hollenbaugh JA, Zand MS, Holden-Wiltse J, Mosmann TR, Perelson AS, Wu H, Topham DJ: Quantifying the early immune response and adaptive immune response kinetics in mice infected with influenza A virus. J. Virol. 2010, 84 (13): 6687-6698. 10.1128/JVI.00266-10.PubMedCentralPubMed
32.
go back to reference Doherty PC, Turner SJ, Webby RG, Thomas PG: Influenza and the challenge for immunology. Nature Immunol. 2006, 7 (5): 449-455. 10.1038/ni1343. Doherty PC, Turner SJ, Webby RG, Thomas PG: Influenza and the challenge for immunology. Nature Immunol. 2006, 7 (5): 449-455. 10.1038/ni1343.
33.
go back to reference Larson E, Dominik J, Rowberg A, Higbee G: Influenza virus population dynamics in the respiratory tract of experimentally infected mice. Infect. Immun. 1976, 13 (2): 438-447.PubMedCentralPubMed Larson E, Dominik J, Rowberg A, Higbee G: Influenza virus population dynamics in the respiratory tract of experimentally infected mice. Infect. Immun. 1976, 13 (2): 438-447.PubMedCentralPubMed
34.
go back to reference Perelson AS, Neumann A, Markowitz M, Leonard J, Ho D: HIV-1 dynamics in vivo: Virion clearance rate, infected cell life-span, and viral generation time. Science. 1996, 271 (5255): 1582-1586. 10.1126/science.271.5255.1582.PubMed Perelson AS, Neumann A, Markowitz M, Leonard J, Ho D: HIV-1 dynamics in vivo: Virion clearance rate, infected cell life-span, and viral generation time. Science. 1996, 271 (5255): 1582-1586. 10.1126/science.271.5255.1582.PubMed
35.
go back to reference Perelson AS, Essunger P, Cao Y, Vesanen M, Hurley A, Saksela K, Markowitz M, Ho DD: Decay characteristics of HIV-1 infected compartments during combination therapy. Nature. 1997, 387 (6629): 188-191. 10.1038/387188a0.PubMed Perelson AS, Essunger P, Cao Y, Vesanen M, Hurley A, Saksela K, Markowitz M, Ho DD: Decay characteristics of HIV-1 infected compartments during combination therapy. Nature. 1997, 387 (6629): 188-191. 10.1038/387188a0.PubMed
36.
go back to reference Ribeiro RM, Layden-Almer J, Powers KA, Layden TJ, Perelson AS: Dynamics of alanine aminotransferase during hepatitis C virus treatment. Hepatology. 2003, 38 (2): 509-517. 10.1053/jhep.2003.50344.PubMed Ribeiro RM, Layden-Almer J, Powers KA, Layden TJ, Perelson AS: Dynamics of alanine aminotransferase during hepatitis C virus treatment. Hepatology. 2003, 38 (2): 509-517. 10.1053/jhep.2003.50344.PubMed
37.
go back to reference Neumann AU, Lam NP, Dahari H, Gretch DR, Wiley TE, Layden TJ, Perelson AS: Hepatitis C viral dynamics in vivo and the antiviral efficacy of interferon-alpha therapy. Science. 1998, 282 (5386): 103-107. 10.1126/science.282.5386.103.PubMed Neumann AU, Lam NP, Dahari H, Gretch DR, Wiley TE, Layden TJ, Perelson AS: Hepatitis C viral dynamics in vivo and the antiviral efficacy of interferon-alpha therapy. Science. 1998, 282 (5386): 103-107. 10.1126/science.282.5386.103.PubMed
38.
go back to reference Neumann AU, Lam NP, Dahari H, Davidian M, Wiley TE, Mika BP, Perelson AS, Layden TJ: Differences in viral dynamics between genotypes 1 and 2 of hepatitis C virus. J. Infect. Dis. 2000, 182: 28-35. 10.1086/315661.PubMed Neumann AU, Lam NP, Dahari H, Davidian M, Wiley TE, Mika BP, Perelson AS, Layden TJ: Differences in viral dynamics between genotypes 1 and 2 of hepatitis C virus. J. Infect. Dis. 2000, 182: 28-35. 10.1086/315661.PubMed
39.
go back to reference Handel A, Longini IM, Antia R: Neuraminidase inhibitor resistance in influenza: Assessing the danger of its generation and spread. PLoS Comput. Biol. 2007, 3 (12): e240-10.1371/journal.pcbi.0030240.PubMedCentralPubMed Handel A, Longini IM, Antia R: Neuraminidase inhibitor resistance in influenza: Assessing the danger of its generation and spread. PLoS Comput. Biol. 2007, 3 (12): e240-10.1371/journal.pcbi.0030240.PubMedCentralPubMed
40.
go back to reference Dobrovolny HM, Gieschke R, Davies BE, Jumbe NL, Beauchemin CA: Neuraminidase inhibitors for treatment of human and avian strain influenza: A comparative study. J. Theor. Biol. 2011, 269 (1): 234-244. 10.1016/j.jtbi.2010.10.017. submittedPubMed Dobrovolny HM, Gieschke R, Davies BE, Jumbe NL, Beauchemin CA: Neuraminidase inhibitors for treatment of human and avian strain influenza: A comparative study. J. Theor. Biol. 2011, 269 (1): 234-244. 10.1016/j.jtbi.2010.10.017. submittedPubMed
41.
go back to reference Baron MJ, Dobrovolny HM, Gieschke R, Davies BE, Jumbe NL, Beauchemin CA: Exploring cell tropism as a possible contributor to influenza infection severity. PLoS ONE. 2010, 5 (11): e13811-10.1371/journal.pone.0013811. submittedPubMedCentralPubMed Baron MJ, Dobrovolny HM, Gieschke R, Davies BE, Jumbe NL, Beauchemin CA: Exploring cell tropism as a possible contributor to influenza infection severity. PLoS ONE. 2010, 5 (11): e13811-10.1371/journal.pone.0013811. submittedPubMedCentralPubMed
42.
go back to reference Möhler L, Flockerzi D, Sann H, Reichl U: Mathematical model of influenza A virus production in large-scale microcarrier culture. Biotechnol. Bioeng. 2005, 90: 46-58. 10.1002/bit.20363.PubMed Möhler L, Flockerzi D, Sann H, Reichl U: Mathematical model of influenza A virus production in large-scale microcarrier culture. Biotechnol. Bioeng. 2005, 90: 46-58. 10.1002/bit.20363.PubMed
43.
go back to reference Sidorenko Y, Voigt A, Schulze-Horsel J, Reichl U, Kienle A: Stochastic population balance modeling of influenza virus replication in vaccine production processes. II. Detailed description of the replication mechanism. Chem. Eng. Sci. 2008, 63 (8): 2299-2304. 10.1016/j.ces.2007.12.034. Sidorenko Y, Voigt A, Schulze-Horsel J, Reichl U, Kienle A: Stochastic population balance modeling of influenza virus replication in vaccine production processes. II. Detailed description of the replication mechanism. Chem. Eng. Sci. 2008, 63 (8): 2299-2304. 10.1016/j.ces.2007.12.034.
44.
go back to reference Sidorenko Y, Schulze-Horsel J, Voigt A, Reichl U, Kienle A: Stochastic population balance modeling of influenza virus replication in vaccine production processes. Chem. Eng. Sci. 2008, 63: 157-169. 10.1016/j.ces.2007.09.014. Sidorenko Y, Schulze-Horsel J, Voigt A, Reichl U, Kienle A: Stochastic population balance modeling of influenza virus replication in vaccine production processes. Chem. Eng. Sci. 2008, 63: 157-169. 10.1016/j.ces.2007.09.014.
45.
go back to reference Schulze-Horsel J, Schulze M, Agalaridis G, Genzel Y, Reichl U: Infection dynamics and virus-induced apoptosis in cell culture-based influenza vaccine production — Flow cytometry and mathematical modeling. Vaccine. 2009, 27 (20): 2712-2722. 10.1016/j.vaccine.2009.02.027.PubMed Schulze-Horsel J, Schulze M, Agalaridis G, Genzel Y, Reichl U: Infection dynamics and virus-induced apoptosis in cell culture-based influenza vaccine production — Flow cytometry and mathematical modeling. Vaccine. 2009, 27 (20): 2712-2722. 10.1016/j.vaccine.2009.02.027.PubMed
46.
go back to reference Sidorenko Y, Reichl U: Structured model of influenza virus replication in MDCK cells. Biotechnol Bioeng. 2004, 88: 1-14. 10.1002/bit.20096.PubMed Sidorenko Y, Reichl U: Structured model of influenza virus replication in MDCK cells. Biotechnol Bioeng. 2004, 88: 1-14. 10.1002/bit.20096.PubMed
47.
go back to reference Beauchemin CA, McSharry JJ, Drusano GL, Nguyen JT, Went GT, Ribeiro RM, Perelson AS: Modeling amantadine treatment of influenza A virus in vitro. J. Theor. Biol. 2008, 254 (2): 439-451. 10.1016/j.jtbi.2008.05.031.PubMedCentralPubMed Beauchemin CA, McSharry JJ, Drusano GL, Nguyen JT, Went GT, Ribeiro RM, Perelson AS: Modeling amantadine treatment of influenza A virus in vitro. J. Theor. Biol. 2008, 254 (2): 439-451. 10.1016/j.jtbi.2008.05.031.PubMedCentralPubMed
48.
go back to reference Holder BP, Simon P, Liao LE, Abed Y, Bouhy X, Beauchemin CAA, Boivin G: Assessing fitness of an oseltamivir-resistant seasonal A/H1N1 influenza strain using a mathematical model. PLoS ONE. 2011, accepted Holder BP, Simon P, Liao LE, Abed Y, Bouhy X, Beauchemin CAA, Boivin G: Assessing fitness of an oseltamivir-resistant seasonal A/H1N1 influenza strain using a mathematical model. PLoS ONE. 2011, accepted
49.
go back to reference Holder BP, Liao LE, Simon P, Boivin G, Beauchemin CAA: Design considerations in building in silico equivalents of common experimental influenza virus assays and the benefits of such an approach. Autoimmunity. 2011, 44 (4): 10.3109/08916934.2011.523267. in press Holder BP, Liao LE, Simon P, Boivin G, Beauchemin CAA: Design considerations in building in silico equivalents of common experimental influenza virus assays and the benefits of such an approach. Autoimmunity. 2011, 44 (4): 10.3109/08916934.2011.523267. in press
50.
go back to reference Francis T, Stuart-Harris CH: Studies on the nasal histology of epidemic influenza virus infection in the ferret I. The development and repair of the nasal lesion. J. Exp. Med. 1938, 68 (6): 789-U7. 10.1084/jem.68.6.789.PubMedCentralPubMed Francis T, Stuart-Harris CH: Studies on the nasal histology of epidemic influenza virus infection in the ferret I. The development and repair of the nasal lesion. J. Exp. Med. 1938, 68 (6): 789-U7. 10.1084/jem.68.6.789.PubMedCentralPubMed
51.
go back to reference Stuart-Harris CH: Maxwell Finland lecture: The influenza viruses and the human respiratory tract. Rev Infect Dis. 1979, 1 (4): 592-599. 10.1093/clinids/1.4.592.PubMed Stuart-Harris CH: Maxwell Finland lecture: The influenza viruses and the human respiratory tract. Rev Infect Dis. 1979, 1 (4): 592-599. 10.1093/clinids/1.4.592.PubMed
52.
go back to reference Rocha E, Cox NJ, Black RA, Harmon MW, Harrison CJ, Kendal AP: Antigenic and genetic variation in influenza A (H1N1) virus isolates recovered from a persistently infected immunodeficient child. J. Virol. 1991, 65 (5): 2340-2350.PubMedCentralPubMed Rocha E, Cox NJ, Black RA, Harmon MW, Harrison CJ, Kendal AP: Antigenic and genetic variation in influenza A (H1N1) virus isolates recovered from a persistently infected immunodeficient child. J. Virol. 1991, 65 (5): 2340-2350.PubMedCentralPubMed
53.
go back to reference Boivin G, Goyette N, Bernatchez H: Prolonged excretion of amantadine-resistant influenza A virus quasi species after cessation of antiviral therapy in an immunocompromised patient. Clin. Infect. Dis. 2002, 34 (5): E23-E25. 10.1086/338870.PubMed Boivin G, Goyette N, Bernatchez H: Prolonged excretion of amantadine-resistant influenza A virus quasi species after cessation of antiviral therapy in an immunocompromised patient. Clin. Infect. Dis. 2002, 34 (5): E23-E25. 10.1086/338870.PubMed
54.
go back to reference Weinstock DM, Gubareva LV, Zuccotti G: Prolonged shedding of multidrug-resistant influenza A virus in an immunocompromised patient. N. Engl. J. Med. 2003, 348 (9): 867-868. 10.1056/NEJM200302273480923.PubMed Weinstock DM, Gubareva LV, Zuccotti G: Prolonged shedding of multidrug-resistant influenza A virus in an immunocompromised patient. N. Engl. J. Med. 2003, 348 (9): 867-868. 10.1056/NEJM200302273480923.PubMed
55.
go back to reference Klimov AI, Rocha E, Hayden FG, Shult PA, Roumillat LF, Cox NJ: Prolonged shedding of amantadine-resistant influenzae A viruses by immunodeficient patients: detection by polymerase chain reaction-restriction analysis. J. Infect. Dis. 1995, 172 (5): 1352-1355. 10.1093/infdis/172.5.1352.PubMed Klimov AI, Rocha E, Hayden FG, Shult PA, Roumillat LF, Cox NJ: Prolonged shedding of amantadine-resistant influenzae A viruses by immunodeficient patients: detection by polymerase chain reaction-restriction analysis. J. Infect. Dis. 1995, 172 (5): 1352-1355. 10.1093/infdis/172.5.1352.PubMed
56.
go back to reference Glies C, Shuttleworth EM: Postmortem findings in 46 influenza deaths. Lancet. 1957, 273 (7007): 1224-1225. 10.1016/S0140-6736(57)90180-0. Glies C, Shuttleworth EM: Postmortem findings in 46 influenza deaths. Lancet. 1957, 273 (7007): 1224-1225. 10.1016/S0140-6736(57)90180-0.
57.
go back to reference Hers JF, Masurel N, Mulder J: Bacteriology and histopathology of the respiratory tract and lungs in fatal Asian influenza. Lancet. 1958, 2 (7057): 1141-1143. 10.1016/S0140-6736(58)92404-8.PubMed Hers JF, Masurel N, Mulder J: Bacteriology and histopathology of the respiratory tract and lungs in fatal Asian influenza. Lancet. 1958, 2 (7057): 1141-1143. 10.1016/S0140-6736(58)92404-8.PubMed
58.
go back to reference Tran TH, Nguyen TL, Nguyen TD, Luong TS, Pham PM, van Vinh Chau Nguyen, Pham TS, Vo CD, Le TQM, Ngo TT, Dao BK, Le PP, Nguyen TT, Hoang TL, Cao VT, Le TG, Nguyen DT, Le HN, Nguyen KT, Le HS, Le VT, Christiane D, Tran TT, de Jong Menno, Schultsz C, Cheng P, Lim W, Horby P, Farrar J, World Health Organization International Avian Influenza Investigative Team: Avian influenza A (H5N1) in 10 patients in Vietnam. N. Engl. J. Med. 2004, 350 (12): 1179-1188. 10.1056/NEJMoa040419.PubMed Tran TH, Nguyen TL, Nguyen TD, Luong TS, Pham PM, van Vinh Chau Nguyen, Pham TS, Vo CD, Le TQM, Ngo TT, Dao BK, Le PP, Nguyen TT, Hoang TL, Cao VT, Le TG, Nguyen DT, Le HN, Nguyen KT, Le HS, Le VT, Christiane D, Tran TT, de Jong Menno, Schultsz C, Cheng P, Lim W, Horby P, Farrar J, World Health Organization International Avian Influenza Investigative Team: Avian influenza A (H5N1) in 10 patients in Vietnam. N. Engl. J. Med. 2004, 350 (12): 1179-1188. 10.1056/NEJMoa040419.PubMed
59.
go back to reference de Jong MD, Simmons CP, Thanh TT, Hien VM, Smith GJD, Chau TNB, Hoang DM, Chau NVV, Khanh TH, Dong VC, Qui PT, Cam BV, Ha DQ, Guan Y, Peiris JSM, Chinh NT, Hien TT, Farrar J: Fatal outcome of human influenza A (H5N1) is associated with high viral load and hypercytokinemia. Nat. Med. 2006, 12 (10): 1203-1207. 10.1038/nm1477.PubMedCentralPubMed de Jong MD, Simmons CP, Thanh TT, Hien VM, Smith GJD, Chau TNB, Hoang DM, Chau NVV, Khanh TH, Dong VC, Qui PT, Cam BV, Ha DQ, Guan Y, Peiris JSM, Chinh NT, Hien TT, Farrar J: Fatal outcome of human influenza A (H5N1) is associated with high viral load and hypercytokinemia. Nat. Med. 2006, 12 (10): 1203-1207. 10.1038/nm1477.PubMedCentralPubMed
60.
go back to reference Morens DM, Fauci AS: The 1918 influenza pandemic: Insights for the 21st century. J. Infect. Dis. 2007, 195 (7): 1018-1028. 10.1086/511989.PubMed Morens DM, Fauci AS: The 1918 influenza pandemic: Insights for the 21st century. J. Infect. Dis. 2007, 195 (7): 1018-1028. 10.1086/511989.PubMed
61.
go back to reference Morens DM, Taubenberger JK, Fauci AS: Predominant role of bacterial pneumonia as a cause of death in pandemic influenza: Implications for pandemic influenza preparedness. J. Infect. Dis. 2008, 198 (7): 962-970. 10.1086/591708.PubMedCentralPubMed Morens DM, Taubenberger JK, Fauci AS: Predominant role of bacterial pneumonia as a cause of death in pandemic influenza: Implications for pandemic influenza preparedness. J. Infect. Dis. 2008, 198 (7): 962-970. 10.1086/591708.PubMedCentralPubMed
62.
go back to reference La Gruta NL, Kedzierska K, Stambas J, Doherty PC: A question of self-preservation: Immunopathology in influenza virus infection. Immunol Cell Biol. 2007, 85 (2): 85-92. 10.1038/sj.icb.7100026.PubMed La Gruta NL, Kedzierska K, Stambas J, Doherty PC: A question of self-preservation: Immunopathology in influenza virus infection. Immunol Cell Biol. 2007, 85 (2): 85-92. 10.1038/sj.icb.7100026.PubMed
63.
go back to reference Szretter KJ, Gangappa S, Lu X, Smith C, Shieh WJ, Zaki SR, Sambhara S, Tumpey TM, Katz JM: Role of host cytokine responses in the pathogenesis of avian H5N1 influenza viruses in mice. J. Virol. 2007, 81 (6): 2736-2744. 10.1128/JVI.02336-06.PubMedCentralPubMed Szretter KJ, Gangappa S, Lu X, Smith C, Shieh WJ, Zaki SR, Sambhara S, Tumpey TM, Katz JM: Role of host cytokine responses in the pathogenesis of avian H5N1 influenza viruses in mice. J. Virol. 2007, 81 (6): 2736-2744. 10.1128/JVI.02336-06.PubMedCentralPubMed
64.
go back to reference Salomon R, Hoffmann E, Webster RG: Inhibition of the cytokine response does not protect against lethal H5N1 influenza infection. Proc. Natl. Acad. Sci. U.S.A. 2007, 104 (30): 12479-12481. 10.1073/pnas.0705289104.PubMedCentralPubMed Salomon R, Hoffmann E, Webster RG: Inhibition of the cytokine response does not protect against lethal H5N1 influenza infection. Proc. Natl. Acad. Sci. U.S.A. 2007, 104 (30): 12479-12481. 10.1073/pnas.0705289104.PubMedCentralPubMed
65.
go back to reference Peiris JSM, Cheung CY, Leung CYH, Nicholls JM: Innate immune responses to influenza A H5N1: Friend or foe?. Trends Immunol. 2009, 30 (12): 574-584. 10.1016/j.it.2009.09.004.PubMed Peiris JSM, Cheung CY, Leung CYH, Nicholls JM: Innate immune responses to influenza A H5N1: Friend or foe?. Trends Immunol. 2009, 30 (12): 574-584. 10.1016/j.it.2009.09.004.PubMed
66.
go back to reference Baskin CR, Bielefeldt-Ohmann H, Tumpey TM, Sabourin PJ, Long JP, Garía-Sastre A, Tolnay AE, Albrecht R, Pyles JA, Olson PH, Aicher LD, Rosenzweig ER, Murali-Krishna K, Clark EA, Kotur MS, Fornek JL, Proll S, Palermo RE, Sabourin CL, Katze MG: Early and sustained innate immune response defines pathology and death in nonhuman primates infected by highly pathogenic influenza virus. Proc. Natl. Acad. Sci. U.S.A. 2009, 106 (9): 3455-3460. 10.1073/pnas.0813234106.PubMedCentralPubMed Baskin CR, Bielefeldt-Ohmann H, Tumpey TM, Sabourin PJ, Long JP, Garía-Sastre A, Tolnay AE, Albrecht R, Pyles JA, Olson PH, Aicher LD, Rosenzweig ER, Murali-Krishna K, Clark EA, Kotur MS, Fornek JL, Proll S, Palermo RE, Sabourin CL, Katze MG: Early and sustained innate immune response defines pathology and death in nonhuman primates infected by highly pathogenic influenza virus. Proc. Natl. Acad. Sci. U.S.A. 2009, 106 (9): 3455-3460. 10.1073/pnas.0813234106.PubMedCentralPubMed
67.
go back to reference Thomas PG, Keating R, Hulse-Post DJ, Doherty PC: Cell-mediated protection in influenza infection. Emerg Infect Dis. 2006, 12: 48-54. 10.3201/eid1201.051237.PubMedCentralPubMed Thomas PG, Keating R, Hulse-Post DJ, Doherty PC: Cell-mediated protection in influenza infection. Emerg Infect Dis. 2006, 12: 48-54. 10.3201/eid1201.051237.PubMedCentralPubMed
68.
go back to reference Maines TR, Szretter KJ, Perrone L, Belser JA, Bright RA, Zeng H, Tumpey TM, Katz JM: Pathogenesis of emerging avian influenza viruses in mammals and the host innate immune response. Immunol Rev. 2008, 225: 68-84. 10.1111/j.1600-065X.2008.00690.x.PubMed Maines TR, Szretter KJ, Perrone L, Belser JA, Bright RA, Zeng H, Tumpey TM, Katz JM: Pathogenesis of emerging avian influenza viruses in mammals and the host innate immune response. Immunol Rev. 2008, 225: 68-84. 10.1111/j.1600-065X.2008.00690.x.PubMed
69.
go back to reference Bocharov GA, Romanyukha AA: Mathematical model of antiviral immune response III. Influenza A virus infection. J. Theor. Biol. 1994, 167 (4): 323-360. 10.1006/jtbi.1994.1074.PubMed Bocharov GA, Romanyukha AA: Mathematical model of antiviral immune response III. Influenza A virus infection. J. Theor. Biol. 1994, 167 (4): 323-360. 10.1006/jtbi.1994.1074.PubMed
70.
go back to reference Hancioglu B, Swigon D, Clermont G: A dynamical model of human immune response to influenza A virus infection. J. Theor. Biol. 2007, 246: 70-86. 10.1016/j.jtbi.2006.12.015.PubMed Hancioglu B, Swigon D, Clermont G: A dynamical model of human immune response to influenza A virus infection. J. Theor. Biol. 2007, 246: 70-86. 10.1016/j.jtbi.2006.12.015.PubMed
71.
go back to reference Chang DB, Young CS: Simple scaling laws for influenza A rise time, duration, and severity. J. Theor. Biol. 2007, 246 (4): 621-635. 10.1016/j.jtbi.2007.02.004.PubMed Chang DB, Young CS: Simple scaling laws for influenza A rise time, duration, and severity. J. Theor. Biol. 2007, 246 (4): 621-635. 10.1016/j.jtbi.2007.02.004.PubMed
72.
go back to reference Tridane A, Kuang Y: Modeling the interaction of cytotoxic T lymphocytes and influenza virus infected epithelial cells. Math Biosci Eng. 2010, 7: 171-185. 10.3934/mbe.2010.7.171.PubMed Tridane A, Kuang Y: Modeling the interaction of cytotoxic T lymphocytes and influenza virus infected epithelial cells. Math Biosci Eng. 2010, 7: 171-185. 10.3934/mbe.2010.7.171.PubMed
73.
go back to reference Lee HY, Topham DJ, Park SY, Hollenbaugh J, Treanor J, Mosmann TR, Jin X, Ward BM, Miao H, Holden-Wiltse J, Perelson AS, Zand M, Wu H: Simulation and prediction of the adaptive immune response to influenza A virus infection. J. Virol. 2009, 83 (14): 7151-7165. 10.1128/JVI.00098-09.PubMedCentralPubMed Lee HY, Topham DJ, Park SY, Hollenbaugh J, Treanor J, Mosmann TR, Jin X, Ward BM, Miao H, Holden-Wiltse J, Perelson AS, Zand M, Wu H: Simulation and prediction of the adaptive immune response to influenza A virus infection. J. Virol. 2009, 83 (14): 7151-7165. 10.1128/JVI.00098-09.PubMedCentralPubMed
74.
go back to reference Saenz RA, Quinlivan M, Elton D, MacRae S, Blunden AS, Mumford JA, Daly JM, Disgard P, Cullinane A, Grenfell BT, McCauley JW, Wood JLN, Gog JR: Dynamics of influenza virus infection and pathology. J. Virol. 2010, 84 (8): 3974-3983. 10.1128/JVI.02078-09.PubMedCentralPubMed Saenz RA, Quinlivan M, Elton D, MacRae S, Blunden AS, Mumford JA, Daly JM, Disgard P, Cullinane A, Grenfell BT, McCauley JW, Wood JLN, Gog JR: Dynamics of influenza virus infection and pathology. J. Virol. 2010, 84 (8): 3974-3983. 10.1128/JVI.02078-09.PubMedCentralPubMed
75.
go back to reference Handel A, Longini IM, Antia R: Towards a quantitative understanding of the within-host dynamics of influenza A infections. J. R. Soc. Interface. 2010, 7 (42): 35-47. 10.1098/rsif.2009.0067.PubMedCentralPubMed Handel A, Longini IM, Antia R: Towards a quantitative understanding of the within-host dynamics of influenza A infections. J. R. Soc. Interface. 2010, 7 (42): 35-47. 10.1098/rsif.2009.0067.PubMedCentralPubMed
76.
go back to reference Beauchemin C, Samuel J, Tuszynski J: A simple cellular automaton model for influenza A viral infections. J. Theor. Biol. 2005, 232 (2): 223-234. 10.1016/j.jtbi.2004.08.001. Draft available on arXiv:q-bio.CB/0402012PubMed Beauchemin C, Samuel J, Tuszynski J: A simple cellular automaton model for influenza A viral infections. J. Theor. Biol. 2005, 232 (2): 223-234. 10.1016/j.jtbi.2004.08.001. Draft available on arXiv:q-bio.CB/0402012PubMed
77.
go back to reference Beauchemin C: Probing the effects of the well-mixed assumption on viral infection dynamics. J. Theor. Biol. 2006, 242 (2): 464-477. 10.1016/j.jtbi.2006.03.014. Draft available on arXiv:q-bio.CB/0505043PubMed Beauchemin C: Probing the effects of the well-mixed assumption on viral infection dynamics. J. Theor. Biol. 2006, 242 (2): 464-477. 10.1016/j.jtbi.2006.03.014. Draft available on arXiv:q-bio.CB/0505043PubMed
78.
go back to reference Perelson AS, Nelson PW: Mathematical analysis of HIV-1 dynamics in vivo. SIAM Review. 1999, 41: 3-44. 10.1137/S0036144598335107. Perelson AS, Nelson PW: Mathematical analysis of HIV-1 dynamics in vivo. SIAM Review. 1999, 41: 3-44. 10.1137/S0036144598335107.
79.
go back to reference Nowak MA, May RM: Virus Dynamics: Mathematical Principles of Immunology and Virology. 2000, Oxford: Oxford University Press Nowak MA, May RM: Virus Dynamics: Mathematical Principles of Immunology and Virology. 2000, Oxford: Oxford University Press
80.
go back to reference Brydon EWA, Smith H, Sweet C: Influenza A virus-induced apoptosis in bronchiolar epithelial (NCI-H292) cells limits pro-inflammatory cytokine release. J Gen Virol. 2003, 84 (Pt 9): 2389-2400. 10.1099/vir.0.18913-0.PubMed Brydon EWA, Smith H, Sweet C: Influenza A virus-induced apoptosis in bronchiolar epithelial (NCI-H292) cells limits pro-inflammatory cytokine release. J Gen Virol. 2003, 84 (Pt 9): 2389-2400. 10.1099/vir.0.18913-0.PubMed
81.
go back to reference Zhirnov OP, Konakova TE, Wolff T, Klenk HD: NS1 protein of influenza A virus down-regulates apoptosis. J. Virol. 2002, 76 (4): 1617-1625. 10.1128/JVI.76.4.1617-1625.2002.PubMedCentralPubMed Zhirnov OP, Konakova TE, Wolff T, Klenk HD: NS1 protein of influenza A virus down-regulates apoptosis. J. Virol. 2002, 76 (4): 1617-1625. 10.1128/JVI.76.4.1617-1625.2002.PubMedCentralPubMed
82.
go back to reference Hornícková Z: Different progress of MDCK cell death after infection by two different influenza virus isolates. Cell Biochem Funct. 1997, 15 (2): 87-93. 10.1002/(SICI)1099-0844(19970601)15:2<87::AID-CBF726>3.0.CO;2-6.PubMed Hornícková Z: Different progress of MDCK cell death after infection by two different influenza virus isolates. Cell Biochem Funct. 1997, 15 (2): 87-93. 10.1002/(SICI)1099-0844(19970601)15:2<87::AID-CBF726>3.0.CO;2-6.PubMed
83.
go back to reference Stray SJ, Air GM: Apoptosis by influenza viruses correlates with efficiency of viral mRNA synthesis. Virus Res. 2001, 77: 3-17. 10.1016/S0168-1702(01)00260-X.PubMed Stray SJ, Air GM: Apoptosis by influenza viruses correlates with efficiency of viral mRNA synthesis. Virus Res. 2001, 77: 3-17. 10.1016/S0168-1702(01)00260-X.PubMed
84.
go back to reference Price GE, Smith H, Sweet C: Differential induction of cytotoxicity and apoptosis by influenza virus strains of differing virulence. J Gen Virol. 1997, 78 (Pt 11): 2821-2829.PubMed Price GE, Smith H, Sweet C: Differential induction of cytotoxicity and apoptosis by influenza virus strains of differing virulence. J Gen Virol. 1997, 78 (Pt 11): 2821-2829.PubMed
85.
go back to reference Takizawa T, Matsukawa S, Higuchi Y, Nakamura S, Nakanishi Y, Fukuda R: Induction of programmed cell death (apoptosis) by influenza virus infection in tissue culture cells. J Gen Virol. 1993, 74 (Pt 11): 2347-2355. 10.1099/0022-1317-74-11-2347.PubMed Takizawa T, Matsukawa S, Higuchi Y, Nakamura S, Nakanishi Y, Fukuda R: Induction of programmed cell death (apoptosis) by influenza virus infection in tissue culture cells. J Gen Virol. 1993, 74 (Pt 11): 2347-2355. 10.1099/0022-1317-74-11-2347.PubMed
86.
go back to reference Hinshaw VS, Olsen CW, Dybdahl-Sissoko N, Evans D: Apoptosis: A mechanism of cell killing by influenza A and B viruses. J. Virol. 1994, 68 (6): 3667-3673.PubMedCentralPubMed Hinshaw VS, Olsen CW, Dybdahl-Sissoko N, Evans D: Apoptosis: A mechanism of cell killing by influenza A and B viruses. J. Virol. 1994, 68 (6): 3667-3673.PubMedCentralPubMed
87.
go back to reference Horsfall FL: On the reproduction of influenza virus; quantitative studies with procedures which enumerate infective and hemagglutinating virus particles. J. Exp. Med. 1954, 100 (2): 135-161. 10.1084/jem.100.2.135.PubMedCentralPubMed Horsfall FL: On the reproduction of influenza virus; quantitative studies with procedures which enumerate infective and hemagglutinating virus particles. J. Exp. Med. 1954, 100 (2): 135-161. 10.1084/jem.100.2.135.PubMedCentralPubMed
88.
go back to reference Horsfall FL: Reproduction of influenza viruses; quantitative investigations with particle enumeration procedures on the dynamics of influenza A and B virus reproduction. J. Exp. Med. 1955, 102 (4): 441-473. 10.1084/jem.102.4.441.PubMedCentralPubMed Horsfall FL: Reproduction of influenza viruses; quantitative investigations with particle enumeration procedures on the dynamics of influenza A and B virus reproduction. J. Exp. Med. 1955, 102 (4): 441-473. 10.1084/jem.102.4.441.PubMedCentralPubMed
89.
90.
go back to reference Choppin PW: Multiplication of two kinds of influenza A2 virus particles in monkey kidney cells. Virology. 1963, 21: 342-352. 10.1016/0042-6822(63)90195-8.PubMed Choppin PW: Multiplication of two kinds of influenza A2 virus particles in monkey kidney cells. Virology. 1963, 21: 342-352. 10.1016/0042-6822(63)90195-8.PubMed
91.
go back to reference Cairns HJF: The asynchrony of infection by influenza virus. Virology. 1957, 3: 1-14. 10.1016/0042-6822(57)90019-3.PubMed Cairns HJF: The asynchrony of infection by influenza virus. Virology. 1957, 3: 1-14. 10.1016/0042-6822(57)90019-3.PubMed
92.
go back to reference Henle W, Henle G, Rosenberg EB: The demonstraiont of one-step growth curves of influenza viruses through the blocking effect of irradiated virus on further infection. J. Exp. Med. 1947, 86 (5): 423-437. 10.1084/jem.86.5.423.PubMedCentralPubMed Henle W, Henle G, Rosenberg EB: The demonstraiont of one-step growth curves of influenza viruses through the blocking effect of irradiated virus on further infection. J. Exp. Med. 1947, 86 (5): 423-437. 10.1084/jem.86.5.423.PubMedCentralPubMed
93.
go back to reference Ilyushina NA, Rudneva IA, Shilov AA, Klenk HD, Kaverin NV: Postreassortment changes in a model system: HA-NA adjustment in an H3N2 avian-human reassortant influenza virus. Arch Virol. 2005, 150 (7): 1327-1338. 10.1007/s00705-005-0490-4.PubMed Ilyushina NA, Rudneva IA, Shilov AA, Klenk HD, Kaverin NV: Postreassortment changes in a model system: HA-NA adjustment in an H3N2 avian-human reassortant influenza virus. Arch Virol. 2005, 150 (7): 1327-1338. 10.1007/s00705-005-0490-4.PubMed
94.
go back to reference Jaqaman K, Danuser G: Linking data to models: data regression. Nat Rev Mol Cell Biol. 2006, 7 (11): 813-819. 10.1038/nrm2030.PubMed Jaqaman K, Danuser G: Linking data to models: data regression. Nat Rev Mol Cell Biol. 2006, 7 (11): 813-819. 10.1038/nrm2030.PubMed
95.
go back to reference Smith AM, Adler FR, Perelson AS: An accurate two-phase approximate solution to an acute viral infection model. J. Math. Biol. 2010, 60: 711-726. 10.1007/s00285-009-0281-8.PubMedCentralPubMed Smith AM, Adler FR, Perelson AS: An accurate two-phase approximate solution to an acute viral infection model. J. Math. Biol. 2010, 60: 711-726. 10.1007/s00285-009-0281-8.PubMedCentralPubMed
96.
go back to reference Miao H, Xia X, Perelson AS, Wu H: On identifiability of nonlinear ODE models and applications in viral dynamics. SIAM Rev. 2011, 53 (1): 10.1137/090757009. in print Miao H, Xia X, Perelson AS, Wu H: On identifiability of nonlinear ODE models and applications in viral dynamics. SIAM Rev. 2011, 53 (1): 10.1137/090757009. in print
97.
go back to reference Yoshikawa T, Matsuo K, Matsuo K, Suzuki Y, Nomoto A, Tamura SI, Kurata T, Sata T: Total viral genome copies and virus-Ig complexes after infection with influenza virus in the nasal secretions of immunized mice. J. Gen. Virol. 2004, 85 (Pt 8): 2339-2346. 10.1099/vir.0.79892-0.PubMed Yoshikawa T, Matsuo K, Matsuo K, Suzuki Y, Nomoto A, Tamura SI, Kurata T, Sata T: Total viral genome copies and virus-Ig complexes after infection with influenza virus in the nasal secretions of immunized mice. J. Gen. Virol. 2004, 85 (Pt 8): 2339-2346. 10.1099/vir.0.79892-0.PubMed
98.
go back to reference Ma ZM, Stone M, Piatak Mike, Schweighardt B, Haigwood NL, Montefiori D, Lifson JD, Busch MP, Miller CJ: High specific infectivity of plasma virus from the pre-ramp-up and ramp-up stages of acute simian immunodeficiency virus infection. J. Virol. 2009, 83 (7): 3288-3297. 10.1128/JVI.02423-08.PubMedCentralPubMed Ma ZM, Stone M, Piatak Mike, Schweighardt B, Haigwood NL, Montefiori D, Lifson JD, Busch MP, Miller CJ: High specific infectivity of plasma virus from the pre-ramp-up and ramp-up stages of acute simian immunodeficiency virus infection. J. Virol. 2009, 83 (7): 3288-3297. 10.1128/JVI.02423-08.PubMedCentralPubMed
99.
go back to reference Vaidya NK, Ribeiro RM, Miller CJ, Perelson AS: Viral dynamics during primary simian immunodeficiency virus infection: Effect of time-dependent virus infectivity. J. Virol. 2010, 84 (9): 4302-4310. 10.1128/JVI.02284-09.PubMedCentralPubMed Vaidya NK, Ribeiro RM, Miller CJ, Perelson AS: Viral dynamics during primary simian immunodeficiency virus infection: Effect of time-dependent virus infectivity. J. Virol. 2010, 84 (9): 4302-4310. 10.1128/JVI.02284-09.PubMedCentralPubMed
100.
go back to reference Blower SM, Chou T: Modeling the emergence of the ’hot zones’: tuberculosis and the amplification dynamics of drug resistance. Nat Med. 2004, 10 (10): 1111-1116. 10.1038/nm1102.PubMed Blower SM, Chou T: Modeling the emergence of the ’hot zones’: tuberculosis and the amplification dynamics of drug resistance. Nat Med. 2004, 10 (10): 1111-1116. 10.1038/nm1102.PubMed
101.
go back to reference Earn D, Dushoff J, Levin S: Ecology and evolution of the flu. Trends Ecol. Evol. 2002, 17 (7): 334-340. 10.1016/S0169-5347(02)02502-8. Earn D, Dushoff J, Levin S: Ecology and evolution of the flu. Trends Ecol. Evol. 2002, 17 (7): 334-340. 10.1016/S0169-5347(02)02502-8.
102.
go back to reference Perelson AS: Modelling viral and immune system dynamics. Nature Rev. Immunol. 2002, 2: 28-36. 10.1038/nri700. Perelson AS: Modelling viral and immune system dynamics. Nature Rev. Immunol. 2002, 2: 28-36. 10.1038/nri700.
103.
go back to reference Govorkova EA, Fang HB, Tan M, Webster RG: Neuraminidase inhibitor-rimantadine combinations exert additive and synergistic anti-influenza virus effects in MDCK cells. Antimicrob. Agents Chemother. 2004, 48 (12): 4855-4863. 10.1128/AAC.48.12.4855-4863.2004.PubMedCentralPubMed Govorkova EA, Fang HB, Tan M, Webster RG: Neuraminidase inhibitor-rimantadine combinations exert additive and synergistic anti-influenza virus effects in MDCK cells. Antimicrob. Agents Chemother. 2004, 48 (12): 4855-4863. 10.1128/AAC.48.12.4855-4863.2004.PubMedCentralPubMed
104.
go back to reference Ilyushina NA, Bovin NV, Webster RG, Govorkova EA: Combination chemotherapy, a potential strategy for reducing the emergence of drug-resistant influenza A variants. Antiviral Res. 2006, 70 (3): 121-131. 10.1016/j.antiviral.2006.01.012.PubMed Ilyushina NA, Bovin NV, Webster RG, Govorkova EA: Combination chemotherapy, a potential strategy for reducing the emergence of drug-resistant influenza A variants. Antiviral Res. 2006, 70 (3): 121-131. 10.1016/j.antiviral.2006.01.012.PubMed
105.
go back to reference Ilyushina NA, Hoffmann E, Salomon R, Webster RG, Govorkova EA: Amantadine-oseltamivir combination therapy for H5N1 influenza virus infection in mice. Antivir. Ther. 2007, 12 (3): 363-370.PubMed Ilyushina NA, Hoffmann E, Salomon R, Webster RG, Govorkova EA: Amantadine-oseltamivir combination therapy for H5N1 influenza virus infection in mice. Antivir. Ther. 2007, 12 (3): 363-370.PubMed
106.
go back to reference Ilyushina NA, Hay A, Yilmaz N, Boon ACM, Webster RG, Govorkova EA: Oseltamivir-ribavirin combination therapy for highly pathogenic H5N1 influenza virus infection in mice. Antimicrob. Agents Chemother. 2008, 52 (11): 3889-3897. 10.1128/AAC.01579-07.PubMedCentralPubMed Ilyushina NA, Hay A, Yilmaz N, Boon ACM, Webster RG, Govorkova EA: Oseltamivir-ribavirin combination therapy for highly pathogenic H5N1 influenza virus infection in mice. Antimicrob. Agents Chemother. 2008, 52 (11): 3889-3897. 10.1128/AAC.01579-07.PubMedCentralPubMed
107.
go back to reference Nguyen JT, Hoopes JD, Smee DF, Prichard MN, Driebe EM, Engelthaler DM, Le MH, Keim PS, Spence RP, Went GT: Triple combination of oseltamivir, amantadine, and ribavirin displays synergistic activity against multiple influenza virus strains in vitro. Antimicrob. Agents Chemother. 2009, 53 (10): 4115-4126. 10.1128/AAC.00476-09.PubMedCentralPubMed Nguyen JT, Hoopes JD, Smee DF, Prichard MN, Driebe EM, Engelthaler DM, Le MH, Keim PS, Spence RP, Went GT: Triple combination of oseltamivir, amantadine, and ribavirin displays synergistic activity against multiple influenza virus strains in vitro. Antimicrob. Agents Chemother. 2009, 53 (10): 4115-4126. 10.1128/AAC.00476-09.PubMedCentralPubMed
108.
go back to reference Smee DF, Hurst BL, Wong MH, Bailey KW, Morrey JD: Effects of double combinations of amantadine, oseltamivir, and ribavirin on influenza A (H5N1) virus infections in cell culture and in mice. Antimicrob. Agents Chemother. 2009, 53 (5): 2120-2128. 10.1128/AAC.01012-08.PubMedCentralPubMed Smee DF, Hurst BL, Wong MH, Bailey KW, Morrey JD: Effects of double combinations of amantadine, oseltamivir, and ribavirin on influenza A (H5N1) virus infections in cell culture and in mice. Antimicrob. Agents Chemother. 2009, 53 (5): 2120-2128. 10.1128/AAC.01012-08.PubMedCentralPubMed
109.
go back to reference Smee DF, Hurst BL, Wong MH, Tarbet EB, Babu YS, Klumpp K, Morrey JD: Combinations of oseltamivir and peramivir for the treatment of influenza A (H1N1) virus infections in cell culture and in mice. Antiviral Res. 2010, 88 (1): 38-44. 10.1016/j.antiviral.2010.07.003.PubMedCentralPubMed Smee DF, Hurst BL, Wong MH, Tarbet EB, Babu YS, Klumpp K, Morrey JD: Combinations of oseltamivir and peramivir for the treatment of influenza A (H1N1) virus infections in cell culture and in mice. Antiviral Res. 2010, 88 (1): 38-44. 10.1016/j.antiviral.2010.07.003.PubMedCentralPubMed
110.
go back to reference Nguyen JT, Hoopes JD, Le MH, Smee DF, Patick AK, Faix DJ, Blair PJ, de Jong MD, Prichard MN, Went GT: Triple combination of amantadine, ribavirin, and oseltamivir is highly active and synergistic against drug resistant influenza virus strains in vitro. PLoS One. 2010, 5 (2): e9332-10.1371/journal.pone.0009332.PubMedCentralPubMed Nguyen JT, Hoopes JD, Le MH, Smee DF, Patick AK, Faix DJ, Blair PJ, de Jong MD, Prichard MN, Went GT: Triple combination of amantadine, ribavirin, and oseltamivir is highly active and synergistic against drug resistant influenza virus strains in vitro. PLoS One. 2010, 5 (2): e9332-10.1371/journal.pone.0009332.PubMedCentralPubMed
111.
go back to reference Brown LE, Kelso A: Prospects for an influenza vaccine that induces cross-protective cytotoxic T lymphocytes. Immunol Cell Biol. 2009, 87 (4): 300-308. 10.1038/icb.2009.16.PubMed Brown LE, Kelso A: Prospects for an influenza vaccine that induces cross-protective cytotoxic T lymphocytes. Immunol Cell Biol. 2009, 87 (4): 300-308. 10.1038/icb.2009.16.PubMed
112.
go back to reference Rimmelzwaan GF, Fouchier RA, Osterhaus AD: Influenza virus-specific cytotoxic T lymphocytes: A correlate of protection and a basis for vaccine development. Curr Opin Biotechnol. 2007, 18 (6): 529-536. 10.1016/j.copbio.2007.11.002.PubMed Rimmelzwaan GF, Fouchier RA, Osterhaus AD: Influenza virus-specific cytotoxic T lymphocytes: A correlate of protection and a basis for vaccine development. Curr Opin Biotechnol. 2007, 18 (6): 529-536. 10.1016/j.copbio.2007.11.002.PubMed
113.
go back to reference Gilchrist MA, Coombs D: Evolution of virulence: Interdependence, constraints, and selection using nested models. Theor. Popul. Biol. 2006, 69 (2): 145-153. 10.1016/j.tpb.2005.07.002.PubMed Gilchrist MA, Coombs D: Evolution of virulence: Interdependence, constraints, and selection using nested models. Theor. Popul. Biol. 2006, 69 (2): 145-153. 10.1016/j.tpb.2005.07.002.PubMed
114.
go back to reference Mideo N, Day T: On the evolution of reproductive restraint in malaria. Proc Biol Sci. 2008, 275 (1639): 1217-1224. 10.1098/rspb.2007.1545.PubMedCentralPubMed Mideo N, Day T: On the evolution of reproductive restraint in malaria. Proc Biol Sci. 2008, 275 (1639): 1217-1224. 10.1098/rspb.2007.1545.PubMedCentralPubMed
115.
go back to reference Young D, Stark J, Kirschner D: Systems biology of persistent infection: Tuberculosis as a case study. Nat Rev Microbiol. 2008, 6 (7): 520-528. 10.1038/nrmicro1919.PubMed Young D, Stark J, Kirschner D: Systems biology of persistent infection: Tuberculosis as a case study. Nat Rev Microbiol. 2008, 6 (7): 520-528. 10.1038/nrmicro1919.PubMed
116.
go back to reference Luciani F, Sisson SA, Jiang H, Francis AR, Tanaka MM: The epidemiological fitness cost of drug resistance in Mycobacterium tuberculosis. Proc. Natl. Acad. Sci. U.S.A. 2009, 106 (34): 14711-14715. 10.1073/pnas.0902437106.PubMedCentralPubMed Luciani F, Sisson SA, Jiang H, Francis AR, Tanaka MM: The epidemiological fitness cost of drug resistance in Mycobacterium tuberculosis. Proc. Natl. Acad. Sci. U.S.A. 2009, 106 (34): 14711-14715. 10.1073/pnas.0902437106.PubMedCentralPubMed
117.
go back to reference Steinmeyer SH, Wilke CO, Pepin KM: Methods of modelling viral disease dynamics across the within- and between-host scales: The impact of virus dose on host population immunity. Philos Trans R Soc Lond B Biol Sci. 2010, 365 (1548): 1931-1941. 10.1098/rstb.2010.0065.PubMedCentralPubMed Steinmeyer SH, Wilke CO, Pepin KM: Methods of modelling viral disease dynamics across the within- and between-host scales: The impact of virus dose on host population immunity. Philos Trans R Soc Lond B Biol Sci. 2010, 365 (1548): 1931-1941. 10.1098/rstb.2010.0065.PubMedCentralPubMed
118.
go back to reference Maines TR, Jayaraman A, Belser JA, Wadford DA, Pappas C, Zeng H, Gustin KM, Pearce MB, Viswanathan K, Shriver ZH, Raman R, Cox NJ, Sasisekharan R, Katz JM, Tumpey TM: Transmission and pathogenesis of swine-origin 2009 A(H1N1) influenza viruses in ferrets and mice. Science. 2009, 325 (5939): 484-487.PubMedCentralPubMed Maines TR, Jayaraman A, Belser JA, Wadford DA, Pappas C, Zeng H, Gustin KM, Pearce MB, Viswanathan K, Shriver ZH, Raman R, Cox NJ, Sasisekharan R, Katz JM, Tumpey TM: Transmission and pathogenesis of swine-origin 2009 A(H1N1) influenza viruses in ferrets and mice. Science. 2009, 325 (5939): 484-487.PubMedCentralPubMed
119.
120.
go back to reference Coombs D, Gilchrist MA, Ball CL: Evaluating the importance of within- and between-host selection pressures on the evolution of chronic pathogens. Theor. Popul. Biol. 2007, 72 (4): 576-591. 10.1016/j.tpb.2007.08.005.PubMed Coombs D, Gilchrist MA, Ball CL: Evaluating the importance of within- and between-host selection pressures on the evolution of chronic pathogens. Theor. Popul. Biol. 2007, 72 (4): 576-591. 10.1016/j.tpb.2007.08.005.PubMed
121.
go back to reference Chen SC, Chio CP, Jou LJ, Liao CM: Viral kinetics and exhaled droplet size affect indoor transmission dynamics of influenza infection. Indoor Air. 2009, 19 (5): 401-413. 10.1111/j.1600-0668.2009.00603.x.PubMed Chen SC, Chio CP, Jou LJ, Liao CM: Viral kinetics and exhaled droplet size affect indoor transmission dynamics of influenza infection. Indoor Air. 2009, 19 (5): 401-413. 10.1111/j.1600-0668.2009.00603.x.PubMed
122.
go back to reference Blower SM, Dowlatabadi H: Sensitivity and uncertainty analysis of complex-models of disease transmission — An HIV model, as an example. International Statistical Review. 1994, 62 (2): 229-243. 10.2307/1403510. Blower SM, Dowlatabadi H: Sensitivity and uncertainty analysis of complex-models of disease transmission — An HIV model, as an example. International Statistical Review. 1994, 62 (2): 229-243. 10.2307/1403510.
123.
go back to reference Marino S, Hogue IB, Ray CJ, Kirschner DE: A methodology for performing global uncertainty and sensitivity analysis in systems biology. J. Theor. Biol. 2008, 254: 178-196. 10.1016/j.jtbi.2008.04.011.PubMedCentralPubMed Marino S, Hogue IB, Ray CJ, Kirschner DE: A methodology for performing global uncertainty and sensitivity analysis in systems biology. J. Theor. Biol. 2008, 254: 178-196. 10.1016/j.jtbi.2008.04.011.PubMedCentralPubMed
124.
go back to reference Handel A, Longini IM, Antia R: Intervention strategies for an influenza pandemic taking into account secondary bacterial infections. Epidemics. 2009, 1 (3): 185-195. 10.1016/j.epidem.2009.09.001.PubMedCentralPubMed Handel A, Longini IM, Antia R: Intervention strategies for an influenza pandemic taking into account secondary bacterial infections. Epidemics. 2009, 1 (3): 185-195. 10.1016/j.epidem.2009.09.001.PubMedCentralPubMed
125.
go back to reference Davidian M, Giltinan DM: Nonlinear Models for Repeated Measurement Data. Monographs on statistics and applied probability. 1995, Chapman & Hall, 359- Davidian M, Giltinan DM: Nonlinear Models for Repeated Measurement Data. Monographs on statistics and applied probability. 1995, Chapman & Hall, 359-
126.
go back to reference Gelman A, Hill J: Data Analysis Using Regression and Multilevel/Hierarchical Models. 2006, Cambridge University Press Gelman A, Hill J: Data Analysis Using Regression and Multilevel/Hierarchical Models. 2006, Cambridge University Press
127.
go back to reference Carlin BP, Louis TA: Bayesian Methods for Data Analysis. 2008, Chapman & Hall/CRC, 3rd Carlin BP, Louis TA: Bayesian Methods for Data Analysis. 2008, Chapman & Hall/CRC, 3rd
128.
go back to reference Carrat F, Vergu E, Ferguson NM, Lemaitre M, Cauchemez S, Leach S, Valleron AJ: Time lines of infection and disease in human influenza: A review of volunteer challenge studies. Am J Epidemiol. 2008, 167 (7): 775-785. 10.1093/aje/kwm375.PubMed Carrat F, Vergu E, Ferguson NM, Lemaitre M, Cauchemez S, Leach S, Valleron AJ: Time lines of infection and disease in human influenza: A review of volunteer challenge studies. Am J Epidemiol. 2008, 167 (7): 775-785. 10.1093/aje/kwm375.PubMed
129.
go back to reference Liao CM, Yang SC, Chio CP, Chen SC: Understanding influenza virus-specific epidemiological properties by analysis of experimental human infections. Epidemiol Infect. 2010, 138 (6): 825-835. 10.1017/S0950268809991178.PubMed Liao CM, Yang SC, Chio CP, Chen SC: Understanding influenza virus-specific epidemiological properties by analysis of experimental human infections. Epidemiol Infect. 2010, 138 (6): 825-835. 10.1017/S0950268809991178.PubMed
130.
go back to reference Lau LLH, Cowling BJ, Fang VJ, Chan K, Lau EHY, Lipsitch M, Cheng CKY, Houck PM, Uyeki TM, Peiris JSM, Leung GM: Viral shedding and clinical illness in naturally acquired influenza virus infections. J. Infect. Dis. 2010, 201 (10): 1509-1516. 10.1086/652241.PubMedCentralPubMed Lau LLH, Cowling BJ, Fang VJ, Chan K, Lau EHY, Lipsitch M, Cheng CKY, Houck PM, Uyeki TM, Peiris JSM, Leung GM: Viral shedding and clinical illness in naturally acquired influenza virus infections. J. Infect. Dis. 2010, 201 (10): 1509-1516. 10.1086/652241.PubMedCentralPubMed
Metadata
Title
A review of mathematical models of influenza A infections within a host or cell culture: lessons learned and challenges ahead
Authors
Catherine AA Beauchemin
Andreas Handel
Publication date
01-12-2011
Publisher
BioMed Central
Published in
BMC Public Health / Issue Special Issue 1/2011
Electronic ISSN: 1471-2458
DOI
https://doi.org/10.1186/1471-2458-11-S1-S7

Other articles of this Special Issue 1/2011

BMC Public Health 1/2011 Go to the issue