Modeling Influenza Virus Infection: A Roadmap for Influenza Research

Influenza A virus (IAV) infection represents a global threat causing seasonal outbreaks and pandemics. Additionally, secondary bacterial infections, caused mainly by Streptococcus pneumoniae, are one of the main complications and responsible for the enhanced morbidity and mortality associated with IAV infections. In spite of the significant advances in our knowledge of IAV infections, holistic comprehension of the interplay between IAV and the host immune response (IR) remains largely fragmented. During the last decade, mathematical modeling has been instrumental to explain and quantify IAV dynamics. In this paper, we review not only the state of the art of mathematical models of IAV infection but also the methodologies exploited for parameter estimation. We focus on the adaptive IR control of IAV infection and the possible mechanisms that could promote a secondary bacterial coinfection. To exemplify IAV dynamics and identifiability issues, a mathematical model to explain the interactions between adaptive IR and IAV infection is considered. Furthermore, in this paper we propose a roadmap for future influenza research. The development of a mathematical modeling framework with a secondary bacterial coinfection, immunosenescence, host genetic factors and responsiveness to vaccination will be pivotal to advance IAV infection understanding and treatment optimization.

[1]  Ruy M Ribeiro,et al.  Modeling amantadine treatment of influenza A virus in vitro. , 2008, Journal of theoretical biology.

[2]  Guy Boivin,et al.  The H275Y Neuraminidase Mutation of the Pandemic A/H1N1 Influenza Virus Lengthens the Eclipse Phase and Reduces Viral Output of Infected Cells, Potentially Compromising Fitness in Ferrets , 2012, Journal of Virology.

[3]  T. Waldmann,et al.  Vaccinia Virus-Based Multivalent H5N1 Avian Influenza Vaccines Adjuvanted with IL-15 Confer Sterile Cross-Clade Protection in Mice1 , 2009, The Journal of Immunology.

[4]  A H Rowberg,et al.  Influenza virus population dynamics in the respiratory tract of experimentally infected mice , 1976, Infection and immunity.

[5]  Ursula Klingmüller,et al.  Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood , 2009, Bioinform..

[6]  K. Van Reeth.  Cytokines in the pathogenesis of influenza. , 2000, Veterinary microbiology.

[7]  C. Beauchemin,et al.  Exploring the effect of biological delays in kinetic models of influenza within a host or cell culture , 2011, BMC public health.

[8]  D. E. Rogers,et al.  Studies on influenza in the pandemic of 1957-1958. II. Pulmonary complications of influenza. , 1959, The Journal of clinical investigation.

[9]  J. McCullers.  Insights into the Interaction between Influenza Virus and Pneumococcus , 2006, Clinical Microbiology Reviews.

[10]  J. Tratschin,et al.  Immunogenic and replicative properties of classical swine fever virus replicon particles modified to induce IFN-α/β and carry foreign genes. , 2011, Vaccine.

[11]  C. Whitney,et al.  Bacterial coinfections in lung tissue specimens from fatal cases of 2009 pandemic influenza A (H1N1) - United States, May-August 2009. , 2009, MMWR. Morbidity and mortality weekly report.

[12]  S. Akira,et al.  TLR7 Contributes to the Rapid Progression but Not to the Overall Fatal Outcome of Secondary Pneumococcal Disease following Influenza A Virus Infection , 2012, Journal of Innate Immunity.

[13]  M. Katze,et al.  Influenza Virus A/Anhui/1/2013 (H7N9) Replicates Efficiently in the Upper and Lower Respiratory Tracts of Cynomolgus Macaques , 2014, mBio.

[14]  R. K. Evans,et al.  Potent immunogenicity and efficacy of a universal influenza vaccine candidate comprising a recombinant fusion protein linking influenza M2e to the TLR5 ligand flagellin. , 2008, Vaccine.

[15]  M. Meyer-Hermann,et al.  Innate Immune System Dynamics to Influenza Virus , 2012 .

[16]  W. John Edmunds,et al.  Assessing Optimal Target Populations for Influenza Vaccination Programmes: An Evidence Synthesis and Modelling Study , 2013, PLoS medicine.

[17]  A. Vicino,et al.  Vaginal Immunization to Elicit Primary T-Cell Activation and Dissemination , 2013, PloS one.

[18]  M. Elowitz,et al.  Functional roles for noise in genetic circuits , 2010, Nature.

[19]  Michael R. Kosorok,et al.  Robust semiparametric M-estimation and the weighted bootstrap , 2005 .

[20]  Daniel Bottomly,et al.  Expression Quantitative Trait Loci for Extreme Host Response to Influenza A in Pre-Collaborative Cross Mice , 2012, G3: Genes | Genomes | Genetics.

[21]  A. Vallejo,et al.  CD28 extinction in human T cells: altered functions and the program of T‐cell senescence , 2005, Immunological reviews.

[22]  Hrishikesh D. Vinod.  Maximum Entropy Bootstrap Algorithm Enhancements , 2013 .

[23]  Linda R. Petzold,et al.  Stochastic modelling of gene regulatory networks , 2005 .

[24]  Vitaly V. Ganusov,et al.  Mathematical modeling provides kinetic details of the human immune response to vaccination , 2015, Front. Cell. Infect. Microbiol..

[25]  Paul Kellam,et al.  IFITM3 restricts the morbidity and mortality associated with influenza , 2012, Nature.

[26]  H. Künsch,et al.  Practical identifiability analysis of large environmental simulation models , 2001 .

[27]  James M. McCaw,et al.  Reducing Uncertainty in Within-Host Parameter Estimates of Influenza Infection by Measuring Both Infectious and Total Viral Load , 2013, PloS one.

[28]  J. Banga,et al.  Structural Identifiability of Systems Biology Models: A Critical Comparison of Methods , 2011, PloS one.

[29]  Mark R. Soboleski,et al.  Single-Dose Mucosal Immunization with a Candidate Universal Influenza Vaccine Provides Rapid Protection from Virulent H5N1, H3N2 and H1N1 Viruses , 2010, PloS one.

[30]  N. D. Clarke,et al.  Towards a Rigorous Assessment of Systems Biology Models: The DREAM3 Challenges , 2010, PloS one.

[31]  P. Wei,et al.  IFITM3 rs12252 T>C polymorphism is associated with the risk of severe influenza: a meta-analysis , 2015, Epidemiology and Infection.

[32]  R. Kennedy,et al.  A systems biology approach to the effect of aging, immunosenescence and vaccine response. , 2014, Current opinion in immunology.

[33]  Hana M. Dobrovolny,et al.  Assessing Mathematical Models of Influenza Infections Using Features of the Immune Response , 2013, PloS one.

[34]  B. Lambrecht,et al.  Sustained desensitization to bacterial Toll-like receptor ligands after resolutionof respiratory influenza infection , 2008, The Journal of experimental medicine.

[35]  P. Wilson,et al.  Targeting B cell responses in universal influenza vaccine design. , 2011, Trends in immunology.

[36]  Robert T. Chen,et al.  Use of the inactivated intranasal influenza vaccine and the risk of Bell's palsy in Switzerland. , 2004, The New England journal of medicine.

[37]  Q. Sattentau,et al.  Polyethyleneimine is a potent mucosal adjuvant for viral glycoprotein antigens , 2012, Nature Biotechnology.

[38]  Samit R. Joshi,et al.  Aging of the innate immune system. , 2010, Current opinion in immunology.

[39]  Lisa E. Gralinski,et al.  Modeling Host Genetic Regulation of Influenza Pathogenesis in the Collaborative Cross , 2013, PLoS pathogens.

[40]  T. Moran,et al.  Type I Interferon Induction during Influenza Virus Infection Increases Susceptibility to Secondary Streptococcus pneumoniae Infection by Negative Regulation of γδ T Cells , 2012, Journal of Virology.

[41]  G. Bocharov,et al.  Mathematical model of antiviral immune response. III. Influenza A virus infection. , 1994, Journal of theoretical biology.

[42]  F. Horsfall.  On the reproduction of influenza virus; quantitative studies with procedures which enumerate infective and hemagglutinating virus particles. , 1954 .

[43]  P. Lang,et al.  Effectiveness of influenza vaccine in aging and older adults: comprehensive analysis of the evidence , 2012, Clinical Interventions in Aging.

[44]  James M. McCaw,et al.  Innate Immunity and the Inter-exposure Interval Determine the Dynamics of Secondary Influenza Virus Infection and Explain Observed Viral Hierarchies , 2015, PLoS Comput. Biol..

[45]  Lisa E. Gralinski,et al.  The Genome Architecture of the Collaborative Cross Mouse Genetic Reference Population , 2012, Genetics.

[46]  J. Reifman,et al.  Simulation of B Cell Affinity Maturation Explains Enhanced Antibody Cross-Reactivity Induced by the Polyvalent Malaria Vaccine AMA1 , 2014, The Journal of Immunology.

[47]  M. Tebianian,et al.  Influenza A viruses: why focusing on M2e-based universal vaccines , 2011, Virus Genes.

[48]  D. Metzger,et al.  Inhibition of pulmonary antibacterial defense by interferon-γ during recovery from influenza infection , 2008, Nature Medicine.

[49]  P. Nelson,et al.  TMPRSS2 Is a Host Factor That Is Essential for Pneumotropism and Pathogenicity of H7N9 Influenza A Virus in Mice , 2014, Journal of Virology.

[50]  Daniel S. Chertow,et al.  Bacterial coinfection in influenza: a grand rounds review. , 2013, JAMA.

[51]  L. Reperant,et al.  Adaptive pathways of zoonotic influenza viruses: from exposure to establishment in humans. , 2012, Vaccine.

[52]  C. Beauchemin,et al.  Exploring Cell Tropism as a Possible Contributor to Influenza Infection Severity , 2010, PloS one.

[53]  Paul G Thomas,et al.  Influenza and the challenge for immunology , 2006, Nature Immunology.

[54]  Udo Reichl,et al.  Multiscale Modeling of Influenza A Virus Infection Supports the Development of Direct-Acting Antivirals , 2013, PLoS Comput. Biol..

[55]  Jens Timmer,et al.  Joining forces of Bayesian and frequentist methodology: a study for inference in the presence of non-identifiability , 2012, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[56]  The survival and turnover of mature and immature CD8 T cells. , 1995, Immunology.

[57]  U Reichl,et al.  Infection dynamics and virus-induced apoptosis in cell culture-based influenza vaccine production-Flow cytometry and mathematical modeling. , 2009, Vaccine.

[58]  D. O. White,et al.  Early events in the eclipse phase of influenza and parainfluenza virus infection. , 1966, Virology.

[59]  Sarah R. Lukens,et al.  The inflammatory response to influenza A virus (H1N1): An experimental and mathematical study. , 2015, Journal of theoretical biology.

[60]  A. Monto,et al.  Response to the 2009 pandemic: Effect on influenza control in wealthy and poor countries , 2011, Vaccine.

[61]  C. Clegg,et al.  Clinical vaccine development for H5N1 influenza , 2013, Expert review of vaccines.

[62]  Guy Boivin,et al.  Assessing the In Vitro Fitness of an Oseltamivir-Resistant Seasonal A/H1N1 Influenza Strain Using a Mathematical Model , 2011, PloS one.

[63]  T. Ben-Yedidia,et al.  Epitope-based vaccine against influenza , 2007, Expert review of vaccines.

[64]  Richard A. Miller.  The Aging Immune System: Primer and Prospectus , 1996, Science.

[65]  N. Lycke.  Recent progress in mucosal vaccine development: potential and limitations , 2012, Nature Reviews Immunology.

[66]  M. Meyer-Hermann.  Overcoming the Dichotomy of Quantity and Quality in Antibody Responses , 2014, The Journal of Immunology.

[67]  Andreas Handel,et al.  Neuraminidase Inhibitor Resistance in Influenza: Assessing the Danger of Its Generation and Spread , 2007, PLoS Comput. Biol..

[68]  M. Kenward,et al.  An Introduction to the Bootstrap , 2007 .

[69]  A. Vicino,et al.  A Stochastic Model for CD4+ T Cell Proliferation and Dissemination Network in Primary Immune Response , 2015, PloS one.

[70]  J. McCullers.  The co-pathogenesis of influenza viruses with bacteria in the lung , 2014, Nature Reviews Microbiology.

[71]  B. Grubeck‐Loebenstein,et al.  The aging immune system: Primary and secondary alterations of immune reactivity in the elderly , 1997, Experimental Gerontology.

[72]  A. Perelson,et al.  Simulation and Prediction of the Adaptive Immune Response to Influenza A Virus Infection , 2009, Journal of Virology.

[73]  I. Chou,et al.  Recent developments in parameter estimation and structure identification of biochemical and genomic systems. , 2009, Mathematical biosciences.

[74]  A. Shahangian,et al.  Type I IFNs mediate development of postinfluenza bacterial pneumonia in mice. , 2009, The Journal of clinical investigation.

[75]  Michael S Murillo,et al.  Towards multiscale modeling of influenza infection. , 2013, Journal of theoretical biology.

[76]  Alan S. Perelson,et al.  Effects of Aging on Influenza Virus Infection Dynamics , 2014, Journal of Virology.

[77]  David R. Anderson,et al.  Multimodel Inference , 2004 .

[78]  Sudhir Gupta,et al.  Characterization of naı̈ve, memory and effector CD8+ T cells: effect of age , 2004, Experimental Gerontology.

[79]  S. Harrison,et al.  Long-COVID Symptoms in Individuals Infected with Different SARS-CoV-2 Variants of Concern: A Systematic Review of the Literature , 2022, Viruses.

[80]  L. Stanberry,et al.  Safety and immunogenicity of a novel nanoemulsion mucosal adjuvant W805EC combined with approved seasonal influenza antigens. , 2012, Vaccine.

[81]  Andreas Handel,et al.  A review of mathematical models of influenza A infections within a host or cell culture: lessons learned and challenges ahead , 2011, BMC public health.

[82]  Chin‐Yun Lee,et al.  Influenza pandemics: past, present and future. , 2006, Journal of the Formosan Medical Association = Taiwan yi zhi.

[83]  A. Perelson,et al.  Kinetics of Coinfection with Influenza A Virus and Streptococcus pneumoniae , 2013, PLoS pathogens.

[84]  G. Nabel,et al.  Induction of Broadly Neutralizing H1N1 Influenza Antibodies by Vaccination , 2010, Science.

[85]  Anthony S Fauci,et al.  Predominant role of bacterial pneumonia as a cause of death in pandemic influenza: implications for pandemic influenza preparedness. , 2008, The Journal of infectious diseases.

[86]  K. Schughart,et al.  Systems biology and systems genetics - novel innovative approaches to study host-pathogen interactions during influenza infection. , 2014, Current opinion in virology.

[87]  T. Ben-Yedidia,et al.  Safety and Immunogenicity of Multimeric-001—a Novel Universal Influenza Vaccine , 2012, Journal of Clinical Immunology.

[88]  S. Siegel,et al.  Influenza promotes pneumococcal growth during coinfection by providing host sialylated substrates as a nutrient source. , 2014, Cell host & microbe.

[89]  P. Palese,et al.  Toward a universal influenza virus vaccine: prospects and challenges. , 2013, Annual review of medicine.

[90]  Kelli L Boyd,et al.  Influenza enhances susceptibility to natural acquisition of and disease due to Streptococcus pneumoniae in ferrets. , 2010, The Journal of infectious diseases.

[91]  M. Jordana,et al.  Influenza Infection Leads to Increased Susceptibility to Subsequent Bacterial Superinfection by Impairing NK Cell Responses in the Lung , 2010, The Journal of Immunology.

[92]  Stephen B. Martin,et al.  Viable Influenza A Virus in Airborne Particles from Human Coughs , 2014, Journal of occupational and environmental hygiene.

[93]  Daniel S. Chertow,et al.  Lethal Synergism of 2009 Pandemic H1N1 Influenza Virus and Streptococcus pneumoniae Coinfection Is Associated with Loss of Murine Lung Repair Responses , 2011, mBio.

[94]  Andreas Handel,et al.  Towards a quantitative understanding of the within-host dynamics of influenza A infections , 2010, Journal of The Royal Society Interface.

[95]  James M. McCaw,et al.  Interval Between Infections and Viral Hierarchy Are Determinants of Viral Interference Following Influenza Virus Infection in a Ferret Model , 2015, The Journal of infectious diseases.

[96]  L. Gottlieb,et al.  Asian influenza A in Boston, 1957-1958. I. Observations in thirty-two influenza-associated fatal cases. , 1959, A.M.A. archives of internal medicine.

[97]  Takeshi Kurata,et al.  Defense mechanisms against influenza virus infection in the respiratory tract mucosa. , 2004, Japanese journal of infectious diseases.

[98]  M. Hilty,et al.  Lowering the threshold of lung innate immune cell activation alters susceptibility to secondary bacterial superinfection. , 2011, The Journal of infectious diseases.

[99]  Jeffrey W. Smith,et al.  Stochastic Gene Expression in a Single Cell , 2022 .

[100]  D. Calado,et al.  Germinal Centers , 2017, Methods in Molecular Biology.

[101]  Xiaohua Xia,et al.  On Identifiability of Nonlinear ODE Models and Applications in Viral Dynamics , 2011, SIAM Rev..

[102]  T. Siu,et al.  Fatal viral infection-associated encephalopathy in two Chinese boys: a genetically determined risk factor of thermolabile carnitine palmitoyltransferase II variants , 2011, Journal of Human Genetics.

[103]  E. D. Kilbourne.  Influenza Pandemics of the 20th Century , 2006, Emerging infectious diseases.

[104]  S. Hensley,et al.  Challenges of selecting seasonal influenza vaccine strains for humans with diverse pre-exposure histories. , 2014, Current opinion in virology.

[105]  A. Monto,et al.  Influenza Control in the 21st Century: Optimizing Protection of Older Adults , 2022 .

[106]  C. R. Deboor,et al.  A practical guide to splines , 1978 .

[107]  C W Potter,et al.  A history of influenza , 2001, Journal of applied microbiology.

[108]  A. Zuckerman,et al.  Principles and practice of clinical virology , 1999 .

[109]  C. Beauchemin,et al.  Impact of the H275Y and I223V Mutations in the Neuraminidase of the 2009 Pandemic Influenza Virus In Vitro and Evaluating Experimental Reproducibility , 2015, PloS one.

[110]  P. Kozlowski,et al.  Mucosal vaccines: the promise and the challenge , 2006, Nature Reviews Immunology.

[111]  Ron A M Fouchier,et al.  Antigenic and Genetic Characteristics of Swine-Origin 2009 A(H1N1) Influenza Viruses Circulating in Humans , 2009, Science.

[112]  Hong Zhang,et al.  Possible origin of current influenza A H1N1 viruses. , 2009, The Lancet. Infectious diseases.

[113]  Michael Meyer-Hermann,et al.  A theory of germinal center B cell selection, division, and exit. , 2012, Cell reports.

[114]  Isabelle Bassi,et al.  Functional RNA delivery targeted to dendritic cells by synthetic nanoparticles. , 2012, Therapeutic delivery.

[115]  Gilles Clermont,et al.  A Dynamical Model of Human Immune Response to Influenza a Virus Infection , 2006 .

[116]  J. Paulsson.  Summing up the noise in gene networks , 2004, Nature.

[117]  A. Perelson,et al.  Influenza A virus infection kinetics: quantitative data and models , 2011, Wiley interdisciplinary reviews. Systems biology and medicine.

[118]  C. Weyand,et al.  Aging and T-cell diversity , 2007, Experimental Gerontology.

[119]  A. Harmsen,et al.  Both Influenza-Induced Neutrophil Dysfunction and Neutrophil-Independent Mechanisms Contribute to Increased Susceptibility to a Secondary Streptococcus pneumoniae Infection , 2006, Infection and Immunity.

[120]  B. Grenfell,et al.  The immune response and within-host emergence of pandemic influenza virus , 2014, The Lancet.

[121]  A. Larbi,et al.  Cellular signaling in the aging immune system. , 2014, Current opinion in immunology.

[122]  W. Hinrichs,et al.  Needle-free influenza vaccination. , 2010, The Lancet. Infectious diseases.

[123]  P. Doherty,et al.  Immunity to seasonal and pandemic influenza A viruses. , 2011, Microbes and infection.

[124]  Ruy M Ribeiro,et al.  Dynamics of hepatitis B virus infection. , 2002, Microbes and infection.

[125]  Y. Kawaoka,et al.  The Host Protease TMPRSS2 Plays a Major Role in In Vivo Replication of Emerging H7N9 and Seasonal Influenza Viruses , 2014, Journal of Virology.

[126]  C. Weyand,et al.  Understanding immunosenescence to improve responses to vaccines , 2013, Nature Immunology.

[127]  S. T. Buckland,et al.  An Introduction to the Bootstrap. , 1994 .

[128]  T. Ross,et al.  Impaired immune responses in the lungs of aged mice following influenza infection , 2009, Respiratory Research.

[129]  Alan S. Perelson,et al.  Modeling Within-Host Dynamics of Influenza Virus Infection Including Immune Responses , 2012, PLoS Comput. Biol..

[130]  J. McVernon,et al.  Prior Population Immunity Reduces the Expected Impact of CTL-Inducing Vaccines for Pandemic Influenza Control , 2015, PloS one.

[131]  Antonio Vicino,et al.  Identification of a branching process model for adaptive immune response , 2013, 52nd IEEE Conference on Decision and Control.

[132]  Stephanie A. Jones,et al.  Influenza vaccination of pregnant women and protection of their infants. , 2014, The New England journal of medicine.

[133]  H. Kiyono,et al.  Mucosal adjuvants for vaccines to control upper respiratory infections in the elderly , 2014, Experimental Gerontology.

[134]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[135]  R. C. Layton,et al.  Higher Level of Replication Efficiency of 2009 (H1N1) Pandemic Influenza Virus than Those of Seasonal and Avian Strains: Kinetics from Epithelial Cell Culture and Computational Modeling , 2010, Journal of Virology.

[136]  M. Farzan,et al.  Ifitm3 Limits the Severity of Acute Influenza in Mice , 2012, PLoS pathogens.

[137]  Alan S. Perelson,et al.  Quantifying the Early Immune Response and Adaptive Immune Response Kinetics in Mice Infected with Influenza A Virus , 2010, Journal of Virology.

[138]  Simon Wain-Hobson.  Virus Dynamics: Mathematical Principles of Immunology and Virology , 2001, Nature Medicine.

[139]  M A Nowak,et al.  The dynamics of hepatitis B virus infection. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[140]  P. Nelson,et al.  Tmprss2 Is Essential for Influenza H1N1 Virus Pathogenesis in Mice , 2013, PLoS pathogens.

[141]  C. Beauchemin,et al.  Neuraminidase inhibitors for treatment of human and avian strain influenza: A comparative modeling study. , 2011, Journal of theoretical biology.

[142]  J. Mcghee,et al.  Cutting Edge: The Mucosal Adjuvant Cholera Toxin Redirects Vaccine Proteins into Olfactory Tissues , 2000, The Journal of Immunology.

[143]  A Flahault,et al.  Influenza vaccine: the challenge of antigenic drift. , 2007, Vaccine.

[144]  Tim Schmitz,et al.  Principles And Practice Of Clinical Virology , 2016 .

[145]  Y. Kuang,et al.  Modeling the interaction of cytotoxic T lymphocytes and influenza virus infected epithelial cells. , 2010, Mathematical biosciences and engineering : MBE.

[146]  Alan S. Perelson,et al.  Effect of 1918 PB1-F2 Expression on Influenza A Virus Infection Kinetics , 2011, PLoS Comput. Biol..

[147]  B. Grubeck‐Loebenstein,et al.  Vaccines for the elderly. , 2012, Clinical microbiology and infection : the official publication of the European Society of Clinical Microbiology and Infectious Diseases.

[148]  Thijs Kuiken,et al.  H5N1 Virus Attachment to Lower Respiratory Tract , 2006, Science.

[149]  K. Klugman,et al.  The role of influenza in the severity and transmission of respiratory bacterial disease. , 2014, The Lancet. Respiratory medicine.

[150]  Hulin Wu,et al.  Sieve Estimation of Constant and Time-Varying Coefficients in Nonlinear Ordinary Differential Equation Models by Considering Both Numerical Error and Measurement Error. , 2010, Annals of statistics.

[151]  Jennifer L. Reed,et al.  Severe Human Lower Respiratory Tract Illness Caused by Respiratory Syncytial Virus and Influenza Virus Is Characterized by the Absence of Pulmonary Cytotoxic Lymphocyte Responses , 2007, The Journal of infectious diseases.

[152]  A. Handel,et al.  A Simple Mathematical Model Helps To Explain the Immunodominance of CD8 T Cells in Influenza A Virus Infections , 2008, Journal of Virology.

[153]  Xiaohua Xia,et al.  Identifiability of nonlinear systems with application to HIV/AIDS models , 2003, IEEE Trans. Autom. Control..

[154]  Klaus Schughart,et al.  Host Genetic Background Strongly Influences the Response to Influenza A Virus Infections , 2009, PloS one.

[155]  Ann Cullinane,et al.  Dynamics of Influenza Virus Infection and Pathology , 2010, Journal of Virology.

[156]  Carl T. Bergstrom,et al.  Models of CD8+ responses: 1. What is the antigen-independent proliferation program. , 2003, Journal of theoretical biology.

[157]  Laetitia Canini,et al.  Population Modeling of Influenza A/H1N1 Virus Kinetics and Symptom Dynamics , 2010, Journal of Virology.

[158]  K. M. Robinson,et al.  The immunology of influenza virus-associated bacterial pneumonia. , 2015, Current opinion in immunology.

[159]  A. Perelson.  Modelling viral and immune system dynamics , 2002, Nature Reviews Immunology.

[160]  C. Liao,et al.  Using experimental human influenza infections to validate a viral dynamic model and the implications for prediction , 2011, Epidemiology and Infection.

[161]  J. Li,et al.  An association between immunosenescence and CD4(+)CD25(+) regulatory T cells: a systematic review. , 2010, Biomedical and environmental sciences : BES.

[162]  J. McCullers,et al.  Live Attenuated Influenza Vaccine Enhances Colonization of Streptococcus pneumoniae and Staphylococcus aureus in Mice , 2014, mBio.

[163]  E. Kovacs,et al.  Aging of the Innate Immune System: An Update. , 2011, Current immunology reviews.

[164]  A. Oberg,et al.  Vaccinomics, adversomics, and the immune response network theory: individualized vaccinology in the 21st century. , 2013, Seminars in immunology.

[165]  A. Perelson,et al.  Kinetics of Influenza A Virus Infection in Humans , 2006, Journal of Virology.

[166]  O. Lesur,et al.  Innate immunosenescence: effect of aging on cells and receptors of the innate immune system in humans. , 2012, Seminars in immunology.

[167]  Sarah A. Scott,et al.  Phospholipase D Facilitates Efficient Entry of Influenza Virus, Allowing Escape from Innate Immune Inhibition* , 2014, The Journal of Biological Chemistry.

[168]  Pu Li,et al.  Identification of parameter correlations for parameter estimation in dynamic biological models , 2013, BMC Systems Biology.

[169]  Udo Reichl,et al.  Mathematical model of influenza A virus production in large-scale microcarrier culture. , 2005, Biotechnology and bioengineering.

[170]  F. Ansaldi,et al.  Adjuvants and alternative routes of administration towards the development of the ideal influenza vaccine , 2011, Human vaccines.

[171]  Michael Meyer-Hermann,et al.  Ebola virus infection modeling and identifiability problems , 2015, Front. Microbiol..