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Stat Biosci. 2015 May 1;7(1):147-166.

Quantifying Immune Response to Influenza Virus Infection via Multivariate Nonlinear ODE Models with Partially Observed State Variables and Time-Varying Parameters.

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Department of Biostatistics and Computational Biology, University of Rochester School of Medicine and Dentistry, 601 Elmwood Avenue, Box 630, Rochester, New York 14642.
David H. Smith Center for Vaccine Biology & Immunology, Department of Microbiology and Immunology, University of Rochester School of Medicine and Dentistry, NY, 14642.
Department of Medicine, Division of Nephrology, University of Rochester School of Medicine and Dentistry, 601 Elmwood Avenue, Box 675, Rochester, New York 14642.


Influenza A virus (IAV) infection continues to be a global health threat, as evidenced by the outbreak of the novel A/California/7/2009 IAV strain. Previous flu vaccines have proven less effective than hoped for emerging IAV strains, indicating a more thorough understanding of immune responses to primary infection is needed. One issue is the difficulty in directly measuring many key parameters and variables of the immune response. To address these issues, we considered a comprehensive workflow for statistical inference for ordinary differential question (ODE) models with partially observed variables and time-varying parameters, including identifiability analysis, two-stage and NLS estimation, and model selection etc‥ In particular, we proposed a novel one-step method to verify parameter identifiability and formulate estimating equations simultaneously. Thus, the pseudo-LS method can now deal with general ODE models with partially observed state variables for the first time. Using this workflow, we verified the relative significance of various immune factors to virus control, including target epithelial cells, cytotoxic T-lymphocyte (CD8+) cells and IAV specific antibodies (IgG and IgM). Factors other than cytotoxic T-lymphocyte (CTL) killing contributed the most to the loss of infected epithelial cells, though the effects of CTL are still significant. IgM antibody was found to be the major contributor to neutralization of free infectious viral particles. Also, the maximum viral load, which correlates well with mortality, was found to depend more on viral replication rates than infectivity. In contrast to current hypotheses, the results obtained via our methods suggest that IgM antibody and viral replication rates may be worth of further explorations in vaccine development.


Identifiability analysis; Influenza A virus infection; Multivariate differential equation model; Partially observed state variables; Time-varying parameter estimation; Two-stage smoothing-based estimation

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