The logistic growth model as an approximating model for viral load measurements of influenza A virus

Detailed kinetic models of viral replication have led to greater understanding of disease progression and the effects of therapy. Viral load is important as a driver of the immune response to the viral infection and in determining the infectiousness of an infected individual. However in many cases when examining the immune response or spread of infection, it may be sufficient to have a more parsimonious model of viral load than the detailed kinetic models. Here we review properties of detailed kinetic models of Influenza A virus and discuss the use of a logistic growth model to approximate viral load. We make application of the tools of identifiability analysis and model selection to assess the logistic growth model as a proxy for viral load. We find that the parameters of the logistic growth model can be related to the parameters of a detailed viral kinetic model, the logistic growth model makes a strong fit to viral load data with a small number of parameters, and that these parameters can be reliably identified from viral load data generated by a detailed kinetic model.

[1]  Akira Sasaki,et al.  Modeling host-parasite coevolution: a nested approach based on mechanistic models. , 2002, Journal of theoretical biology.

[2]  K. Legge,et al.  Lymph node dendritic cells control CD8+ T cell responses through regulated FasL expression. , 2005, Immunity.

[3]  D. Cummings,et al.  Strategies for containing an emerging influenza pandemic in Southeast Asia , 2005, Nature.

[4]  Flute , 1941 .

[5]  N. Ferguson,et al.  Time lines of infection and disease in human influenza: a review of volunteer challenge studies. , 2008, American journal of epidemiology.

[6]  Xing Xie,et al.  Monoclonal antibody specific to HA2 glycopeptide protects mice from H3N2 influenza virus infection , 2015, Veterinary Research.

[7]  F. Hayden,et al.  Local and systemic cytokine responses during experimental human influenza A virus infection. Relation to symptom formation and host defense. , 1998, The Journal of clinical investigation.

[8]  J. Robins,et al.  Transmissibility of 1918 pandemic influenza , 2004, Nature.

[9]  James D. Murray.  Mathematical Biology: I. An Introduction , 2007 .

[10]  A S Perelson,et al.  Drug concentration heterogeneity facilitates the evolution of drug resistance. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[11]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

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

[13]  S. Schultz-Cherry,et al.  Visualizing real-time influenza virus infection, transmission and protection in ferrets , 2015, Nature Communications.

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

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

[16]  Alan S. Perelson,et al.  Mathematical Analysis of HIV-1 Dynamics in Vivo , 1999, SIAM Rev..

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

[18]  T. Iwasaki,et al.  Defense mechanisms against primary influenza virus infection in mice. I. The roles of interferon and neutralizing antibodies and thymus dependence of interferon and antibody production. , 1977, Journal of immunology.

[19]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[20]  Dennis L. Chao,et al.  FluTE, a Publicly Available Stochastic Influenza Epidemic Simulation Model , 2010, PLoS Comput. Biol..

[21]  David R. Anderson,et al.  Model selection and multimodel inference : a practical information-theoretic approach , 2003 .

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

[23]  Sergei S. Pilyugin,et al.  Global analysis of within host virus models with cell-to-cell viral transmission , 2014 .

[24]  Frederick R Adler,et al.  An accurate two-phase approximate solution to an acute viral infection model , 2010, Journal of mathematical biology.

[25]  P. Verhulst,et al.  Deuxième Mémoire sur la Loi d'Accroissement de la Population. , 2022 .

[26]  Fabio Cavallini,et al.  Fitting a Logistic Curve to Data , 1993 .

[27]  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.

[29]  Harel Dahari,et al.  Triphasic decline of hepatitis C virus RNA during antiviral therapy , 2007, Hepatology.

[30]  S. Ellner,et al.  Dynamic Models in Biology , 2006 .

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

[32]  M. Nowak,et al.  Virus dynamics: Mathematical principles of immunology and virology , 2001 .

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

[34]  A. Perelson,et al.  Dynamics of HIV infection of CD4+ T cells. , 1993, Mathematical biosciences.

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

[36]  David R. Anderson,et al.  Model Selection and Multimodel Inference , 2003 .

[37]  Evan Haskell,et al.  Modeling of Humoral Immune Response to Repeated Influenza A Virus Infections , 2015 .

[38]  Nicolas Bacaër,et al.  A Short History of Mathematical Population Dynamics , 2010 .