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The logistic growth model as an approximating model for viral load measurements of influenza a virus. (English) Zbl 07313777
Summary: 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.
MSC:
92 Biology and other natural sciences
62 Statistics
Software:
DEDiscover; FluTE
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[2] Akaike, H., Information theory and an extension of the maximum likelihood principle, (Selected Papers of Hirotugu Akaike (1998), Springer), 199-213
[4] Arenas, A. R.; Muhammad, S.; Nguyen, L.; Andreansky, S.; Haskell, E., Modeling of humoral immune response to repeated influenza A virus infections, Biomath. Commun., 2 (2015)
[5] Bacaër, N., A Short History of Mathematical Population Dynamics (2011), Springer Science & Business Media
[6] Baccam, P.; Beauchemin, C.; Macken, C. A.; Hayden, F. G.; Perelson, A. S., Kinetics of influenza A virus infection in humans, J. Virol., 80, 7590-7599 (2006)
[7] Bocharov, G.; Romanyukha, A., Mathematical model of antiviral immune response III. Influenza A virus infection, J. Theor. Biol., 167, 323-360 (1994)
[8] Burnham, K. P.; Anderson, D. R., Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach (2002), Springer Science & Business Media
[9] Canini, L.; Carrat, F., Population modeling of influenza a/h1n1 virus kinetics and symptom dynamics, J. Virol., 85, 2764-2770 (2011)
[10] Carrat, F.; Vergu, E.; Ferguson, N. M.; Lemaitre, M.; Cauchemez, S.; Leach, S.; Valleron, A. J., Time lines of infection and disease in human influenza: a review of volunteer challenge studies, Am. J. Epidemiol., 167, 775-785 (2008)
[11] Cavallini, F., Fitting a logistic curve to data, College Math. J., 24, 247-253 (1993)
[12] Chao, D. L.; Halloran, M. E.; Obenchain, V. J.; Longini, I. M., FluTE, a publicly available stochastic influenza epidemic simulation model, PLoS Comput. Biol., 6, e1000656 (2010)
[13] Dahari, H.; Ribeiro, R. M.; Perelson, A. S., Triphasic decline of hepatitis C virus RNA during antiviral therapy, Hepatology, 46, 16-21 (2007)
[14] Dobrovolny, H. M.; Reddy, M. B.; Kamal, M. A.; Rayner, C. R.; Beauchemin, C. A., Assessing mathematical models of influenza infections using features of the immune response, PLoS One, 8, e57088 (2013)
[15] Ellner, S. P.; Guckenheimer, J., Dynamic Models in Biology (2011), Princeton University Press
[16] Ferguson, N. M.; Cummings, D. A.; Cauchemez, S.; Fraser, C.; Riley, S.; Meeyai, A.; Iamsirithaworn, S.; Burke, D. S., Strategies for containing an emerging influenza pandemic in southeast asia, Nature, 437, 209-214 (2005)
[17] Gilchrist, M. A.; Sasaki, A., Modeling host-parasite coevolution: a nested approach based on mechanistic models, J. Theor. Biol., 218, 289-308 (2002)
[18] Hancioglu, B.; Swigon, D.; Clermont, G., A dynamical model of human immune response to influenza A virus infection, J. Theor. Biol., 246, 70-86 (2007)
[19] Hayden, F. G.; Fritz, R.; Lobo, M. C.; Alvord, W.; Strober, W.; Straus, S. E., Local and systemic cytokine responses during experimental human influenza A virus infection. Relation to symptom formation and host defense, J. Clin. Investig., 101, 643 (1998)
[20] Iwasaki, T.; Nozima, T., 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, J. Immunol., 118, 256-263 (1977)
[21] Karlsson, E. A.; Meliopoulos, V. A.; Savage, C.; Livingston, B.; Mehle, A.; Schultz-Cherry, S., Visualizing real-time influenza virus infection, transmission and protection in ferrets, Nature Commun., 6 (2015)
[22] Kepler, T. B.; Perelson, A. S., Drug concentration heterogeneity facilitates the evolution of drug resistance, Proc. Natl. Acad. Sci. USA, 95, 11514-11519 (1998)
[23] Lee, H. Y.; Topham, D. J.; Park, S. Y.; Hollenbaugh, J.; Treanor, J.; Mosmann, T. R.; Jin, X.; Ward, B. M.; Miao, H.; Holden-Wiltse, J., Simulation and prediction of the adaptive immune response to influenza A virus infection, J. Virol., 83, 7151-7165 (2009)
[24] Legge, K. L.; Braciale, T. J., Lymph node dendritic cells control CD8+ T cell responses through regulated FasL expression, Immunity, 23, 649-659 (2005)
[25] Miao, H.; Hollenbaugh, J. A.; Zand, M. S.; Holden-Wiltse, J.; Mosmann, T. R.; Perelson, A. S.; Wu, H.; Topham, D. J., Quantifying the early immune response and adaptive immune response kinetics in mice infected with influenza A virus, J. Virol., 84, 6687-6698 (2010)
[26] Miao, H.; Xia, X.; Perelson, A. S.; Wu, H., On identifiability of nonlinear ODE models and applications in viral dynamics, SIAM Rev., 53, 3-39 (2011)
[27] Mills, C. E.; Robins, J. M.; Lipsitch, M., Transmissibility of 1918 pandemic influenza, Nature, 432, 904-906 (2004)
[28] Murray, J. D., (Mathematical Biology I: An Introduction. Mathematical Biology I: An Introduction, Interdisciplinary Applied Mathematics, vol. 17 (2002), Springer: Springer New York, NY, USA)
[29] Murray, J. D., (Mathematical Biology II: Spatial Models and Biomedical Applications. Mathematical Biology II: Spatial Models and Biomedical Applications, Interdisciplinary Applied Mathematics, vol. 18 (2003), Springer-Verlag New York Incorporated)
[30] Nowak, M.; May, R. M., Virus Dynamics: Mathematical Principles of Immunology and Virology (2000), Oxford University Press
[31] Perelson, A. S.; Kirschner, D. E.; De Boer, R., Dynamics of hiv infection of cd4+ t cells, Math. Biosci., 114, 81-125 (1993)
[32] Perelson, A. S.; Nelson, P. W., Mathematical analysis of HIV-1 dynamics in vivo, SIAM Rev., 41, 3-44 (1999)
[33] Pourbashash, H.; Pilyugin, S. S.; McCluskey, C.; De Leenheer, P., Global analysis of within host virus models with cell-to-cell viral transmission, Discrete Contin. Dyn. Syst. Ser. B, 19, 3341-3357 (2014)
[34] Smith, A. M.; Adler, F. R.; Perelson, A. S., An accurate two-phase approximate solution to an acute viral infection model, J. Math. Biol., 60, 711-726 (2010)
[35] Verhulst, P., La loi d’accroissement de la population, Nouv. Mem. Acad. Roy. Soc. Belle-lettr. Brux., 18, 1 (1845)
[37] Xia, X.; Moog, C. H., Identifiability of nonlinear systems with application to HIV/AIDS models, IEEE Trans. Automat. Control, 48, 330-336 (2003)
[38] Xie, X.; Lin, Y.; Pang, M.; Zhao, Y.; Kalhoro, D. H.; Lu, C.; Liu, Y., Monoclonal antibody specific to HA2 glycopeptide protects mice from H3N2 influenza virus infection, Veterin. Res., 46, 33 (2015)
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