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Matem. Mod., 2001, Volume 13, Number 8, Pages 65–84 (Mi mm771)  

This article is cited in 7 scientific papers (total in 7 papers)

A variational principle for modeling infection immunity by the example of pneumonia

A. A. Romanyukhaa, S. G. Rudnev

a Institute of Numerical Mathematics, Russian Academy of Sciences

Abstract: The paper deals with investigation of general principles which regulate infection immunity depending on environmental factors. An approach is considered basing on the assumption that a relationship exists between the organism's fitness and energy expenditures on various functions. By the example of the mathematical model of pneumonia a quantitative energy cost estimates of the main processes of disease and of the health maintenance are compared. The problem of determining the values of model parameters is formulated using the minimality criterion of infection immunity energy expenditures. Particular case of the problem is considered for which dependence of optimal defense regimens from infection rate and microorganism's properties is studied.

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Received: 24.03.2000

Citation: A. A. Romanyukha, S. G. Rudnev, “A variational principle for modeling infection immunity by the example of pneumonia”, Matem. Mod., 13:8 (2001), 65–84

Citation in format AMSBIB
\Bibitem{RomRud01}
\by A.~A.~Romanyukha, S.~G.~Rudnev
\paper A~variational principle for modeling infection immunity by the example of pneumonia
\jour Matem. Mod.
\yr 2001
\vol 13
\issue 8
\pages 65--84
\mathnet{http://mi.mathnet.ru/mm771}
\zmath{https://zbmath.org/?q=an:0980.92019}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Romanyukha, A. S. Karkach, “Individualno-orientirovannaya model dinamiki infektsionnogo protsessa v neodnorodnoi populyatsii”, Matem. modelirovanie, 15:5 (2003), 95–105  mathnet  zmath
    2. A. S. Karkach, A. A. Romanyukha, “The Energy Criterion for Quality of Immune Defence and Pathogenicity of Microorganisms”, Autom. Remote Control, 64:6 (2003), 975–984  mathnet  crossref  mathscinet  zmath  isi
    3. S. G. Rudnev, A. A. Romanyukha, A. I. Yashin, “Modelirovanie razvitiya T-sistemy immuniteta i otsenka effektivnosti raspredeleniya resursov”, Matem. modelirovanie, 19:11 (2007), 25–42  mathnet  zmath
    4. I. P. Bolodurina, Yu. P. Lugovskova, “Optimalnoe upravlenie immunologicheskimi reaktsiyami organizma cheloveka”, Probl. upravl., 5 (2009), 44–52  mathnet
    5. Marchuk G.I., Romanyukha A.A., “Mathematical modelling and the homeostatic function of the immune system”, Russian J Numer Anal Math Modelling, 25:6 (2010), 563–580  crossref  mathscinet  zmath  isi  elib  scopus
    6. Orekhova I.A., “Prikladnoe ispolzovanie differentsialnykh uravnenii s zapazdyvayuschim argumentom”, Nauka Krasnoyarya, 2012, no. 3, 30–38  elib
    7. M. A. Skvortsova, “Asimptoticheskie svoistva reshenii v modeli protivobakterialnogo immunnogo otveta”, Sib. elektron. matem. izv., 15 (2018), 1198–1215  mathnet  crossref
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