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On a Mathematical Model of Adaptive Immune Response to Viral Infection

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Numerical Analysis and Its Applications (NAA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8236))

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Abstract

In this paper we study a mathematical model formulated within the framework of the kinetic theory for active particles. The model is a bilinear system of integro-differential equations (IDE) of Boltzmann type and it describes the interactions between virus population and the adaptive immune system. The population of cytotoxic T lymphocytes is additionally divided into precursor and effector cells. Conditions for existence and uniqueness of the solution are studied. Numerical simulations of the model are presented and discussed.

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References

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Author information

Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, University of Warmia and Mazury, Słoneczna 54, 10-710, Olsztyn, Poland

    Mikhail Kolev

  2. Faculty of Mathematics and Natural Sciences, South-West University “N. Rilski”, Ivan Mihajlov 66, 2700, Blagoevgrad, Bulgaria

    Ana Markovska

  3. Faculty of Technical Sciences, University of Warmia and Mazury, Oczapowskiego 11, 10-719, Olsztyn, Poland

    Adam Korpusik

Authors
  1. Mikhail Kolev
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  2. Ana Markovska
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  3. Adam Korpusik
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Editor information

Editors and Affiliations

  1. Institute of Information and Communication Technlogies, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl25A, 1113, Sofia, Bulgaria

    Ivan Dimov

  2. Department of Applied Analysis, Pázm\’{a}ny P\’{e}ter s\’{e}t\’{a}ny 1/C,, Eötvös Loránd University, 1117, Budapest, Hungary

    István Faragó

  3. University of Rousse, 8 Studentska Str.,, 7017, Rousse, Bulgaria

    Lubin Vulkov

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Kolev, M., Markovska, A., Korpusik, A. (2013). On a Mathematical Model of Adaptive Immune Response to Viral Infection. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2012. Lecture Notes in Computer Science, vol 8236. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41515-9_39

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  • DOI: https://doi.org/10.1007/978-3-642-41515-9_39

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41514-2

  • Online ISBN: 978-3-642-41515-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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