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On a Mathematical Model of Adaptive Immune Response to Viral Infection

  • Mikhail Kolev
  • Ana Markovska
  • Adam Korpusik
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8236)

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.

Keywords

numerical simulations integro-differential equations nonlinear dynamics kinetic model 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Mikhail Kolev
    • 1
  • Ana Markovska
    • 2
  • Adam Korpusik
    • 3
  1. 1.Faculty of Mathematics and Computer ScienceUniversity of Warmia and MazuryOlsztynPoland
  2. 2.Faculty of Mathematics and Natural SciencesSouth-West University “N. Rilski”BlagoevgradBulgaria
  3. 3.Faculty of Technical SciencesUniversity of Warmia and MazuryOlsztynPoland

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