Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Simulation of Flow in Fractured Poroelastic Media: A Comparison of Different Discretization Approaches Read chapter Read first chapter

2015 | OriginalPaper | Chapter

Numerical Investigation of Adaptive Immune Response to Viral Infection

Authors : Mikhail Kolev, Ana Markovska, Boiana Garkova

Published in: Finite Difference Methods,Theory and Applications

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this paper we present a new mathematical model describing acquired immune response to viral infection. The model is formulated as a system of six ordinary differential equations (ODE). Conditions for existence, uniqueness and non-negativity of the solutions are studied. Numerical simulations for the case of dominating cellular immunity and various initial values of concentrations of virus particles are presented and discussed.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Splitting Scheme for Poroelasticity and Thermoelasticity Problems
next chapter Efficient Application of the Two-Grid Technique for Solving Time-Fractional Non-linear Parabolic Problem
Literature
1.
Abbas, A., Lichtman, A.: Basic Immunology: Functions and Disorders of the Immune System. Elsevier, Philadelphia (2009)
2.
Arlotti, L., Bellomo, N., Lachowicz, M.: Kinetic equations modelling population dynamics. Transp. Theory Statist. Phys. 29, 125–139 (2000)MATHMathSciNetCrossRef
3.
Belleni-Morante, A.: Applied Semigroups and Evolution Equations. Oxford University Press, Oxford (1979)MATH
4.
Bellomo, N., Carbonaro, B.: Toward a mathematical theory of living systems focusing on developmental biology and evolution: a review and perspectives. Phys. Life Rev. 8, 1–18 (2011)CrossRef
5.
Bellomo, N., Bianca, C.: Towards a Mathematical Theory of Complex Biological Systems. World Scientific, Singapore (2011)MATH
6.
Bianca, C.: Mathematical modelling for keloid formation triggered by virus: malignant effects and immune system competition. Math. Models Methods Appl. Sci. 21, 389–419 (2011)MATHMathSciNetCrossRef
7.
Hartman, P.: Ordinary Differential Equations. John Wiley and Sons, New York (1964)MATH
8.
Kolev, M., Korpusik, A., Markovska, A.: Adaptive immunity and CTL differentiation - a kinetic modeling approach. Math. Eng. Sci. Aerosp. 3, 285–293 (2012)MATH
9.
Kolev, M., Garkova, B.: Numerical implementation of reaction-diffusion-chemotaxis model of cancer invasion using nonstandard finite difference method. In: Proceedings of the XIX National Conference on Applications of Mathematics in Biology and Medicine, Jastrzebia Gora, Poland, pp. 60–65 (2013)
10.
Marchuk, G.: Mathematical modeling of Immune Response in Infections Diseases. Kluwer Academic Publishers, Dordrecht (1997)CrossRef
11.
12.
Metadata
Title
Numerical Investigation of Adaptive Immune Response to Viral Infection
Authors
Mikhail Kolev
Ana Markovska
Boiana Garkova
Copyright Year
2015
Book
Finite Difference Methods,Theory and Applications

Print ISBN: 978-3-319-20238-9

Electronic ISBN: 978-3-319-20239-6

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-20239-6_26

Premium Partner

    Image Credits