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A General Framework for Multiscale Modeling of Tumor–Immune System Interactions

  • Marina Dolfin
  • Mirosław LachowiczEmail author
  • Zuzanna Szymańska
Chapter
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)

Abstract

In this paper we review methods that allow the construction of a consistent set of models that may describe the interactions between a tumor and the immune system on microscopic, mesoscopic, and macroscopic scales. The presented structures may be a basis for a description on the sub–cellular, cellular, and macroscopic levels. Important open problems are indicated.

Keywords

Tumor Immune system Asymptotic analysis Multiscale description Kinetic equations Systems of nonlinear ODEs 

Notes

Acknowledgment

M.D. acknowledges a support from the National Group for Mathematical Physics through the grant Visiting Professors 2013. M.L. acknowledges a support from the National Science Centre of Poland through grant N N201 605640. Z.S. acknowledges a support from the National Science Centre of Poland through grant DEC-2011/01/D/ST1/04133.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Marina Dolfin
    • 1
  • Mirosław Lachowicz
    • 2
    Email author
  • Zuzanna Szymańska
    • 3
  1. 1.Department of Civil, Computer, Construction and Environmental Engineering and of Applied Mathematics (DICIEAMA)University of Messina, Contrada Di DioMessinaItaly
  2. 2.Institute of Applied Mathematics and Mechanics, Faculty of Mathematics, Informatics and MechanicsUniversity of WarsawWarsawPoland
  3. 3.ICMUniversity of WarsawWarsawPoland

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