Computational and Mathematical Methods in Medicine
Volume 10 (2009), Issue 1, Pages 9-38
doi:10.1080/17486700801982713
Original Article

Mathematical Modelling of Immune Response in Tissues

B. Su,1 W. Zhou,1 K. S. Dorman,2 and D. E. Jones3

1Department of Mathematics, Iowa State University, Ames, IA 50010, USA
2Department of Genetics Development and Cell Biology, Iowa State University, Ames, IA 50010, USA
3Department of Veterinary Pathology, Iowa State University, Ames, IA 50010, USA

Received 14 December 2007; Accepted 11 January 2008

Copyright © 2009 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We have developed a spatial–temporal mathematical model (PDE) to capture fundamental aspects of the immune response to antigen. We have considered terms that broadly describe intercellular communication, cell movement, and effector function (activation or inhibition). The PDE model is robust to variation in antigen load and it can account for (1) antigen recognition, (2) an innate immune response, (3) an adaptive immune response, (4) the elimination of antigen and subsequent resolution of the immune response or (5) equilibrium of the immune response to the presence of persistent antigen (chronic infection) and the formation of a granuloma.