Mathematical modelling of immune response in tissues

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.

Keywords:

• immune system; biological sensor; regulatory mechanism; chemotaxis process; homogenization; numerical simulation

AMS Subject Classification:

• 35M10
• 35K55
• 92B05
• 92C37
• 92C50

Acknowledgements

The authors are grateful to Y. Liu and P. Sacks for their numerous assists on parameter estimates and numerical simulations. B. Su is partially supported by NSF Grant Nos. DMS 0406014 and DMS 0708479.