Research Output per year
In this paper, a mathematical model describing the one-dimensional growth of a solid tumour (for example, a malignant melanoma of the skin) in the presence of an immune system response, is-presented. In particular, attention is focussed upon the interaction of tumour cells with so-called tumour-infiltrating cytotoxic lymphocytes (TICLs), in a small, multicellular tumour, without central necrosis and at some stage prior to angiogenesis. At this stage the immune cells and the tumour cells are in a state of dynamic equilibrium (cancer dormancy). The resulting system of three nonlinear partial differential equations is analysed and numerical simulations are presented. The numerical simulations demonstrate the existence of cell distributions that are quasi-stationary in time but unstable and heterogeneous in space. The resulting rich spatio-temporal dynamic behaviour of the system is compared with actual experimental evidence.
|Publication status||Published - 1997|
|Event||International Conference on Mathematical Models in Medical and Health Sciences - Nashville, United States|
Duration: 28 May 1997 → 31 May 1997
|Conference||International Conference on Mathematical Models in Medical and Health Sciences|
|Period||28/05/97 → 31/05/97|
- Tumour necrosis factor
- T cell recognition
- Mathematical models
Davidson, F. & Stepanova, L. A., 1998, Mathematical models in medical and health science. Mary Ann, H., Gieri, S. & Glenn F., W. (eds.). Vanderbilt University Press
Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
Chaplain, M., Kuznetsov, V. A., James, Z. H., & Stepanova, L. A. (1997). Spatio-temporal dynamics of the immune system response to cancer. Paper presented at International Conference on Mathematical Models in Medical and Health Sciences, Nashville, United States.