Spatio-temporal dynamics of the immune system response to cancer

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.