The past decade's technological advances have led to the development of immunotherapies, which differ from conventional anti-cancer therapies by targeting tumour-immune interactions to enhance the effectiveness of the anti-tumour immune response. However, these interactions are based on complex mechanisms that make it difficult to design treatments to effectively boost the immune response. For this reason, mathematical models are useful tools for reproducing and predicting the spatio-temporal dynamics of interactions between tumour and immune cells, in order to test the potential of new therapeutic techniques in a flexible and affordable way. In this talk, we present discrete and continuum models describing the spatio-temporal dynamics of the interactions between tumour and immune cells, with the goal to investigate the biological settings which allow for the clearance or the escape of the tumour. The discrete models track the dynamics of single cells, thus permitting the representation of single cell-scale mechanisms, and are sufficiently detailed and specific to qualitatively investigate and reproduce empirical observations. As for the continuum models, they are formally derived from the discrete models through suitable asymptotic methods. The results of computational simulations of the discrete models show that there is an excellent quantitative agreement between them and numerical solutions of the corresponding continuum models, and further clarify the conditions for successful and unsuccessful immune surveillance.
Romain Duboscq, David Lafontaine
