Mathematical Modelling of Tumour-immune interaction: discrete and continuum approaches
vendredi 17 décembre 2021, 11h00 - 12h00
The recent successes of immunotherapy for the treatment of tumours has highlighted the importance of the interactions between tumour cells and immune cells. However, these interactions are based on complex mechanisms, making it difficult to design effective treatments aimed at strengthening the immune response. Therefore, mathematical models are usefull to reproduce and predict the spatio-temporal dynamics of tumour growth, describing the interaction of the tumour with the immune cells.
In this talk, we start by presenting a stochastic individual-based model capturing the interactions between tumour cells and immune cells. Considering different initial compositions of the tumour, we investigate how intra-tumour heterogeneity (ITH) affects the anti-tumour immune response. In our model, ITH can vary with the number of tumour antigens (i.e. the number of sub-populations of tumour cells) and with the level of antigen presentation (i.e. the immunogenicity of tumour cells). Computational simulations show that both components play a role in the anti-tumour immune response. In the second part of the talk, we re-formulate the individual-based model, and we introduce a continuum model formally obtained as the deterministic continuum limit of such individual-based model. We report on computational results of the individual-based model, and show that there is a good agreement between them and numerical results of the continuum model.