  We present a spatial hybrid discrete-continuum modelling framework for the
interaction dynamics between tumour cells and cytotoxic T cells, which play a
pivotal role in the immune response against tumours. In this framework, tumour
cells and T cells are modelled as individual agents while chemokines that drive
the chemotactic movement of T cells towards the tumour are modelled as a
continuum. We formally derive the continuum counterpart of this model, which is
given by a coupled system that comprises an integro-differential equation for
the density of tumour cells, a partial differential equation for the density of
T cells, and a partial differential equation for the concentration of
chemokines. We report on computational results of the hybrid model and show
that there is an excellent quantitative agreement between them and numerical
solutions of the corresponding continuum model. These results shed light on the
mechanisms that underlie the emergence of different levels of infiltration of T
cells into the tumour and elucidate how T-cell infiltration shapes anti-tumour
immune response. Moreover, to present a proof of concept for the idea that,
exploiting the computational efficiency of the continuum model, extensive
numerical simulations could be carried out, we investigate the impact of T-cell
infiltration on the response of tumour cells to different types of anti-cancer
immunotherapy.
