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We present a spatial hybrid discrete-continuum modelling framework for theinteraction dynamics between tumour cells and cytotoxic T cells, which play apivotal role in the immune response against tumours. In this framework, tumourcells and T cells are modelled as individual agents while chemokines that drivethe chemotactic movement of T cells towards the tumour are modelled as acontinuum. We formally derive the continuum counterpart of this model, which isgiven by a coupled system that comprises an integro-differential equation forthe density of tumour cells, a partial differential equation for the density ofT cells, and a partial differential equation for the concentration ofchemokines. We report on computational results of the hybrid model and showthat there is an excellent quantitative agreement between them and numericalsolutions of the corresponding continuum model. These results shed light on themechanisms that underlie the emergence of different levels of infiltration of Tcells into the tumour and elucidate how T-cell infiltration shapes anti-tumourimmune response. Moreover, to present a proof of concept for the idea that,exploiting the computational efficiency of the continuum model, extensivenumerical simulations could be carried out, we investigate the impact of T-cellinfiltration on the response of tumour cells to different types of anti-cancerimmunotherapy.

A hybrid discrete-continuum modelling approach to explore the impact of T-cell infiltration on anti-tumour immune response