Modelling the Immune Response to Cancer: An Individual-Based Approach Accounting for the Difference in Movement Between Inactive and Activated T Cells

A growing body of experimental evidence indicates that immune cells move in an unrestricted search pattern if they are in the pre-activated state, whilst they tend to stay within a more restricted area upon activation induced by the presence of tumour antigens. This change in movement is not often considered in the existing mathematical models of the interactions between immune cells and cancer cells. With the aim to fill such a gap in the existing literature, in this work we present a spatially structured individual-based model of tumour–immune competition that takes explicitly into account the difference in movement between inactive and activated immune cells. In our model, a Lévy walk is used to capture the movement of inactive immune cells, whereas Brownian motion is used to describe the movement of antigen-activated immune cells. The effects of activation of immune cells, the proliferation of cancer cells and the immune destruction of cancer cells are also modelled. We illustrate the ability of our model to reproduce qualitatively the spatial trajectories of immune cells observed in experimental data of single-cell tracking. Computational simulations of our model further clarify the conditions for the onset of a successful immune action against cancer cells and may suggest possible targets to improve the efficacy of cancer immunotherapy. Overall, our theoretical work highlights the importance of taking into account spatial interactions when modelling the immune response to cancer cells.