Mathematical Perspectives on Tumour–Immune Dynamics in a Changing Landscape (PIMS network-wide colloquium)

Immune cell infiltration in solid tumours was once regarded as clear evidence of the body’s attempt to eradicate a malignant threat. It is, however, now well established that tumours can co-opt immune cells, reprogramming them from tumour-suppressive defenders into tumour-promoting collaborators. Immunotherapy aims to disrupt this process by enhancing or restoring effective immune function. Despite its clinical success in some settings, patient responses to immunotherapy remain highly variable, reflecting the underlying complexity of tumour–immune interactions. In this talk, we explore how diverse mathematical approaches—including mechanistic mathematical modelling and topological data analysis—can help to unravel these intricate interactions. We present recent results illustrating how these complementary methods provide understanding of tumour–immune behaviour and may help explain differential responses to immunotherapy.