Using a hybrid cellular automaton, we investigate the transient and asymptotic dynamics of the cell-mediated immune response to tumour growth. We analyse the correspondence between this dynamics and the three phases of the theory of immunoedition: elimination, equilibrium and escape. Our results demonstrate that the immune system can keep a tumour dormant for long periods of time, but that this dormancy is based on a frail equilibrium between the mechanisms that spur the immune response and the growth of the tumour. Thus, we question the capacity of the cell-mediated immune response to sustain long periods of dormancy, as those appearing in recurrent disease. We suggest that its role might be rather to synergize with other types of tumour dormancy.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'.
Keywords: immune cells; mathematical modelling; tumour growth.
© 2017 The Author(s).