The success of oncolytic virotherapies depends on the tumour microenvironment, which contains a large number of infiltrating immune cells. In this theoretical study, we derive an ODE model to investigate the interactions between breast cancer tumour cells, an oncolytic virus (Vesicular Stomatitis Virus), and tumour-infiltrating macrophages with different phenotypes which can impact the dynamics of oncolytic viruses. The complexity of the model requires a combined analytical-numerical approach to understand the transient and asymptotic dynamics of this model. We use this model to propose new biological hypotheses regarding the impact on tumour elimination/relapse/persistence of: (i) different macrophage polarisation/re-polarisation rates; (i...