| Summary: | Replicating oncolytic viruses provide promising treatment strategies against cancer. However, the success of these viral therapies depends mainly on the complex interactions between the virus particles and the host immune cells. Among these immune cells, macrophages represent one of the first line of defence against viral infections. In this paper, we consider a mathematical model that describes the interactions between a commonly-used oncolytic virus, the Vesicular Stomatitis Virus (VSV), and two extreme types of macrophages: the pro-inflammatory M1 cells (which seem to resist infection with VSV) and the anti-inflammatory M2 cells (which can be infected with VSV). We first show the existence of bounded solutions for this differential equations model. Then we investigate the long-term behaviour of the model by focusing on steady states and limit cycles, and study changes in this long-term dynamics as we vary different model parameters. Moreover, through sensitivity analysis we show that the parameters that have the highest impact on the level of virus particles in the system are the viral burst size (from infected macrophages), the virus infection rate, the M1$\to$M2 polarisation rate, and the M1-induced anti-viral immunity.
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