This mathematical model of the role of the innate immune responses generated by macrophages in the context of anti-tumour oncolytic viral therapies is described in the publication:
Nada Almuallem, Dumitru Trucu, Raluca Eftimie. "Oncolytic viral therapies and the delicate balance between virus-macrophage-tumour interactions: A mathematical approach". Mathematical Biosciences and Engineering, 2021, 18(1): 764-799.
doi: 10.3934/mbe.2021041

Comment:
This model is represented by Equations 2.1a-f of the publication manuscript.
Abstract:
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; (ii) different infection rates of macrophages and tumour cells with the oncolytic virus; (iii) different viral burst sizes for macrophages and tumour cells. We show that increasing the rate at which the oncolytic virus infects the tumour cells can delay tumour relapse and even eliminate tumour. Increasing the rate at which the oncolytic virus particles infect the macrophages can trigger transitions between steady-state dynamics and oscillatory dynamics, but it does not lead to tumour elimination unless the tumour infection rate is also very large. Moreover, we confirm numerically that a large tumour-induced M1→M2 polarisation leads to fast tumour growth and fast relapse (if the tumour was reduced before by a strong anti-tumour immune and viral response). The increase in viral-induced M2→M1 re-polarisation reduces temporarily the tumour size, but does not lead to tumour elimination. Finally, we show numerically that the tumour size is more sensitive to the production of viruses by the infected macrophages.