A mathematical model for the role of macrophages in the persistence and elimination of oncolytic viruses

Abstract

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.

The role of noise in the tumour-immune interactions reveals memoryless shifting response

“…We set the system into the active tumour state, and ran 10,000 simulations using the SSA to calculate the average time the system requires to eliminate the tumour. As illustrated by Fig (8), when β 1 i is low, the MFPT is high, and when β 1 is increased the MFPT is reduced. This shows that a sufficient level of treatment can accelerate the transition between higher tumour state to a tumour-free state.…”

“…However, this is not the case when the vitamin intake is increased. Fig (8) shows that the mean of the elimination of time as a function of the vitamin intake, γ. This figure illustrates that the mean is slightly improved as γ is increased.…”

“…Many mathematical models have been introduced to investigate the development of the tumour in the host [3][4][5][6][7][8]. These models, depending on the level of their complexity, can predict the tumour cells proliferation.…”