Replication-competent viruses have the potential to overcome the delivery barrier in tumors that has plagued traditional gene-therapy approaches to cancer treatment. However, recent clinical data suggests that a cytokine-based immune response against the virus-infected tumor cells may severely limit the efficacy of the replication-competent approach. This paper generalizes our earlier spatial model to incorporate an immune response against the infected tumor cells. An approximate but accurate condition is derived for the virus—if uniformly injected throughout the tumor—to eradicate the tumor in the presence of the immune response. To validate the model using clinical data describing the temporal interaction of tumor necrosis factor and free virus in the plasma, we needed the immune response to be time-delayed and experience either saturated stimulation or second-order clearance. The resulting estimates of some unknown parameters provide some implications for the delivery of treatment.
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Wu, J.T., Kirn, D.H. & Wein, L.M. Analysis of a three-way race between tumor growth, a replication-competent virus and an immune response. Bull. Math. Biol. 66, 605–625 (2004). https://doi.org/10.1016/j.bulm.2003.08.016
- Equilibrium Point
- Hopf Bifurcation
- Stable Equilibrium Point
- Free Virus
- Stable Periodic Solution