Modeling the Interaction of Cytotoxic T-Lymphocytes and Oncolytic Viruses in a Tumor Microenvironment

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Abstract. Oncolytic virotherapy has become a promising approach in treating cancer. Understanding the mechanism of interaction between oncolytic viruses (OVs) and the immune system is crucial for the interventional diagnosis and therapy of tumors. In this paper, a mathematical model is formulated to understand the interaction among cytotoxic T-lymphocytes (CTLs), OVs, and tumor cells in which the Gompertz curve is used to describe the tumor proliferation. The basic reproductive number ([Formula: see text]) is first derived, and then the local and global dynamics of the system are analyzed mainly in terms of [Formula: see text] and another threshold [Formula: see text], the basic reproductive number of CTLs which determines the number of positive equilibria. The theoretical results suggest that the system may have periodic solutions and backward bifurcation. Furthermore, numerical simulations are explored to evaluate the influence of CTLs on virotherapy. CTL immune response plays an obstructive role on virotherapy, and once the CTL proliferation rate exceeds a threshold, the tumor will escape. In addition, the whole tumor population is inversely proportional to the viral infection rate as well as the tumor proliferation rate.

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