Ultimate tumor dynamics and eradication using oncolytic virotherapy

In this paper we study ultimate dynamics of one three-dimensional model for tumor growth under oncolytic virotherapy which describes interactions between cytotoxic T-cells, uninfected tumor cells and infected tumor cells. Using the localization theorem of compact invariant sets we derive ultimate upper bounds for all cell populations and establish the property of the existence of the attracting set. Next, we find several conditions under which our system demonstrates convergence dynamics to equilibrium points located in invariant planes corresponding cases of the absence of uninfected or infected tumor cells. These assertions mean global eradication of uninfected or infected tumor cell populations and are presented as algebraic inequalities respecting virus replication rate theta. In particular, we find in Theorems 4 and 5 the following curious phenomenon. Namely, when we vary theta from the instability range of the infected tumor free equilibrium point to the stability range we obtain in the latter range convergence dynamics to one of tumor free equilibrium points; this means that the local eradication of infected tumor cells implies their global eradication. Besides, we give conditions under which the infected tumor cell population persists. Our theoretical studies are supplied by results of numerical simulation. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

Through studying a three-dimensional model for tumor growth, we found conditions under which the system converges to equilibrium points, resulting in global eradication of uninfected or infected tumor cells based on algebraic inequalities related to virus replication rate. Furthermore, we observed the phenomenon where local eradication of infected tumor cells implies their global eradication.