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 θ. In particular, we find in Theorems 4 and 5the following curious phenomenon. Namely, when we vary θ 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.

在本文中，我们研究了溶瘤病毒疗法下肿瘤生长的一个三维模型的最终动力学，该模型描述了细胞毒性T细胞，未感染的肿瘤细胞和感染的肿瘤细胞之间的相互作用。使用紧密不变集的定位定理，我们得出所有细胞群体的最终上限，并建立吸引集存在的性质。接下来，我们发现了几种条件，在这些条件下，我们的系统展示了收敛到位于不变平面上的平衡点的动态动力学，对应于没有未感染或感染的肿瘤细胞的情况。这些主张意味着在全球范围内根除未感染或感染的肿瘤细胞群，并以代数不等式的形式出现，并考虑到病毒复制率θ。特别是，我们在定理4和5中发现了以下奇怪现象。即，当我们从被感染的无肿瘤平衡点的不稳定性范围到稳定范围改变θ时，我们在后一范围内获得了到无肿瘤平衡点之一的收敛动力学。这意味着局部消灭被感染的肿瘤细胞意味着它们的全面消灭。此外，我们给出了感染的肿瘤细胞群体持续存在的条件。我们的理论研究由数值模拟的结果提供。