我们模拟溶瘤病毒治疗期间癌细胞和病毒之间的相互作用。我们的主要目标之一是确定导致治疗失败或成功的参数区域。我们发现，在特定时间接受治疗的肿瘤大小小于未经治疗的大小。我们的分析表明了水平传播率的两个阈值：“失败阈值”，低于该阈值治疗失败，以及“成功阈值”，高于该阈值感染率达到 100% 并且肿瘤缩小到最小尺寸。此外，我们还解释了病毒毒力的变化如何改变成功阈值和最小肿瘤大小。我们的研究表明，溶瘤病毒的最佳毒力取决于病毒动力学的时间尺度。我们确定了病毒毒力的阈值，并展示了该阈值如何取决于病毒动态的时间尺度。我们的结果表明，当病毒动力学的时间尺度很快时，施用毒性更强的病毒会导致肿瘤大小更大程度地减小。相反，当病毒时间尺度较慢时，较高的毒力会引起肿瘤大小的大幅波动。此外，我们在参数空间中引入了“Hopf分叉岛”的概念，这一想法的应用远远超出了本文的结果，并且适用于许多数学模型。我们阐明了 Hopf 分叉岛是什么，并且证明了小岛可能意味着增长非常缓慢的振荡解。版权所有 © 2024 Elsevier Inc. 保留所有权利。

We model interactions between cancer cells and viruses during oncolytic viral therapy. One of our primary goals is to identify parameter regions that yield treatment failure or success. We show that the tumor size under therapy at a particular time is less than the size without therapy. Our analysis demonstrates two thresholds for the horizontal transmission rate: a "failure threshold" below which treatment fails, and a "success threshold" above which infection prevalence reaches 100% and the tumor shrinks to its smallest size. Moreover, we explain how changes in the virulence of the virus alter the success threshold and the minimum tumor size. Our study suggests that the optimal virulence of an oncolytic virus depends on the timescale of virus dynamics. We identify a threshold for the virulence of the virus and show how this threshold depends on the timescale of virus dynamics. Our results suggest that when the timescale of virus dynamics is fast, administering a more virulent virus leads to a greater reduction in the tumor size. Conversely, when the viral timescale is slow, higher virulence can induce oscillations with high amplitude in the tumor size. Furthermore, we introduce the concept of a "Hopf bifurcation Island" in the parameter space, an idea that has applications far beyond the results of this paper and is applicable to many mathematical models. We elucidate what a Hopf bifurcation Island is, and we prove that small Islands can imply very slowly growing oscillatory solutions.Copyright © 2024 Elsevier Inc. All rights reserved.