Centre de Recherches en Cancérologie de Toulouse, Université de Toulouse, INSERM, CNRS, Toulouse, France.
Institut de Mathématiques de Toulouse, Université de Toulouse, CNRS, Toulouse, France.
Bull Math Biol. 2022 May 10;84(6):64. doi: 10.1007/s11538-022-01025-3.
The present work studies models of oncolytic virotherapy without space variable in which virus replication occurs at a faster time scale than tumor growth. We address the questions of the modeling of virus injection in this slow-fast system and of the optimal timing for different treatment strategies. To this aim, we first derive the asymptotic of a three-species slow-fast model and obtain a two-species dynamical system, where the variables are tumor cells and infected tumor cells. We fully characterize the behavior of this system depending on the various biological parameters. In the second part, we address the modeling of virus injection and its expression in the two-species system, where the amount of virus does not appear explicitly. We prove that the injection can be described by an instantaneous jump in the phase plane, where a certain amount of tumors cells are transformed instantly into infected tumor cells. This description allows discussing qualitatively the timing of different injections in the frame of successive treatment strategies. This work is illustrated by numerical simulations. The timing and amount of injected virus may have counterintuitive optimal values; nevertheless, the understanding is clear from the phase space analysis.
本工作研究了无空间变量的溶瘤病毒治疗模型，其中病毒复制的时间尺度比肿瘤生长快。我们在这个慢快系统中解决了病毒注射的建模问题和不同治疗策略的最佳时机问题。为此，我们首先推导出了一个三物种慢快模型的渐近解，并得到了一个双物种动力系统，其中变量是肿瘤细胞和感染的肿瘤细胞。我们根据各种生物学参数充分描述了这个系统的行为。在第二部分，我们研究了病毒注射及其在双物种系统中的表达，其中病毒的数量没有显式出现。我们证明，注射可以通过相平面上的瞬时跳跃来描述，其中一定数量的肿瘤细胞瞬间转化为感染的肿瘤细胞。这种描述允许定性地讨论在连续治疗策略框架下不同注射的时机。通过数值模拟说明了这一点。注射的时间和病毒的数量可能具有反直觉的最佳值；然而，从相空间分析可以清楚地理解这一点。
