School of Mathematics and Statistics, University of Sydney, Sydney, NSW, Australia.
School of Mathematics and Statistics, University of Sydney, Sydney, NSW, Australia.
J Theor Biol. 2019 Nov 7;480:129-140. doi: 10.1016/j.jtbi.2019.08.002. Epub 2019 Aug 7.
Oncolytic viruses are genetically engineered to treat growing tumours and represent a very promising therapeutic strategy. Using a Gompertz growth law, we discuss a model that captures the in vivo dynamics of a cancer under treatment with an oncolytic virus. With the aid of local stability analysis and bifurcation plots, the typical interactions between virus and tumour are investigated. The system shows a singular equilibrium and a number of nonlinear behaviours that have interesting biological consequences, such as long-period oscillations and bistable states where two different outcomes can occur depending on the initial conditions. Complete tumour eradication appears to be possible only for parameter combinations where viral characteristics match well with the tumour growth rate. Interestingly, the model shows that therapies with a high initial injection or involving a highly effective virus do not universally result in successful strategies for eradication. Further, the use of additional, "boosting" injection schedules does not always lead to complete eradication. Our framework, instead, suggests that low viral loads can be in some cases more effective than high loads, and that a less resilient virus can help avoid high amplitude oscillations between tumours and virus. Finally, the model points to a number of interesting findings regarding the role of oscillations and bistable states between a tumour and an oncolytic virus. Strategies for the elimination of such fluctuations depend strongly on the initial viral load and the combination of parameters describing the features of the tumour and virus.
溶瘤病毒经过基因工程改造，用于治疗不断生长的肿瘤，是一种极具前景的治疗策略。我们利用戈珀特增长定律，讨论了一个模型，该模型捕捉了癌症在溶瘤病毒治疗下的体内动力学。借助局部稳定性分析和分岔图，研究了病毒和肿瘤之间的典型相互作用。该系统显示出奇异平衡点和多种非线性行为，具有有趣的生物学后果，如长周期振荡和双稳态，其中两种不同的结果可能取决于初始条件。似乎只有在病毒特性与肿瘤增长率很好匹配的参数组合下，才能完全消除肿瘤。有趣的是，该模型表明，具有高初始注射或涉及高效病毒的疗法并不总是导致成功的根除策略。此外，使用额外的“增强”注射方案并不总是导致完全根除。相反，我们的框架表明，在某些情况下，低病毒载量可能比高病毒载量更有效，并且较不具有弹性的病毒可以帮助避免肿瘤和病毒之间的高振幅振荡。最后，该模型指出了关于肿瘤和溶瘤病毒之间的振荡和双稳态的一些有趣发现。消除此类波动的策略强烈依赖于初始病毒载量以及描述肿瘤和病毒特征的参数组合。
