Bifurcations and Chaotic Dynamics in a Tumour-Immune-Virus System
Bifurcations and Chaotic Dynamics in a Tumour-Immune-Virus System
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DOI：
10.1051/mmnp/201611505
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发表时间：
2016-01-01
影响因子：
2.2
通讯作者：
Earn, D. J. D.
中科院分区：
文献类型：
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作者：
Eftimie, R.;Macnamara, C. K.;Earn, D. J. D.
尽管越来越多的证据表明溶瘤病毒可以有效治疗癌症，但了解肿瘤细胞，溶瘤病毒和免疫细胞之间相互作用的细节，可能导致肿瘤控制或肿瘤逃逸仍然是一个悬而未决的问题。癌症溶瘤疗法的数学建模已被用于研究所观察到的肿瘤生长时间模式背后的生物学机制。然而，许多模型表现出非常复杂的动态，这使得它们难以调查。在这种情况下，分叉图可以通过识别（在参数空间中）不同行为之间的特定过渡点来实现模型动态的可视化。在这里，我们描述和研究两个简单的数学模型溶瘤病毒癌症治疗，恒定和免疫依赖的承载能力。虽然这两种模型都可以表现出复杂的动力学，即不动点，周期轨道和混沌行为，但只有具有免疫依赖承载能力的模型才能在生物现实情况下表现出它们，即，在肿瘤变得太大而实验终止之前。此外，在分叉图的帮助下，我们发现了病毒-肿瘤动力学中的两个意想不到的行为：（i）对于短病毒半衰期，肿瘤大小似乎太小而无法检测，而对于长病毒半衰期，肿瘤生长到可以检测到的更大的大小;（ii）一些模型参数对肿瘤的瞬态和渐近动力学具有相反的影响。
Despite mounting evidence that oncolytic viruses can be effective in treating cancer, understanding the details of the interactions between tumour cells, oncolytic viruses and immune cells that could lead to tumour control or tumour escape is still an open problem. Mathematical modelling of cancer oncolytic therapies has been used to investigate the biological mechanisms behind the observed temporal patterns of tumour growth. However, many models exhibit very complex dynamics, which renders them difficult to investigate. In this case, bifurcation diagrams could enable the visualisation of model dynamics by identifying (in the parameter space) the particular transition points between different behaviours. Here, we describe and investigate two simple mathematical models for oncolytic virus cancer therapy, with constant and immunity dependent carrying capacity. While both models can exhibit complex dynamics, namely fixed points, periodic orbits and chaotic behaviours, only the model with immunity-dependent carrying capacity can exhibit them for biologically realistic situations, i.e., before the tumour grows too large and the experiment is terminated. Moreover, with the help of the bifurcation diagrams we uncover two unexpected behaviours in virus-tumour dynamics: (i) for short virus half-life, the tumour size seems to be too small to be detected, while for long virus half-life the tumour grows to larger sizes that can be detected; (ii) some model parameters have opposite effects on the transient and asymptotic dynamics of the tumour.