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EFFICIENT NUMERICAL METHOD FOR A MODEL ARISING IN BIOLOGICAL STOICHIOMETRY OF TUMOUR DYNAMICS

机译：肿瘤动力学生物化学计量模型的高效数值方法

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摘要

In this paper, we extend a system of coupled first order non-linear system of delay differential equations (DDEs) arising in modeling of stoichiometry of tumour dynamics, to a system of diffusion-reaction system of partial delay differential equations (PDDEs). Since tumor cells are further modified by blood supply through the vascularization process, we determine the local uniform steady states of the homogeneous tumour growth model with respect to the vascularization process. We show that the steady states are globally stable, determine the existence of Hopf bifurcation of the homogeneous tumour growth model with respect to the vascularization process. We derive, analyse and implement a fitted operator finite difference method (FOFDM) to solve the extended model. This FOFDM is analyzed for convergence and we observe seen that it has second-order accuracy. Some numerical results confirming theoretical observations are also presented. These results are comparable with those obtained in the literature.
机译：在本文中，我们扩展了在肿瘤动力学化化学计量建模中产生的延迟微分方程（DDES）的耦合第一阶非线性系统系统，对部分延迟微分方程（PDDES）的扩散 - 反应系统系统。由于通过血管化过程进一步通过血液供应来修饰肿瘤细胞，因此我们确定均匀肿瘤生长模型的局部均匀稳定状态相对于血管化过程。我们表明稳定状态是全球稳定的，确定均匀肿瘤生长模型的跳跃分叉相对于血管化过程的存在。我们得出，分析和实施拟合操作员有限差分法（FOFDM）来解决扩展模型。该FOFDM分析为收敛，我们观察到它具有二阶精度。还提出了一些证实理论观察的数值结果。这些结果与文献中获得的结果相当。

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