Efficient numerical method for a model arising in biological stoichiometry of tumor dynamics
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Date
2019
Journal Title
Journal ISSN
Volume Title
Publisher
American Institute of Mathematical Sciences
Abstract
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.
Description
Keywords
Biological stoichiometry, Tumour dynamics, Delay differential equations, Numerical methods, Error analysis
Citation
Kolade, M. et al. 2019. Efficient numerical method for a model arising in biological stoichiometry of tumour dynamics