Abstract
In this paper, we consider a model for the population kinetics of human tumor cells in vitro, differentiated by phases of the cell division cycle and length of time within each phase. Since it is not easy to isolate the effects of cancer treatment on the cell cycle of human cancer lines, during the process of radiotherapy or chemotherapy, therefore, we include the spatial effects of cells in each phase and analyse the extended model. The extended model is not easy to solve analytically, because perturbation by cancer therapy causes the flow cytometric profile to change in relation to one another. Hence, making it difficult for the resulting model to be solved analytically. Thus, in [16] it is reported that the non-standard schemes are reliable and propagate sharp fronts accurately, even when the advection, reaction processes are highly dominant and the initial data are not smooth. As a result, we construct a fitted operator finite difference method (FOFDM) coupled with non-standard finite difference method (NSFDM) to solve the extended model. The FOFDM and NSFDM are analyzed for convergence and are seen that they are unconditionally stable and have the accuracy of O(∆t + (∆x)^2), where ∆t and ∆x denote time and space step-sizes, respectively. Some numerical results confirming theoretical observations are presented.
Highlights
Since it is not easy to isolate the effects of cancer treatment on the cell cycle of human cancer lines, during the process of radiotherapy or chemotherapy, we include the spatial effects of cells in each phase and analyse the extended model
In our views, it is very important to study dynamics for the kinetics of a population of cells differentiated by phases of the cell division cycle such as the ones presented by Jackiewicz et al.,[12] as a way toward avoiding incorrect treatment decisions especially, if a biopsy sample is not representative of other parts of the tumor
It is understood that even in the simplified environment of the laboratory with modern techniques and/or technology, it is not always possible to isolate the effects of cancer treatment on the cell cycle of human cancer cell lines
Summary
Department of Mathematics and Applied Mathematics, University of the Western Cape, Cape Town 7535, South Africa Copyright c 2020 the author(s). This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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