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Time delays in a double‐layered radial tumor model with different living cells.
- Source :
-
Mathematical Methods in the Applied Sciences . Aug2024, p1. 10p. - Publication Year :
- 2024
-
Abstract
- This paper deals with the free boundary problem for a double‐layered tumor filled with quiescent cells and proliferating cells, where time delay τ>0$$ \tau >0 $$ in cell proliferation is taken into account. These two types of living cells exhibit different metabolic responses and consume nutrients σ$$ \sigma $$ at different rates λ1$$ {\lambda}_1 $$ and λ2$$ {\lambda}_2 $$ ( λ1⩽λ2$$ {\lambda}_1\leqslant {\lambda}_2 $$). Time delay happens between the time at which a cell commences mitosis and the time at which the daughter cells are produced. The problem is reduced to a delay differential equation on the tumor radius R(t)$$ R(t) $$ over time, and the difficulty arises from the jump discontinuity of the consumption rate function. We give rigorous analysis on this new model and study the dynamical behavior of the global solutions for any initial φ(t)$$ \varphi (t) $$. [ABSTRACT FROM AUTHOR]
- Subjects :
- *DELAY differential equations
*TUMOR growth
*CELL proliferation
*MITOSIS
Subjects
Details
- Language :
- English
- ISSN :
- 01704214
- Database :
- Academic Search Index
- Journal :
- Mathematical Methods in the Applied Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 179292241
- Full Text :
- https://doi.org/10.1002/mma.10456