Numerical stability analysis of a class of nonlinear age-structured tumor cell population models

Hefan Yin; Jianfang Gao; Zhanwen Yang; Hefan Yin; Jianfang Gao; Zhanwen Yang

doi:10.3934/math.20261082

AIMS Mathematics

2026, Volume 11, Issue 8: 26986-27017. doi: 10.3934/math.20261082

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Research article

Numerical stability analysis of a class of nonlinear age-structured tumor cell population models

1.
School of Mathematical Sciences, Harbin Normal University, Harbin 150025, China
2.
Heilongjiang Key Laboratory of Analysis on Machine Learning and Dynamic System, Harbin Normal University, Harbin 150025, China
3.
School of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received: 02 July 2026 Revised: 08 August 2026 Accepted: 17 August 2026 Published: 27 August 2026
MSC : 65M12, 65M70, 65M15

A nonlinear age-structured tumor cell population model where the tumor population is divided into proliferating and quiescent cells is studied in this paper. The discretization of age and time is considered. Based on continuous collocation methods, an age-semi-discrete scheme and the numerical basic reproduction number $ R_h $ are obtained. Some conditions are presented such that $ R_h $ is superconvergent to the real basic reproduction number $ R_0 $, and $ R_h $ is also a threshold of the age-semi-discrete scheme. For the time-full discretization, an implicit-explicit discrete scheme is introduced, of which the computational cost is almost the same as an explicit scheme. The most important point is that the dynamical behavior of the model is preserved by the age-semi-discrete scheme. Finally, several numerical experiments are given to verify our results.
- age-structured,
- proliferating and quiescent cells,
- continuous collocation methods,
- numerical basic reproduction number,
- stability
Citation: Hefan Yin, Jianfang Gao, Zhanwen Yang. Numerical stability analysis of a class of nonlinear age-structured tumor cell population models[J]. AIMS Mathematics, 2026, 11(8): 26986-27017. doi: 10.3934/math.20261082

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Abstract

A nonlinear age-structured tumor cell population model where the tumor population is divided into proliferating and quiescent cells is studied in this paper. The discretization of age and time is considered. Based on continuous collocation methods, an age-semi-discrete scheme and the numerical basic reproduction number $ R_h $ are obtained. Some conditions are presented such that $ R_h $ is superconvergent to the real basic reproduction number $ R_0 $, and $ R_h $ is also a threshold of the age-semi-discrete scheme. For the time-full discretization, an implicit-explicit discrete scheme is introduced, of which the computational cost is almost the same as an explicit scheme. The most important point is that the dynamical behavior of the model is preserved by the age-semi-discrete scheme. Finally, several numerical experiments are given to verify our results.

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