Modeling and analysis of a multilayer solid tumour with cell physiological age and resource limitations

Abstract

We study an avascular spherical solid tumour model with cell physiological age and resource constraints in vivo. We divide the tumour cells into three components: proliferating cells, quiescent cells and dead cells in necrotic core. We assume that the division rate of proliferating cells is nonlinear due to the nutritional and spatial constraints. The proportion of newborn tumour cells entering directly into quiescent state is considered, since this proportion can respond to the therapeutic effect of drug. We establish a nonlinear age-structured tumour cell population model. We investigate the existence and uniqueness of the model solution and explore the local and global stabilities of the tumour-free steady state. The existence and local stability of the tumour steady state are studied. Finally, some numerical simulations are performed to verify the theoretical results and to investigate the effects of different parameters on the model.

KEYWORDS:

• Nonlinear age-structured model
• proliferating cells
• resource limitation
• steady state

MATHEMATICS SUBJECT CLASSIFICATION:

• 92B05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by the National Natural Science Foundation of China [grant number 12271068], the Innovation Development Joint Funds of the Chongqing Natural Science Foundation [grant number 2022NSCQ-LZX0360], Chongqing Municipal Education Commission [grant number KJQN202000730], Joint Training Base Construction Project for Graduate Students in Chongqing [grant number JDLHPYJD2021016] and Group Building Scientific Innovation Project for universities in Chongqing [grant number CXQT21021].