Math. Model. Nat. Phenom.
Volume 18, 2023
|Number of page(s)||26|
|Section||Population dynamics and epidemiology|
|Published online||10 March 2023|
Threshold behavior of an age-structured tumor immune model*
College of Mathematics and Statistics, Chongqing Jiaotong University,
400074, PR China
** Corresponding author: email@example.com
Accepted: 3 January 2023
In this paper, we present and analyze an age-structured tumor immune model. Based on the fact that tumor cells of different ages tend to exhibit different physiological behaviors, we consider the age structure of tumor cells, age-based proliferation function and age-dependent death function in the model. The threshold R0 for the existence of tumor-free steady state is derived. It is found that if R0 > 1, the tumor-free steady state is not only locally stable but also globally stable. Moreover, numerical simulation shows that the threshold R0 may be regarded as an index to reflect the ability of “tumor immune surveillance”, that is, the smaller the R0, the better the ability of tumor immune surveillance. If R0 > 1, it is proved that the tumor steady state is existent and uniformly persistent. The local stability of the tumor steady state is investigated under some further conditions besides R0 > 1. In the end, we estimate the system parameters, verify the theoretical results and analyze some system parameters’ sensitivities.
Mathematics Subject Classification: 34D20 / 92C37 / 35Q92
Key words: Age structure / tumor immune model / steady state / stability / sensitivity analysis
This research was supported by the National Natural Science Foundation of China (12271068), the Innovation Development Joint Funds of the Chongqing Natural Science Foundation (CSTB2022NSCQ-LZX0026), Chongqing Municipal Education Commission (KJQN202000730), Joint Training Base Construction Project for Graduate Students in Chongqing (JDLHPYJD2021016) and Group Building Scientific Innovation Project for universities in Chongqing (CXQT21021).
© The authors. Published by EDP Sciences, 2023
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