Effects of Delay in Tumor-Immune System on Stability
10.16156/j.1004-7220.2023.02.07
- VernacularTitle:肿瘤免疫系统的延迟对稳定性的影响
- Author:
Yangjuan LI
1
;
Weilong DUAN
2
Author Information
1. Engineering Training Center, Putian University
2. City College, Kunming University of Science and Technolog
- Publication Type:Journal Article
- Keywords:
tumor-immune system;
equilibrium;
stability;
time delay
- From:
Journal of Medical Biomechanics
2023;38(2):E248-E254
- CountryChina
- Language:Chinese
-
Abstract:
Objective To study stability of the deterministic tumor-immune system with time delay by means of linear stability analysis method. Methods In tumor-immune system, since it took some time for immune cells to recognize tumor cells and respond appropriately, time delay was considered in this process, then the model was simplified by using Taylor expansion of small delay, and the equilibrium points were solved out. By linear stability analysis method, the stability of these equilibrium points was studied. Finally, the trajectory of the system and that around each equilibrium point were simulated by numerical calculation method, so as to verify the result of theoretical analysis. Results The system had four meaningful equilibrium points with small delay, including a stable focus, a stable node, and two saddles. Moreover, the type and stability of these equilibrium points were not affected by the delay. Numerical simulation demonstrated the conclusion from theoretical analysis. Conclusions Under the condition of small delay, the type and stability of equilibrium points in the system are notaffected by the delay. The results are helpful to further understand dynamic mechanisms of tumor immune response, and provide references for tumor growth and treatment
