Dynamics and Period-doubling Bifurcation of Tumor-immune Model with Hormetic Effect
WANG Jiaqi
XIANG Changcheng
Abstract：To investigate the effects of hormetic effect and dynamic radiotherapy on tumor cell dynamics,a tumor-immune model with hormetic effect was proposed,and a dynamic regulatory factor was introduced for study.The existence and stability of the fixed points of the model were analyzed.The conditions for period-doubling bifurcation were derived using the center manifold theorem and verified through numerical simulations.The results indicated that the hormetic effect during radiotherapy significantly influenced the number of tumor cells,and that the implementation of dynamic radiotherapy eventually stabilized the tumor cell population near the threshold level.This study provided a theoretical reference for the design of radiotherapy strategies that consider both hormetic effect and dynamic radiotherapy.
Keywords：tumor-immune modelstabilityperiod-doubling bifurcationnumerical simulationhormetic effect
Publication Date：2026-03-20
Online Publishing Date：2026-03-26(First online date of this platform, not the publication date of the document)
Pages：9( 92-100 )