2023/09/21 by Yuyue Zhang, Liqi Xie, Yueping Dong +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Bifurcation #Bifurcation diagram #Bogdanov–Takens bifurcation #Computer science #Control theory (sociology) #Evolution and Genetic Dynamics #Hopf bifurcation #Mathematical Biology Tumor Growth #Mathematical analysis #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematics #Nonlinear system #Ode #Physics #Saddle-node bifurcation
paper · doi:10.1137/22m1533979
crossref issued 2023/09/21 · crossref published 2023/09/21 · crossref published-online 2023/09/21 · openalex publication_date 2023/09/21 · crossref created 2023/09/21 · crossref published-print 2023/10/31 · crossref deposited 2023/10/31 · openalex created_date 2025/10/10 · crossref indexed 2026/07/30 · openalex updated_date 2026/07/31
.In this paper, we study a tumor-immune system interaction model with dendritic cell therapy and immune response delay. First, it is shown that the ODE version of the model has a Bogdanov–Takens (BT) singularity or a weak focus with multiplicity at most 1 for different parameter values. As the parameters vary, the ODE model undergoes supercritical Hopf bifurcation and supercritical BT bifurcation. Our analysis indicates that there exists a threshold value of the activation rate of T cells, below which tumor immune escape occurs, above or at which T cells and tumor cells coexist in the form of a stable periodic oscillation or steady state. Second, we study how the immune response delay affects the dynamics of the model. Our results reveal that the delay can destabilize the stable positive equilibrium through Hopf bifurcation. Furthermore, the direction and stability of Hopf bifurcation are derived. When there is a cusp, we show that it is a BT singularity for any delay and the delay model also undergoes BT bifurcation. Finally, numerical simulations are presented to illustrate the theoretical results.Keywordstumor-immune system interaction modeldendritic cell therapyimmune response delayMSC codes34K1892C3737N25