Document Type
Poster
College
Henry M. Rowan College of Engineering
Start Date
25-3-2026 1:00 PM
End Date
25-3-2026 2:00 PM
Abstract
Tumor progression emerges from nonlinear interactions among cancer cells, immune populations, and vascular support networks. While tumor-immune models typically assume instantaneous feedback, biological processes such as antigen presentation, clonal expansion, and angiogenesis introduce intrinsic delays that fundamentally alter system stability. Here, we develop a delay-structured tumor-immune-angiogenesis model to investigate how immune recruitment lag and vascular response delay shape global tumor dynamics. Analytical stability analysis reveals that increasing immune delay induces Hopf bifurcations, leading to sustained oscillations and, at larger delays, deterministic chaos. Mapping immune amplification strength and delay parameters identifies a structured phase diagram containing stable, oscillatory, chaotic, and runaway growth regimes. We further show that periodic therapeutic forcing interacts nonlinearly with intrinsic delays. Frequency sweeps reveal resonance windows in which modest changes in treatment cadence induce bifurcation cascades and chaotic transitions. Largest Lyapunov exponent landscapes confirm the existence of edge-of-chaos bands characterized by maximal trajectory sensitivity. Importantly, adaptive cadence modulation suppresses chaotic oscillations and restores stable dynamics without increasing treatment intensity. These results demonstrate that tumor–immune ecosystems can operate near critical dynamical boundaries where small perturbations produce large outcome variability. Immune delay emerges as a bifurcation control parameter, while therapy timing acts as an external resonance driver. By framing relapse and treatment variability as consequences of delay-induced nonlinear instability, this work establishes a mechanistic foundation for chaos-aware therapy scheduling and dynamical stratification in precision oncology.
Included in
Engineering Commons, Life Sciences Commons, Medicine and Health Sciences Commons, Physical Sciences and Mathematics Commons, Social and Behavioral Sciences Commons
Mapping the Edge of Chaos in Tumor–Immune–Angiogenesis Dynamics: A Systems Framework for Treatment Design
Tumor progression emerges from nonlinear interactions among cancer cells, immune populations, and vascular support networks. While tumor-immune models typically assume instantaneous feedback, biological processes such as antigen presentation, clonal expansion, and angiogenesis introduce intrinsic delays that fundamentally alter system stability. Here, we develop a delay-structured tumor-immune-angiogenesis model to investigate how immune recruitment lag and vascular response delay shape global tumor dynamics. Analytical stability analysis reveals that increasing immune delay induces Hopf bifurcations, leading to sustained oscillations and, at larger delays, deterministic chaos. Mapping immune amplification strength and delay parameters identifies a structured phase diagram containing stable, oscillatory, chaotic, and runaway growth regimes. We further show that periodic therapeutic forcing interacts nonlinearly with intrinsic delays. Frequency sweeps reveal resonance windows in which modest changes in treatment cadence induce bifurcation cascades and chaotic transitions. Largest Lyapunov exponent landscapes confirm the existence of edge-of-chaos bands characterized by maximal trajectory sensitivity. Importantly, adaptive cadence modulation suppresses chaotic oscillations and restores stable dynamics without increasing treatment intensity. These results demonstrate that tumor–immune ecosystems can operate near critical dynamical boundaries where small perturbations produce large outcome variability. Immune delay emerges as a bifurcation control parameter, while therapy timing acts as an external resonance driver. By framing relapse and treatment variability as consequences of delay-induced nonlinear instability, this work establishes a mechanistic foundation for chaos-aware therapy scheduling and dynamical stratification in precision oncology.