<p>Immune effectors and tumor cells often shape the progression of the synthetic stage breast cancer through complex interactions. However, existing models often overlook the spatial and delayed immune dynamics that are critical in capturing immune evasion and tumor resurgence. To address this gap, we developed and analyzed a time-delayed reaction-diffusion model describing tumor-immune interactions during the synthetic stage. The model incorporates key immunological components such as T helper-2 cells, B cells, and cytokine-mediated feedback with spatial diffusion and a biologically motivated time delay. Analysis of the spatially homogeneous system reveals two biologically relevant equilibria: tumor-free and coexistence. The coexistence state is locally stable under baseline conditions, while the tumor-free equilibrium is unstable. Extending the analysis to a spatially distributed system, several cases arise from the dispersion function: stability within a biological parameter regime, diffusion-driven instability in the absence of delay, and delay-driven stability. Our parameter sweep results indicate that diffusion-driven instabilities may occur outside this regime, leading to spatial pattern formation. Numerical simulations using the method of lines reveal that B-cell proliferation occurs predominantly in regions with high tumor cell density, confirming that tumor reduction in the model is primarily driven by B-cell–mediated cytotoxicity, while the delay modulates the system dynamics by influencing transient behavior and, in certain parameter regimes, contributing to enhanced stability. Within biologically relevant regimes, however, the delay does not qualitatively alter the long-term tumor–immune outcome.</p>

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Modeling and Simulation of Breast Cancer Tumor-Immune Interaction with a Time-Delay Reaction-Diffusion Model

  • Kennedy Mensah,
  • Joseph Abeiku Ackora-Prah,
  • Dominic Otoo,
  • Kwame Atta Gyamfi

摘要

Immune effectors and tumor cells often shape the progression of the synthetic stage breast cancer through complex interactions. However, existing models often overlook the spatial and delayed immune dynamics that are critical in capturing immune evasion and tumor resurgence. To address this gap, we developed and analyzed a time-delayed reaction-diffusion model describing tumor-immune interactions during the synthetic stage. The model incorporates key immunological components such as T helper-2 cells, B cells, and cytokine-mediated feedback with spatial diffusion and a biologically motivated time delay. Analysis of the spatially homogeneous system reveals two biologically relevant equilibria: tumor-free and coexistence. The coexistence state is locally stable under baseline conditions, while the tumor-free equilibrium is unstable. Extending the analysis to a spatially distributed system, several cases arise from the dispersion function: stability within a biological parameter regime, diffusion-driven instability in the absence of delay, and delay-driven stability. Our parameter sweep results indicate that diffusion-driven instabilities may occur outside this regime, leading to spatial pattern formation. Numerical simulations using the method of lines reveal that B-cell proliferation occurs predominantly in regions with high tumor cell density, confirming that tumor reduction in the model is primarily driven by B-cell–mediated cytotoxicity, while the delay modulates the system dynamics by influencing transient behavior and, in certain parameter regimes, contributing to enhanced stability. Within biologically relevant regimes, however, the delay does not qualitatively alter the long-term tumor–immune outcome.