Modeling the spatiotemporal dynamic heterogeneity of pre-synthetic stage breast cancer tumor-immune interactions

Breast cancer remains a leading cause of mortality among women worldwide. While metastatic-stage cancer has no cure, understanding the spatiotemporal dynamics of tumor-immune interactions at the pre-synthetic stage is essential for developing effective immunotherapies. Recent advances in cancer modeling emphasize the need to incorporate both spatial and temporal dynamics for accurate simulations. This study presents a continuum model that ensures biological well-posedness. The steady state of the spatially homogeneous model exhibits stability but becomes unstable when spatial effects are incorporated. We performed a parameter sweep analysis to identify stability regions, revealing a critical threshold near η 1 ≈ 0 . 04 where the system transitions from instability to stability. Additionally, the boundaries near α 1 ≈ 0 . 2 and η 4 ≈ 0 . 3 show the most significant sensitivity to stability changes. By employing an explicit finite difference scheme, our simulations demonstrate spatially heterogeneous interactions among tumor cells, NK cells, and cytokines, with NK cells being most effective near the tumor. This suggests active immune recruitment in response to cancer progression. The spatiotemporal dynamics observed in our model are consistent with findings from existing studies, and the temporal behavior aligns with established patterns of immune-tumor interactions, further validating the robustness of our approach. Further analysis shows that higher per-capita growth rates ( ω ) of tumor cells correlate with rapid proliferation, aligning with their direct influence on tumor growth. This study provides valuable insights into spatial and temporal mechanisms of tumor-immune interactions, offering a foundation for optimizing immunotherapy strategies. • A novel continuum model that captures early breast tumor-immune interactions is presented. • The system is stable in homogeneous states but destabilized by spatial effects. • Parameter sweep shows stable and unstable zones via maximum growth rate. • Spatial-temporal heterogeneity shapes tumor-immune dynamics and immunotherapy impact.