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PreprintCC BY 4.0arXiv

Computational Oncology of Chemotaxis-Driven Tumour--Immune Spatial Patterning and Stability

  • Zonghao Liu
  • Jiguang Yu
  • Lei Su
  • Louis Shuo Wang
  • Yang Du
  • Jingfeng Liu
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Abstract

We develop a reaction--diffusion--chemotaxis model for spatial tumour--immune--chemokine dynamics that couples logistic tumour growth, immune-mediated killing, chemokine-dependent immune recruitment, chemotactic migration, and signal production. For the nondimensional system, we establish local classical solvability, nonnegativity, a uniform tumour-density bound, and global mass estimates for the immune and chemokine components. The tumour-free equilibrium is stable precisely when the baseline immune-control index satisfies σ0/δ>1, whereas positive homogeneous coexistence is characterized by a scalar nonlinear equation. Linearization in the Neumann Laplacian eigenbasis yields a mode-dependent cubic dispersion relation, showing that chemotaxis does not alter the tumour-invasion threshold but can destabilize homogeneous coexistence through a finite-wavelength oscillatory instability above a critical sensitivity ξc. A conservative finite-volume discretization with upwind chemotactic fluxes and implicit backward differentiation formula time integration is used to test these predictions. Numerical experiments recover the analytical equilibria and growth rates, identify the dominant unstable mode, reproduce the transition to spatial heterogeneity, and quantify the effects of immune recruitment, decay, and diffusion on the stability boundary. Grid-refinement, mass-balance, residual, and nonnegativity diagnostics support the computational reliability of the results.

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Cite

BibTeXRIS
BibTeX
@misc{liu2026computational,
  title = {{Computational Oncology of Chemotaxis-Driven Tumour--Immune Spatial Patterning and Stability}},
  author = {Zonghao Liu and Jiguang Yu and Lei Su and Louis Shuo Wang and Yang Du and Jingfeng Liu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.03813},
  eprint = {2607.03813},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.03813},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Computational Oncology of Chemotaxis-Driven Tumour--Immune Spatial Patterning and Stability
AU  - Zonghao Liu
AU  - Jiguang Yu
AU  - Lei Su
AU  - Louis Shuo Wang
AU  - Yang Du
AU  - Jingfeng Liu
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2607.03813
UR  - https://arxiv.org/abs/2607.03813
AB  - We develop a reaction--diffusion--chemotaxis model for spatial tumour--immune--chemokine dynamics that couples logistic tumour growth, immune-mediated killing, chemokine-dependent immune recruitment, chemotactic migration, and signal production. For the nondimensional system, we establish local classical solvability, nonnegativity, a uniform tumour-density bound, and global mass estimates for the immune and chemokine components. The tumour-free equilibrium is stable precisely when the baseline immune-control index satisfies σ_0/δ>1, whereas positive homogeneous coexistence is characterized by a scalar nonlinear equation. Linearization in the Neumann Laplacian eigenbasis yields a mode-dependent cubic dispersion relation, showing that chemotaxis does not alter the tumour-invasion threshold but can destabilize homogeneous coexistence through a finite-wavelength oscillatory instability above a critical sensitivity ξ_c. A conservative finite-volume discretization with upwind chemotactic fluxes and implicit backward differentiation formula time integration is used to test these predictions. Numerical experiments recover the analytical equilibria and growth rates, identify the dominant unstable mode, reproduce the transition to spatial heterogeneity, and quantify the effects of immune recruitment, decay, and diffusion on the stability boundary. Grid-refinement, mass-balance, residual, and nonnegativity diagnostics support the computational reliability of the results.
ER  -