1. Tumor growth model with a time delay in cell proliferation
A new PDE model is proposed for non-radially symmetric tumor growth with a time delay in cell proliferation. The time delay represents the time taken for cells to undergo replication. The model is a coupled system of an elliptic equation, a parabolic equation, and a backward ordinary differential equation. It also incorporates the cell location under the presence of time delay (see the figure above, cell location changes in the period of time delay), with the tumor boundary as a free boundary. For the new model, we successfully carried out the stability and bifurcation analysis, and published in two journal papers.
Journal papers
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X. E. Zhao and B. Hu, “The impact of time delay in a tumor model”, Nonlinear Analysis: Real World Applications, 2020. [ DOI | arxiv ]
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X. E. Zhao and B. Hu, “Symmetry-breaking bifurcation for a free-boundary tumor model with time delay”, Journal of Differential Equations, 2021. [ DOI ]
Posters
- X. E. Zhao and B. Hu, “A Free Boundary Tumor Growth Model with a Time Delay in Cell Proliferation”. [ poster ]