Probabilistic approach to a proliferation and migration dichotomy in tumor cell invasion

The proliferation and migration dichotomy of the tumor cell invasion is examined within a two-component continuous time random walk (CTRW) model. The balance equations for the cancer cells of two phenotypes with random switching between cell proliferation and migration are derived. The transport of tumor cells is formulated in terms of the CTRW with an arbitrary waiting time distribution law, while proliferation is modeled by a logistic growth. The overall rate of tumor cell invasion for normal diffusion and subdiffusion is determined.

Figure 1

(Color online) Propagation speed ${\left(u/u_0\right)}^2$ vs ${\beta }_2/{\beta }_1$. The values of ${\beta }_1/U=\left[3,4.5,6.5\right]$ correspond to plots (1), (2), and (3), respectively. The inset corresponds to a solution of Eqs. (57, 58) for the same values of ${\beta }_1/U$ and $\gamma =0.7$.