  Movement behavior of biological entities plays a crucial role in their
destiny through regulating their intraspecific and interspecific interactions
as well as their interaction with surrounding environment. In spite of various
models for population dynamics, the effect of movement behavior and
heterogeneity of environment on population dynamics has remained poorly
understood. We introduced an extended version of Kolmogorov equation which
captures movement behavior and translated our model to a biased random walk on
percolation lattice. Then we explored the effect of mentioned topic on
population dynamics, especially for intratumor heterogeneity, metastasis and
immune surveillance. In the case of tumor, our result reveals that
communication between cell colons and the structure of host tissue together
regulate the intratumor heterogeneity. For metastasis, our model predicts that
the interplay between the structure of metastatic niche and interactions
between metastatic cells arrived from different colons determines that which
kind of seeds, polyclonal or monoclonal, can successfully metastasized there.
Finally, studying the immune cells-tumor cells interaction in this context
reveals the negative effect of the heterogeneous structure of host tissue on
immune surveillance. These findings deepen our understanding of cancer biology
and may have applications in Immunotherapy.
