A non-Markovian model of tumor cell invasion with finite velocity is proposed to describe the proliferation and migration dichotomy of cancer cells. The model considers transitions with age-dependent switching rates between three states: moving tumor cells in the positive direction, moving tumor cells in the negative direction, and resting tumor cells. The first two states correspond to a migratory phenotype, while the third state represents a proliferative phenotype. Proliferation is modeled using a logistic growth equation. The transport of tumor cells is described by a persistent random walk with general residence time distributions. The nonlinear master equations describing the average densities of cancer cells for each of the three states are derived. The present work also includes the analysis of models involving power law distributed random time, highlighting the dominance of the Mittag–Leffler rest state, resulting in subdiffusive behavior.
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