Emerging Allee effect in tumor growth (1407.3147v1)

Abstract: Tumor cells develop different features to adapt to environmental conditions. A prominent example is the ability of tumor cells to switch between migratory and proliferative phenotypes, a phenomenon known as go-or-grow mechanism. It is however unclear how this particular phenotypic plasticity affects overall tumor growth. To address this problem, we formulate and study a mathematical model of spatio-temporal tumor dynamics where different responses to local cell density mediate the go-or-grow dichotomy. Our analysis reveals that two dynamic regimes can be distinguished. If cell motility is allowed to increase with local cell density, any tumor cell population will persist in time, irrespective of its initial size. On the contrary, if cell motility is assumed to decrease with respect to local cell density, an Allee effect emerges, so that any tumor population below a certain size threshold eventually extinguishes. These results suggest that strategies aimed at hindering migration, for instance by enhancing contact inhibition, are worth to be explored as alternatives to those mainly focused at checking tumor proliferation.