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Abstract

A common feature of tumour growth is the production, by the cancer cells themselves, of hormones known as growth factors that increase the rate of cell division. This type of signalling makes the growth rate of the tumour depend on the population size in a non-linear manner, and the growth rate might become low or negative for small population sizes. This is known as the Allee effect which has been studied extensively in ecology. We have developed a computational model that can explain the Allee effect in terms of growth factor signalling, and show by mathematical analysis of the model that the magnitude of the Allee effect depends on the ratio of cell death to proliferation, as well as the properties of the growth factor. In addition we show that the model is consistent with experimental observations from three different cell lines derived from the brain tumour glioblastoma. Our findings indicate that the Allee effect can be exploited in order to improve the treatment of glioblastoma patients.