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A chemotaxis--model for directed tissue growth
In this paper we propose a chemotaxis--growth--system for the modelling of stimulated tissue growth. Such phenomena frequently arise in wound healing and angiogenesis and used to be modeled by reaction-diffusion alone. The model focuses on the role of the epidermal growth factor in increasing mitotic activity but also serving as an chemo-attractant for the migrating cells. We show that travelling wave solutions exist, having a uniquely determined minimal wave speed depending on the diffusivity and the sensitivity of the chemotactic population. In particular, the speed is enhanced for stronger chemotactic sensitivity proposing a mechanism to increase healing rates compared to the model with purely diffusion driven migration.