Existence of traveling wavefronts for Sherratt’s avascular tumor model

In this paper, we revisit Sherratt’s avascular tumor growth system modeled in terms of the continuum densities of proliferating, quiescent and necrotic cells, together with the consideration of the generic nutrient supply from underlying tissue and cell movement of contact inhibition. By adopting a perturbation method combined with the Banach fixed point theorem, we theoretically justify the existence of the traveling wavefronts for this model.

Research highlights► We study the existence of wavefronts for Sherratt’s avascular tumor model. ► Perturbation method coupled with the Banach fixed point theorem are applied. ► Rigorous proof of the existence of the wave patterns is provided. ► The wave-pulse pattern here is different from the wavefronts that we have studied in the past references.