Mathematical analysis of the spatiotemporal concentration of growth inhibitory factor in multicellular spheroids tumour

Abstract

In this work, we look at spatially dependent diffusion of growth inhibitory factor (GIF) in multicell spheroids. The production of GIF is taken to be time-dependent and heterogeneous within the spheroid. Using a semigroup approach, we investigate the dynamical behaviour of the presented mathematical model. Firstly, we investigate the existence and positivity of solutions. Secondly, with a time-independent source of GIF, we prove the existence of a unique steady state which is asymptotically stable. Moreover, with a (asymptotically) (almost) periodic supply of GIF we show the existence of a unique (asymptotically) (almost) periodic solution that defines a global attractor.