Tumor spheroid with almost periodic nutrient and inhibitor supplies

Abstract

We describe the time‐evolution of a tumor spheroid without necrotic core using the quasi‐stationary reaction–diffusion approach. We assume that inhibitor and nutrient supplies are time‐dependent and oscillating by incorporating continuous almost periodic functions in the model. The functional form of the intensity of the mitosis is supposed to be the product of two linear functions depending on the nutrient concentration σ and of the inhibitor concentration, β, respectively. Under some mild conditions, we give criteria predicting two possible global asymptotic limits: either the tumor oscillates converging towards a stable global almost periodic solution or the tumor shrinks as time increases.