Introducing delay dynamics to Bertalanffy's spherical tumour growth model

Abstract

We introduce delay dynamics to an ordinary differential equation model of tumour growth based upon von Bertalanffy's growth model, a model which has received little attention in comparison to other models, such as Gompterz, Greenspan and logistic models. Using existing, previously published data sets we show that our delay model can perform better than delay models based on a Gompertz, Greenspan or logistic formulation. We look for replication of the oscillatory behaviour in the data, as well as a low error value (via a Least-Squares approach) when comparing. We provide the necessary analysis to show that a unique, continuous, solution exists for our model equation and consider the qualitative behaviour of a solution near a point of equilibrium.