Introducing delay dynamics to Bertalanffy's spherical tumour growth model

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• 作者：J.A. Roberts^a ; ^{j.roberts@chester.ac.uk} ; A. Al Themairi^b ; ^{aialthumairi@pnu.edu.sa}
• 关键词：Delay differential equation ; Tumour growth
• 刊名：Applied Numerical Mathematics
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：114
• 期：Complete
• 页码：154-164
• 全文大小：840 K
• 卷排序：114

文摘

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 Gompertz, 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.