Bolton Larisse, Cloot Alain H J J, Schoombie Schalk W, Slabbert Jacobus P
Department of Mathematics and Applied Mathematics (74), University of the Free State, PO Box 339, Bloemfontein 9300, South Africa
Department of Mathematics and Applied Mathematics (74), University of the Free State, PO Box 339, Bloemfontein 9300, South Africa.
Math Med Biol. 2015 Jun;32(2):187-207. doi: 10.1093/imammb/dqt024. Epub 2014 Jan 26.
A fractional-order Gompertz model of orders between 0 and 2 is proposed. The main purpose of this investigation is to determine whether the ordinary or proposed fractional Gompertz model would best fit our experimental dataset. The solutions for the proposed model are obtained using fundamental concepts from fractional calculus. The closed-form equations of both the proposed model and the ordinary Gompertz model are calibrated using an experimental dataset containing tumour growth volumes of a Rhabdomyosarcoma tumour in a mouse. With regard to the proposed model, the order, within the interval mentioned, that resulted in the best fit to the data was used in a further investigation into the prediction capability of the model. This was compared to the prediction capability of the ordinary Gompertz model. The result of the investigation was that a fractional-order Gompertz model of order 0.68 produced a better fit to our experimental dataset than the well-known ordinary Gompertz model.
提出了阶数在0到2之间的分数阶Gompertz模型。本研究的主要目的是确定普通Gompertz模型还是所提出的分数阶Gompertz模型最适合我们的实验数据集。所提出模型的解是使用分数阶微积分的基本概念获得的。所提出模型和普通Gompertz模型的封闭形式方程是使用包含小鼠横纹肌肉瘤肿瘤生长体积的实验数据集进行校准的。对于所提出的模型，在上述区间内导致对数据拟合最佳的阶数被用于进一步研究该模型的预测能力。这与普通Gompertz模型的预测能力进行了比较。研究结果是，阶数为0.68的分数阶Gompertz模型比著名的普通Gompertz模型对我们的实验数据集拟合得更好。
