A proposed fractional-order Gompertz model and its application to tumour growth data.
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.
Department of Mathematics and Applied Mathematics (74), University of the Free State, PO Box 339, Bloemfontein 9300, South Africa boltonlarisse@gmail.com.
Larisse
L
Bolton
Department of Mathematics and Applied Mathematics (74), University of the Free State, PO Box 339, Bloemfontein 9300, South Africa.
Alain H J J
AH
Cloot
Department of Mathematics and Applied Mathematics (74), University of the Free State, PO Box 339, Bloemfontein 9300, South Africa.
Schalk W
SW
Schoombie
iThemba LABS, National Research Foundation, PO Box 722, Somerset West, 7129, South Africa and Department of Medical Imaging and Clinical Oncology, University of Stellenbosch, Stellenbosch 7600, South Africa.
Jacobus P
JP
Slabbert
D000818:Animals; D019295:Computational Biology; D016208:Databases, Factual; D055641:Mathematical Concepts; D051379:Mice; D008954:Models, Biological; D009369:Neoplasms / Q000473:pathology*; D012208:Rhabdomyosarcoma / Q000473:pathology
Gompertz model; Rhabdomyosarcoma; fractional calculus; tumour growth