Introducing delay dynamics to Bertalanffy's spherical tumour growth model

Hdl Handle:
http://hdl.handle.net/10034/620218
Title:
Introducing delay dynamics to Bertalanffy's spherical tumour growth model
Authors:
Roberts, Jason A.; Themairi, Asmaa A.
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.
Affiliation:
University of Chester; University of Princess Nourah bint Abdulrahman
Citation:
Roberts, J. A., & Themairi, A. A. (2017). Introducing delay dynamics to Bertalanffy's spherical tumour growth model. Applied Numerical Mathematics, 114, 154-164. http://dx.doi.org/10.1016/j.apnum.2016.10.009
Publisher:
Elsevier
Journal:
Applied Numerical Mathematics
Publication Date:
21-Oct-2016
URI:
http://hdl.handle.net/10034/620218
DOI:
10.1016/j.apnum.2016.10.009
Additional Links:
http://www.journals.elsevier.com/applied-numerical-mathematics/
Type:
Article
Language:
en
EISSN:
1873-5460
Appears in Collections:
Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorRoberts, Jason A.en
dc.contributor.authorThemairi, Asmaa A.en
dc.date.accessioned2016-10-24T09:45:31Z-
dc.date.available2016-10-24T09:45:31Z-
dc.date.issued2016-10-21-
dc.identifier.citationRoberts, J. A., & Themairi, A. A. (2017). Introducing delay dynamics to Bertalanffy's spherical tumour growth model. Applied Numerical Mathematics, 114, 154-164. http://dx.doi.org/10.1016/j.apnum.2016.10.009en
dc.identifier.doi10.1016/j.apnum.2016.10.009-
dc.identifier.urihttp://hdl.handle.net/10034/620218-
dc.description.abstractWe 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.en
dc.language.isoenen
dc.publisherElsevieren
dc.relation.urlhttp://www.journals.elsevier.com/applied-numerical-mathematics/en
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/en
dc.subjectDelay differential equationsen
dc.subjectMathematical modellingen
dc.titleIntroducing delay dynamics to Bertalanffy's spherical tumour growth modelen
dc.typeArticleen
dc.identifier.eissn1873-5460-
dc.contributor.departmentUniversity of Chester; University of Princess Nourah bint Abdulrahmanen
dc.identifier.journalApplied Numerical Mathematicsen
dc.date.accepted2016-10-18-
or.grant.openaccessYesen
rioxxterms.funderResearch visit to Chester by A. Al Themairi (to facilitate this collaboration) funded by her universityen
rioxxterms.identifier.projectResearch Visit to Chester by A Al Themairi funded by her universityen
rioxxterms.versionAMen
rioxxterms.licenseref.startdate2017-10-21-
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