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dc.contributor.authorEftimie, R.
dc.contributor.authorMacnamara, C. K.
dc.contributor.authorDushoff, Jonathan
dc.contributor.authorBramson, J. L.
dc.contributor.authorEarn, D. J. D.
dc.identifier.citationEftimie , R , Macnamara , C K , Dushoff , J , Bramson , J L & Earn , D J D 2016 , ' Bifurcations and chaotic dynamics in a tumour-immune-virus system ' , Mathematical Modelling of Natural Phenomena , vol. 11 , no. 5 , pp. 65-85 .
dc.identifier.otherPURE: 248518275
dc.identifier.otherPURE UUID: 68594318-09ea-46d2-b43f-b57061ad9cc9
dc.identifier.otherRIS: 10.1051mmnp201611505
dc.identifier.otherScopus: 85002984994
dc.identifier.otherORCID: /0000-0003-4961-6052/work/29043979
dc.identifier.otherWOS: 000389670900005
dc.description.abstractDespite mounting evidence that oncolytic viruses can be effective in treating cancer, understanding the details of the interactions between tumour cells, oncolytic viruses and immune cells that could lead to tumour control or tumour escape is still an open problem. Mathematical modelling of cancer oncolytic therapies has been used to investigate the biological mechanisms behind the observed temporal patterns of tumour growth. However, many models exhibit very complex dynamics, which renders them difficult to investigate. In this case, bifurcation diagrams could enable the visualisation of model dynamics by identifying (in the parameter space) the particular transition points between different behaviours. Here, we describe and investigate two simple mathematical models for oncolytic virus cancer therapy, with constant and immunity-dependent carrying capacity. While both models can exhibit complex dynamics, namely fixed points, periodic orbits and chaotic behaviours, only the model with immunity-dependent carrying capacity can exhibit them for biologically realistic situations, i.e., before the tumour grows too large and the experiment is terminated. Moreover, with the help of the bifurcation diagrams we uncover two unexpected behaviours in virus-tumour dynamics: (i) for short virus half-life, the tumour size seems to be too small to be detected, while for long virus half-life the tumour grows to larger sizes that can be detected; (ii) some model parameters have opposite effects on the transient and asymptotic dynamics of the tumour.
dc.relation.ispartofMathematical Modelling of Natural Phenomenaen
dc.rights© 2016, EDP Sciences. This work has been made available online in accordance with the publisher’s policies. This is the final published version of the work, which was originally published at
dc.subjectCancer modellingen
dc.subjectOncolytic viral therapyen
dc.subjectGlobal dynamicsen
dc.subjectQA Mathematicsen
dc.subjectRC0254 Neoplasms. Tumors. Oncology (including Cancer)en
dc.subjectSDG 3 - Good Health and Well-beingen
dc.titleBifurcations and chaotic dynamics in a tumour-immune-virus systemen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Applied Mathematicsen
dc.description.statusPeer revieweden

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