Stability analysis and numerical simulations via fractional calculus for tumor dormancy models
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Outros Autores: | , , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1016/j.cnsns.2019.01.021 http://hdl.handle.net/11449/187299 |
Resumo: | Fractional calculus is a field of mathematics in considerable expansion and has been understood as a tool with a wide range of applications, including in biological systems. Cancer dormancy is a state in which cancer cells have an intrinsic rate of reduced proliferation over a period of time, after which they arise with an accelerated growth rate, usually triggering metastases. This work investigates via fractional calculus two proposed ordinary differential equation systems via fractional calculus, which address dynamics between tumor cells and the immune system. Analyses and comparison processes are performed through an analytical study about the equilibrium points of each model and numerical simulations by the Nonstandard Finite Difference (NSFD) method. The analytical and numerical results show two important behaviors associated with tumor dormancy. The first refers to qualitative changes in the stability of an equilibrium point, which strongly depend on the order of the derivative and represent scenarios where there is no cancer escape. The second behavior refers to changes in the damping of some solutions, which can represent longer periods of time to exit the state of dormancy. In this case, different orders used in the derivatives are investigated, as well as their influence on the behavior of the solutions against the main parameters of the model. |
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Stability analysis and numerical simulations via fractional calculus for tumor dormancy modelsCaputo derivativesFractional stabilityImmune systemTumor dormancyFractional calculus is a field of mathematics in considerable expansion and has been understood as a tool with a wide range of applications, including in biological systems. Cancer dormancy is a state in which cancer cells have an intrinsic rate of reduced proliferation over a period of time, after which they arise with an accelerated growth rate, usually triggering metastases. This work investigates via fractional calculus two proposed ordinary differential equation systems via fractional calculus, which address dynamics between tumor cells and the immune system. Analyses and comparison processes are performed through an analytical study about the equilibrium points of each model and numerical simulations by the Nonstandard Finite Difference (NSFD) method. The analytical and numerical results show two important behaviors associated with tumor dormancy. The first refers to qualitative changes in the stability of an equilibrium point, which strongly depend on the order of the derivative and represent scenarios where there is no cancer escape. The second behavior refers to changes in the damping of some solutions, which can represent longer periods of time to exit the state of dormancy. In this case, different orders used in the derivatives are investigated, as well as their influence on the behavior of the solutions against the main parameters of the model.São Paulo State University – UNESP, IBB, Distrito de Rubião JúniorFaculdades GalileuSão Paulo State University – UNESPSão Paulo State University – UNESP, IBB, Distrito de Rubião JúniorSão Paulo State University – UNESPUniversidade Estadual Paulista (Unesp)Faculdades GalileuSilva, Jairo G. [UNESP]Ribeiro, Aiara C.O.Camargo, Rubens F. [UNESP]Mancera, Paulo F.A. [UNESP]Santos, Fernando L.P. [UNESP]2019-10-06T15:31:53Z2019-10-06T15:31:53Z2019-06-30info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article528-543http://dx.doi.org/10.1016/j.cnsns.2019.01.021Communications in Nonlinear Science and Numerical Simulation, v. 72, p. 528-543.1007-5704http://hdl.handle.net/11449/18729910.1016/j.cnsns.2019.01.0212-s2.0-85060685593823228941210872348942751579826490000-0002-2080-80530000-0001-7417-3308Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengCommunications in Nonlinear Science and Numerical Simulationinfo:eu-repo/semantics/openAccess2021-10-23T08:53:46Zoai:repositorio.unesp.br:11449/187299Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-06T00:11:44.049586Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Stability analysis and numerical simulations via fractional calculus for tumor dormancy models |
title |
Stability analysis and numerical simulations via fractional calculus for tumor dormancy models |
spellingShingle |
Stability analysis and numerical simulations via fractional calculus for tumor dormancy models Silva, Jairo G. [UNESP] Caputo derivatives Fractional stability Immune system Tumor dormancy |
title_short |
Stability analysis and numerical simulations via fractional calculus for tumor dormancy models |
title_full |
Stability analysis and numerical simulations via fractional calculus for tumor dormancy models |
title_fullStr |
Stability analysis and numerical simulations via fractional calculus for tumor dormancy models |
title_full_unstemmed |
Stability analysis and numerical simulations via fractional calculus for tumor dormancy models |
title_sort |
Stability analysis and numerical simulations via fractional calculus for tumor dormancy models |
author |
Silva, Jairo G. [UNESP] |
author_facet |
Silva, Jairo G. [UNESP] Ribeiro, Aiara C.O. Camargo, Rubens F. [UNESP] Mancera, Paulo F.A. [UNESP] Santos, Fernando L.P. [UNESP] |
author_role |
author |
author2 |
Ribeiro, Aiara C.O. Camargo, Rubens F. [UNESP] Mancera, Paulo F.A. [UNESP] Santos, Fernando L.P. [UNESP] |
author2_role |
author author author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) Faculdades Galileu |
dc.contributor.author.fl_str_mv |
Silva, Jairo G. [UNESP] Ribeiro, Aiara C.O. Camargo, Rubens F. [UNESP] Mancera, Paulo F.A. [UNESP] Santos, Fernando L.P. [UNESP] |
dc.subject.por.fl_str_mv |
Caputo derivatives Fractional stability Immune system Tumor dormancy |
topic |
Caputo derivatives Fractional stability Immune system Tumor dormancy |
description |
Fractional calculus is a field of mathematics in considerable expansion and has been understood as a tool with a wide range of applications, including in biological systems. Cancer dormancy is a state in which cancer cells have an intrinsic rate of reduced proliferation over a period of time, after which they arise with an accelerated growth rate, usually triggering metastases. This work investigates via fractional calculus two proposed ordinary differential equation systems via fractional calculus, which address dynamics between tumor cells and the immune system. Analyses and comparison processes are performed through an analytical study about the equilibrium points of each model and numerical simulations by the Nonstandard Finite Difference (NSFD) method. The analytical and numerical results show two important behaviors associated with tumor dormancy. The first refers to qualitative changes in the stability of an equilibrium point, which strongly depend on the order of the derivative and represent scenarios where there is no cancer escape. The second behavior refers to changes in the damping of some solutions, which can represent longer periods of time to exit the state of dormancy. In this case, different orders used in the derivatives are investigated, as well as their influence on the behavior of the solutions against the main parameters of the model. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-10-06T15:31:53Z 2019-10-06T15:31:53Z 2019-06-30 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1016/j.cnsns.2019.01.021 Communications in Nonlinear Science and Numerical Simulation, v. 72, p. 528-543. 1007-5704 http://hdl.handle.net/11449/187299 10.1016/j.cnsns.2019.01.021 2-s2.0-85060685593 8232289412108723 4894275157982649 0000-0002-2080-8053 0000-0001-7417-3308 |
url |
http://dx.doi.org/10.1016/j.cnsns.2019.01.021 http://hdl.handle.net/11449/187299 |
identifier_str_mv |
Communications in Nonlinear Science and Numerical Simulation, v. 72, p. 528-543. 1007-5704 10.1016/j.cnsns.2019.01.021 2-s2.0-85060685593 8232289412108723 4894275157982649 0000-0002-2080-8053 0000-0001-7417-3308 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Communications in Nonlinear Science and Numerical Simulation |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
528-543 |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
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1808129594047332352 |