A mathematical model of chemotherapy response to tumour growth

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dc.contributor.authorPinho, Suani Tavares Rubim
dc.contributor.authorRodrigues, Diego Samuel [UNESP]
dc.contributor.authorMancera, Paulo Fernando de Arruda [UNESP]
dc.contributor.institutionUniversidade Federal da Bahia (UFBA)
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.contributor.institutionUniversidade de São Paulo (USP)
dc.date.accessioned2022-04-28T18:59:28Z
dc.date.accessioned2016-07-07T12:33:22Z
dc.date.available2022-04-28T18:59:28Z
dc.date.available2016-07-07T12:33:22Z
dc.date.issued2011
dc.description.abstractA simple mathematical model, developed to simulate the chemotherapy response to tumour growth with stabilized vascularization, is presented as a system of three differential equations associated with the normal cells, cancer cells and chemotherapy agent. Cancer cells and normal cells compete by available resources. The response to chemotherapy killing action on both normal and cancer cells obey Michaelis-Menten saturation function on the chemotherapy agent. Our aim is to investigate the efficiency of the chemotherapy in order to eliminate the cancer cells. For that, we analyse the local stability of the equilibria and the global stability of the cure equilibrium for which there is no cancer cells. We show that there is a region of parameter space that the chemotherapy may eliminate the tumour for any initial conditions. Based on numerical simulations, we present the bifurcation diagram in terms of the infusion rate and the killing action on cancer cells, that exhibit, for which infusion conditions, the system evolves to the cure state. Copyright © Applied Mathematics Institute, University of Alberta.en
dc.description.affiliationInstituto de Física, Universidade Federal da Bahia, Campus Universitário de Ondina, 40210-340, Salvador, Brasil
dc.description.affiliationInstituto de Biociências de Botucatu Universidade Estadual Paulista, CP 510, 18618-970, Botucatu
dc.description.affiliationInstituto de Ciências Matemáticas e de Computaçã o Universidade de São Paulo, 13566-590, São Carlos
dc.description.affiliationUniversidade Estadual Paulista Júlio de Mesquita Filho, Departamento de Bioestatística, Instituto de Biociências, Botucatu, Profa Irina Delanova Gemtchujnicóv, Rubião Jr., CEP 18618970, SP, Brasil
dc.description.affiliationUnespInstituto de Biociências de Botucatu Universidade Estadual Paulista, CP 510, 18618-970, Botucatu
dc.description.affiliationUnespUniversidade Estadual Paulista Júlio de Mesquita Filho, Departamento de Bioestatística, Instituto de Biociências, Botucatu, Profa Irina Delanova Gemtchujnicóv, Rubião Jr., CEP 18618970, SP, Brasil
dc.format.extent369-384
dc.identifierhttp://www.math.ualberta.ca/ami/CAMQ/table_of_content/vol_19/19_4e.htm
dc.identifier.citationThe Canadian Applied Mathematics Quarterly, v. 19, n. 4, p. 369-384, 2011.
dc.identifier.issn1073-1849
dc.identifier.issn1938-2634
dc.identifier.lattes8232289412108723
dc.identifier.orcid0000-0002-2080-8053
dc.identifier.scopus2-s2.0-84894387909
dc.identifier.urihttp://hdl.handle.net/11449/243826
dc.language.isoeng
dc.relation.ispartofThe Canadian Applied Mathematics Quarterly
dc.rights.accessRightsAcesso restrito
dc.sourceScopus
dc.sourceCurrículo Lattes
dc.subjectChemotherapyen
dc.subjectMathematical modelen
dc.subjectTumour growthen
dc.titleA mathematical model of chemotherapy response to tumour growthen
dc.typeArtigo
unesp.author.lattes8232289412108723[3]
unesp.author.orcid0000-0002-0016-1715[2]
unesp.author.orcid0000-0002-2080-8053[3]
unesp.campusUniversidade Estadual Paulista (Unesp), Instituto de Biociências, Botucatupt
unesp.departmentBioestatística - IBBpt

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