title: Model for tumour growth with treatment by continuous and pulsed chemotherapy.
abstract: In this work we investigate a mathematical model describing tumour growth under a treatment by chemotherapy that incorporates time-delay related to the conversion from resting to hunting cells. We study the model using values for the parameters according to experimental results and vary some parameters relevant to the treatment of cancer. We find that our model exhibits a dynamical behaviour associated with the suppression of cancer cells, when either continuous or pulsed chemotherapy is applied according to clinical protocols, for a large range of relevant parameters. When the chemotherapy is successful, the predation coefficient of the chemotherapic agent acting on cancer cells varies with the infusion rate of chemotherapy according to an inverse relation. Finally, our model was able to reproduce the experimental results obtained by Michor and collaborators [Nature 435 (2005) 1267] about the exponential decline of cancer cells when patients are treated with the drug glivec.
authors: Programa de Pós-Graduação em Física, Universidade Estadual de Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil.
authors: F S
authors: FS
authors: Borges
authors: Programa de Pós-Graduação em Física, Universidade Estadual de Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil.
authors: K C
authors: KC
authors: Iarosz
authors: Department of Information and Control Engineering, Xian University of Technology, 710048 Xian, PR China.
authors: H P
authors: HP
authors: Ren
authors: Departamento de Matemática e Estatística, Universidade Estadual de Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil. Electronic address: antoniomarcosbatista@gmail.com.
authors: A M
authors: AM
authors: Batista
authors: Institute for Complex Systems and Mathematical Biology, SUPA, University of Aberdeen, AB24 3UE Aberdeen, United Kingdom.
authors: M S
authors: MS
authors: Baptista
authors: Departamento de Física, Universidade Federal do Paraná, 81531-990 Curitiba, PR, Brazil.
authors: R L
authors: RL
authors: Viana
authors: Departamento de Física, Universidade Federal do Paraná, 81531-990 Curitiba, PR, Brazil.
authors: S R
authors: SR
authors: Lopes
authors: Institute for Complex Systems and Mathematical Biology, SUPA, University of Aberdeen, AB24 3UE Aberdeen, United Kingdom.
authors: C
authors: C
authors: Grebogi
mesh_terms: D000970:Antineoplastic Agents / Q000008:administration & dosage*; D008954:Models, Biological; D009369:Neoplasms / Q000188:drug therapy / Q000473:pathology*
chemical_list: D000970:Antineoplastic Agents
keywords: Chemotherapy; Delay; Tumour