title: Avoiding healthy cells extinction in a cancer model.
abstract: We consider a dynamical model of cancer growth including three interacting cell populations of tumor cells, healthy host cells and immune effector cells. For certain parameter choice, the dynamical system displays chaotic motion and by decreasing the response of the immune system to the tumor cells, a boundary crisis leading to transient chaotic dynamics is observed. This means that the system behaves chaotically for a finite amount of time until the unavoidable extinction of the healthy and immune cell populations occurs. Our main goal here is to apply a control method to avoid extinction. For that purpose, we apply the partial control method, which aims to control transient chaotic dynamics in the presence of external disturbances. As a result, we have succeeded to avoid the uncontrolled growth of tumor cells and the extinction of healthy tissue. The possibility of using this method compared to the frequently used therapies is discussed.
authors: Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain.
authors: Álvaro G
authors: ÁG
authors: López
authors: Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain.
authors: Juan
authors: J
authors: Sabuco
authors: Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain.
authors: Jesús M
authors: JM
authors: Seoane
authors: Instituto Superior de Engenharia de Lisboa, Department of Mathematics, Rua Conselheiro Emídio Navarro 1, 1949-014, Lisboa, Portugal.
authors: Jorge
authors: J
authors: Duarte
authors: Instituto Superior de Engenharia de Lisboa, Department of Mathematics, Rua Conselheiro Emídio Navarro 1, 1949-014, Lisboa, Portugal.
authors: Cristina
authors: C
authors: Januário
authors: Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain.
authors: Miguel A F
authors: MA
authors: Sanjuán
mesh_terms: D000465:Algorithms; D016923:Cell Death; D002477:Cells / Q000166:cytology*; D006262:Health; D006801:Humans; D008954:Models, Biological; D009369:Neoplasms / Q000473:pathology*; D013997:Time Factors
keywords: Cancer models; Chaos; Partial control; Therapy; Tumor growth