BioModelsapplication/xmlhttps://www.ebi.ac.uk/biomodels/model/download/BIOMD0000000919?filename=Ledzewicz2013.xmlhttps://www.ebi.ac.uk/biomodels/model/download/BIOMD0000000919?filename=Ledzewicz2013.sedmlhttps://www.ebi.ac.uk/biomodels/model/download/BIOMD0000000919?filename=Ledzewicz2013.cpsprimaryOK200Mohammad Umer Sharif ShohanManually curatedordinary differential equation modelL2V4Immuno-oncologyhttps://www.ebi.ac.uk/biomodels/BIOMD000000091923906150falseBioModelsSBMLModelsLedzewicz2013 On optimal chemotherapy with a strongly targeted agent for a model of tumor immune system interactions with generalized logistic growth2013MODEL2003060003Ledzewicz ULedzewicz U, Olumoye O, Schättler H23906150,
In this paper, a mathematical model for chemotherapy that takes tumor immune-system interactions into account is considered for a strongly targeted agent. We use a classical model originally formulated by Stepanova, but replace exponential tumor growth with a generalised logistic growth model function depending on a parameter v. This growth function interpolates between a Gompertzian model (in the limit v → 0) and an exponential model (in the limit v → ∞). The dynamics is multi-stable and equilibria and their stability will be investigated depending on the parameter v. Except for small values of v, the system has both an asymptotically stable microscopic (benign) equilibrium point and an asymptotically stable macroscopic (malignant) equilibrium point. The corresponding regions of attraction are separated by the stable manifold of a saddle. The optimal control problem of moving an initial condition that lies in the malignant region into the benign region is formulated and the structure of optimal singular controls is determined.. 3, 10.
Dept. of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, Illinois 62026-1653, USA. uledzew@siue.edum.sharifshohan@gmail.comEMBL-EBIBIOMD0000000919In this paper, a mathematical model for chemotherapy that takes tumor immune-system interactions into account is considered for a strongly targeted agent. We use a classical model originally formulated by Stepanova, but replace exponential tumor growth with a generalised logistic growth model function depending on a parameter v. This growth function interpolates between a Gompertzian model (in the limit v → 0) and an exponential model (in the limit v → ∞). The dynamics is multi-stable and equilibria and their stability will be investigated depending on the parameter v. Except for small values of v, the system has both an asymptotically stable microscopic (benign) equilibrium point and an asymptotically stable macroscopic (malignant) equilibrium point. The corresponding regions of attraction are separated by the stable manifold of a saddle. The optimal control problem of moving an initial condition that lies in the malignant region into the benign region is formulated and the structure of optimal singular controls is determined.On optimal chemotherapy with a strongly targeted agent for a model of tumor-immune system interactions with generalized logistic growth.Ledzewicz Urszula U, Olumoye Omeiza O, Schättler Heinz Hdevelopment, Immune, Immune Systems, postnatal development., growth pattern, non-developmental growth, System, Systems, postnatal growth, Chemotherapy, growth and development, Tumor, generalised, growthsmall, other disease, 0998/12, Controlling, Ets, Papers, conformation, region or site annotation, PNT-P1, ETS2, postnatal development, Ets2, DmelCG17077, disorders, D-Ets-2, growth and development, EY3-1, ets94F, function, Pnt, 0123/09, medical condition, Tumor, body system, development, DMPOINT1A, pntegfr, 0608/07, png, reduced, diseases, disease or disorder, sequence, Chemotherapy, condition, system, diseases and disorders, tiny, connected anatomical system, D-ets-2, 3520, pnt-P1, Separated, pnt-P2, l(3)s118306, region, relational structural quality., Pnt-P1, Separation, positional, Divorced, human disease, anatomical systems, pntP2, Pointed-P1, positional polypeptide feature, pointed-RC, reference sample, growth pattern, underdeveloped, non-developmental growth, Separations, postnatal growth, Ets94F, hypoplasia, Divorces, benign, generalised, EK3-2, primary structure of sequence macromolecule, organ system, non-neoplastic, ptd, l(3)07825, PntP2, disease, Ets58AB, PntP1, E(E2F)3D, disorder, site, CG17077, Homo sapiens disease, PNTP2, growth, PNTP1, l(3)j1B7, POINT, Controlled, CG8705other disease, 0998/12, Immune Systems, conformation, region or site annotation, PNT-P1, ETS2, postnatal development, Ets2, DmelCG17077, growth and development, EY3-1, Pnt, Tumor, SCh, body system, DMPOINT1A, pntegfr, 0608/07, png, BANF, reduced, diseases, disease or disorder, system, diseases and disorders, tiny, D-ets-2, 3520, Separated, Pnt-P1, Mathematic, spindle cell hemangioendothelioma, positional, Divorced, human disease, anatomical systems, pointed-RC, reference sample, hypoplasia, Statistic, Divorces, benign, generalised, suprachiasmatic nucleus of hypothalamus, EK3-2, non-neoplastic, l(3)07825, Immune, Abstract, ACN, disorder, site, CG17077, Homo sapiens disease, l(3)j1B7, Controlled, small, Controlling, Ets, Papers, nucleus suprachiasmaticus, disorders, D-Ets-2, ets94F, function, 0123/09, medical condition, development, spindle cell hemangioma, Systems, sequence, Chemotherapy, condition, University, connected anatomical system, pnt-P1, pnt-P2, l(3)s118306, region, relational structural quality., Separation, pntP2, Pointed-P1, positional polypeptide feature, growth pattern, underdeveloped, non-developmental growth, System, Separations, postnatal growth, Ets94F, primary structure of sequence macromolecule, organ system, ptd, PntP2, disease, Ets58AB, PntP1, E(E2F)3D, nucleus suprachiasmaticus hypothalami, PNTP2, spindle -cell hemangioma, SCH, growth, PNTP1, suprachiasmatic nucleus (Spiegel-Zwieg), POINT, SCN, CG8705development, Immune, Immune Systems, postnatal development., growth pattern, non-developmental growth, System, Systems, postnatal growth, Chemotherapy, growth and development, Tumor, generalised, growthfalseLedzewicz2013 - On optimal chemotherapy with a strongly targeted agent for a model of tumor immune system interactions with generalized logistic growth
On optimal chemotherapy with a strongly targeted agent for a model of tumor-immune system interactions with generalized logistic growth.
Ledzewicz U1, Olumoye O, Schättler H.
1
Dept. of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, Illinois 62026-1653, USA. uledzew@siue.edu
Abstract
In this paper, a mathematical model for chemotherapy that takes tumor immune-system interactions into account is considered for a strongly targeted agent. We use a classical model originally formulated by Stepanova, but replace exponential tumor growth with a generalised logistic growth model function depending on a parameter v. This growth function interpolates between a Gompertzian model (in the limit v → 0) and an exponential model (in the limit v → ∞). The dynamics is multi-stable and equilibria and their stability will be investigated depending on the parameter v. Except for small values of v, the system has both an asymptotically stable microscopic (benign) equilibrium point and an asymptotically stable macroscopic (malignant) equilibrium point. The corresponding regions of attraction are separated by the stable manifold of a saddle. The optimal control problem of moving an initial condition that lies in the malignant region into the benign region is formulated and the structure of optimal singular controls is determined
2020-03-062020-03-062020-03-06BIOMD000000091923906150C94515MODEL2003060003BIOMD0000000919GO:0045066GO:0006924GO:0002418GO:00024139606