Bianca2013 - Persistence analysis in a Kolmogorov-type model for cancer-immune system competition

  public model
Model Identifier
BIOMD0000000900
Short description 
Persistence analysis in a Kolmogorov-type model for cancer-immune system competition
AIP Conference Proceedings 1558, 1797 (2013); https://doi.org/10.1063/1.4825874
C. Bianca
Dipartimento di Scienze Matematiche, Politecnico di Torino, Torino, Italy
F. Pappalardo
Dipartimento di Scienza del Farmaco, Università degli Studi di Catania, Catania, Italy
M. Pennisi and M. A. Ragusa
Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Catania, Italy
Format
SBML (L2V4)
Related Publication
  • Persistence analysis in a Kolmogorov-type model for cancer-immune system competition
  • C. Bianca, F. Pappalardo, M. Pennisi and M. A. Ragusa
  • AIP Conference Proceedings 1558 , 10/ 2013 , Volume 1558 , Issue 1 , DOI: 10.1063/1.4825874
  • Dipartimento di Scienze Matematiche, Politecnico di Torino, Torino, Italy Dipartimento di Scienza del Farmaco, Università degli Studi di Catania, Catania, Italy Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Catania, Italy
  • This paper is concerned with analytical investigations on the competition between cancer cells and immune system cells. Specifically the role of the B-cells and T-cells in the evolution of cancer cells is taken into account. The mathematical model is a Kolmogorov-type system of three evolution equations where the growth rate of the cells is described by logistic law and the response of B-cells and T-cells is modeled according to Holling type-II function. The stability analysis of equilibrium points is performed and the persistence of the model is proved.
Contributors
Submitter of the first revision: Mohammad Umer Sharif Shohan
Submitter of this revision: Mohammad Umer Sharif Shohan
Modellers: Mohammad Umer Sharif Shohan

Metadata information

is (2 statements)
BioModels Database BIOMD0000000900
BioModels Database MODEL1912180002

hasTaxon (1 statement)
Taxonomy Homo sapiens

hasProperty (2 statements)
Mathematical Modelling Ontology Ordinary differential equation model
Gene Ontology immune response

isDescribedBy (1 statement)
isDerivedFrom (1 statement)
Curation status
Curated
Modelling approach(es)
ordinary differential equation model
Tags
Immuno-oncology

Connected external resources

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Model files
Bianca2013.xml SBML L2V4 Representation of Bianca2013 - Persistence analysis in a Kolmogorov-type model for cancer-immune system competition 34.72 KB Preview | Download

Additional files
Bianca2013.cps COPASI version 4.24 (Build 197) Representation of Bianca2013 - Persistence analysis in a Kolmogorov-type model for cancer-immune system competition 56.95 KB Preview | Download
Bianca2013.sedml SEDML L1V2 Representation of Bianca2013 - Persistence analysis in a Kolmogorov-type model for cancer-immune system competition 3.74 KB Preview | Download

  • Model originally submitted by : Mohammad Umer Sharif Shohan
  • Submitted: Dec 18, 2019 10:34:03 AM
  • Last Modified: Dec 18, 2019 10:34:03 AM
Revisions
  • Version: 3 public model Download this version
    • Submitted on: Dec 18, 2019 10:34:03 AM
    • Submitted by: Mohammad Umer Sharif Shohan
    • With comment: Automatically added model identifier BIOMD0000000900
Legends
: Variable used inside SBML models


Species
Species Initial Concentration/Amount
C

cancer 		1.0 mmol
B

BTO:0000776 		1.0 mmol
T

T-lymphocyte 		1.0 mmol
Reactions
Reactions Rate Parameters
=> C compartment*alpha_1*C*(1-C/beta_1) beta_1 = 10.0; alpha_1 = 0.05
=> B; C compartment*alpha_2*C*B*(1-B/beta_2)*gamma_1/(1+gamma_1*C) alpha_2 = 0.31; beta_2 = 3.0; gamma_1 = 0.5
=> T; C compartment*alpha_3*C*T*(1-T/beta_3)*gamma_2/(1+gamma_2*C) beta_3 = 3.0; gamma_2 = 0.65; alpha_3 = 0.5
C => ; B, T compartment*(gamma_1/(1+gamma_1*C)*C*B+gamma_2/(1+gamma_2*C)*C*T) gamma_2 = 0.65; gamma_1 = 0.5
T => compartment*delta_2*T delta_2 = 0.173286795139986
B => compartment*delta_1*B delta_1 = 0.0990210257942779
Curator's comment:
(added: 18 Dec 2019, 10:33:53, updated: 18 Dec 2019, 10:33:53)
The model has been encoded in COPASI 4.24 (Build 197) and the figure1 of the publication has been reproduced using COPASI