Bianca2013 - Persistence analysis in a Kolmogorov-type model for cancer-immune system competition
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
Submitter of this revision: Mohammad Umer Sharif Shohan
Modellers: Mohammad Umer Sharif Shohan
Metadata information
is (2 statements)
hasTaxon (1 statement)
hasProperty (2 statements)
isDescribedBy (1 statement)
isDerivedFrom (1 statement)
hasTaxon (1 statement)
hasProperty (2 statements)
isDescribedBy (1 statement)
isDerivedFrom (1 statement)
Curation status
Curated
Modelling approach(es)
Tags
Connected external resources
Name | Description | Size | Actions |
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Model files |
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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 |
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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
Legends
: Variable used inside SBML models
: 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)
(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