Chrobak2011 - A mathematical model of induced cancer-adaptive immune system competition

  public model
Model Identifier
BIOMD0000000815
Short description 
This is a mathematical model describing competition between an artificially induced tumor and the adaptive immune system based on the use of an autonomous system of ordinary differential equations.
Format
SBML (L2V4)
Related Publication
  • A mathematical model of induced cancer-adaptive immune system competition
  • Chrobak, J.M., Herrero, H.
  • Journal of Biological Systems , 9/ 2011 , Volume 19 , Issue 3 , pages: 521-532 , DOI: 10.1142/S0218339011004111
  • Department of Mathematics, University of Castilla-La Mancha, Avda. Camilo José Cela 3, 13071 Ciudad Real, Spain
  • We present a model of competition between an artificially induced tumor and the adaptive immune system based on the use of an autonomous system of ordinary differential equations (ODE). The aim of this work is to reproduce experimental results which find two possible outcomes depending on the initial quantities of the tumor and the adaptive immune cells. The ODE system is positively invariant and its solutions are bounded. The linear stability analysis of the fixed points of the model yields two groups of solutions depending on the initial conditions. In the first one, the immune system wins against the tumor cells, so the cancer disappears (elimination). In the second one, the cancer keeps on growing (escape). These results are coherent with experimental results which show these two possibilities, so the model reproduces the macroscopic behavior of the experiments. From the model some conclusions on the underlying competitive behavior can be derived.
Contributors
Submitter of the first revision: Johannes Meyer
Submitter of this revision: Johannes Meyer
Modellers: Johannes Meyer

Metadata information

is (2 statements)
BioModels Database MODEL1909170003
BioModels Database BIOMD0000000815

hasTaxon (1 statement)
Taxonomy Mus musculus

hasProperty (4 statements)
isDescribedBy (1 statement)
Curation status
Curated
Modelling approach(es)
ordinary differential equation model
Tags
Immuno-oncology

Connected external resources

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Model files
Chrobak2011.xml SBML L2V4 Representation of Chrobak2011 - A mathematical model of induced cancer-adaptive immune system competition 33.33 KB Preview | Download

Additional files
Chrobak2011.cps COPASI file of Chrobak2011 - A mathematical model of induced cancer-adaptive immune system competition 52.16 KB Preview | Download
Chrobak2011.sedml SED-ML file of Chrobak2011 - A mathematical model of induced cancer-adaptive immune system competition 2.34 KB Preview | Download

  • Model originally submitted by : Johannes Meyer
  • Submitted: Sep 17, 2019 2:25:44 PM
  • Last Modified: Sep 17, 2019 2:25:44 PM
Revisions
  • Version: 2 public model Download this version
    • Submitted on: Sep 17, 2019 2:25:44 PM
    • Submitted by: Johannes Meyer
    • With comment: Automatically added model identifier BIOMD0000000815
Legends
: Variable used inside SBML models


Species
Species Initial Concentration/Amount
x Cancer

neoplastic cell 		5.0E-4 item
y Immune System

Immune Cell 		0.01 item
Reactions
Reactions Rate Parameters
=> x_Cancer compartment*a*x_Cancer a = 0.0625
y_Immune_System => compartment*f*y_Immune_System^2 f = 0.03125
y_Immune_System => ; x_Cancer compartment*e*x_Cancer*y_Immune_System e = 0.0859375
x_Cancer => ; y_Immune_System compartment*b*x_Cancer*y_Immune_System b = 0.125
x_Cancer => compartment*c*x_Cancer^2 c = 0.03125
=> y_Immune_System compartment*d*y_Immune_System d = 0.03125
Curator's comment:
(added: 17 Sep 2019, 14:25:26, updated: 17 Sep 2019, 14:25:26)
Reproduced plot of Figure 5 in the original publication. Parameter values and initial conditions are as indicated in figure caption. Model simulated and plot produced using COPASI 4.24 (Build 197).