Malinzi2018 - tumour-immune interaction model

  public model
Short description
The paper describes a spatio-temporal mathematical model, in the form of a moving boundary problem, to explain cancer dormancy is developed. Created by COPASI 4.24 (Build 197) Abstract: A spatio-temporal mathematical model, in the form of a moving boundary problem, to explain cancer dormancy is developed. Analysis of the model is carried out for both temporal and spatio-temporal cases. Stability analysis and numerical simulations of the temporal model replicate experimental observations of immune-induced tumour dormancy. Travelling wave solutions of the spatio-temporal model are determined using the hyperbolic tangent method and minimum wave speeds of invasion are calculated. Travelling wave analysis depicts that cell invasion dynamics are mainly driven by their motion and growth rates. A stability analysis of the spatio-temporal model shows a possibility of dynamical stabilization of the tumour-free steady state. Simulation results reveal that the tumour swells to a dormant level.
Format
SBML (L2V4)
Related Publication
  • Mathematical analysis of a tumour-immune interaction model: A moving boundary problem.
  • Malinzi J, Amima I
  • Mathematical biosciences , 2/ 2019 , Volume 308 , pages: 8-19
  • Department of Mathematics and Applied Mathematics, University of Pretoria, Private Bag X 20, Hatfield, Pretoria 0028, South Africa. Electronic address: josephmalinzi1@gmail.com.
  • A spatio-temporal mathematical model, in the form of a moving boundary problem, to explain cancer dormancy is developed. Analysis of the model is carried out for both temporal and spatio-temporal cases. Stability analysis and numerical simulations of the temporal model replicate experimental observations of immune-induced tumour dormancy. Travelling wave solutions of the spatio-temporal model are determined using the hyperbolic tangent method and minimum wave speeds of invasion are calculated. Travelling wave analysis depicts that cell invasion dynamics are mainly driven by their motion and growth rates. A stability analysis of the spatio-temporal model shows a possibility of dynamical stabilization of the tumour-free steady state. Simulation results reveal that the tumour swells to a dormant level.
Contributors
Szeyi Ng

Metadata information

is
BioModels Database MODEL1909060001
BioModels Database BIOMD0000000809
isDescribedBy
PubMed 30537482
hasProperty
Gene Ontology regulation of immune response to tumor cell
Human Disease Ontology cancer
Experimental Factor Ontology cancer
Gene Ontology dormancy process
Mathematical Modelling Ontology Ordinary differential equation model

Curation status
Curated


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Model files

Malinzi2018 - tumour-immune interaction model.xml SBML L2V4 file for the model 54.70 KB Preview | Download

Additional files

Malinzi2018 - tumour-immune interaction model.sedml Sedml L1V2 file producing figure 2 2.24 KB Preview | Download
Malinzi2018 - tumour-immune interaction model.cps COPASI 4.24 (Build 197) file for the model 70.47 KB Preview | Download
call_mvb.m Correction MATLAB file sent by the author 2.63 KB Preview | Download
mvb.m Correction MATLAB file sent by the author 565.00 bytes Preview | Download
figure 2.png PNG plot of the model simulation Figure 2 47.03 KB Preview | Download

  • Model originally submitted by : Szeyi Ng
  • Submitted: 09-Sep-2019 09:29:21
  • Last Modified: 11-Sep-2019 14:43:08
Revisions
  • Version: 8 public model Download this version
    • Submitted on: 11-Sep-2019 14:43:08
    • Submitted by: Szeyi Ng
    • With comment: Edited model metadata online.
  • Version: 4 public model Download this version
    • Submitted on: 09-Sep-2019 09:29:21
    • Submitted by: Szeyi Ng
    • With comment: Automatically added model identifier BIOMD0000000809
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Curator's comment:
(added: 06 Sep 2019, 17:19:19, updated: 06 Sep 2019, 17:19:19)
There are some errors in the figures in the original publications. I have confirmed with the author and the first figure is what the corrected figure 2 produced using MATLAB. The second figure was produced using COPASI 4.24, setting the time to be 10. There is a correction in the parameters, sigma_1 should be 0.3, with the confirmation of the author. sigma_1 being in 0-1 would give stable solutions.