Malinzi2018 - tumour-immune interaction model
Model Identifier
BIOMD0000000809
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 , PubMed ID: 30537482
- 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
Submitter of the first revision: Szeyi Ng
Submitter of this revision: Szeyi Ng
Modellers: Szeyi Ng
Submitter of this revision: Szeyi Ng
Modellers: Szeyi Ng
Metadata information
is (2 statements)
isDescribedBy (1 statement)
hasProperty (5 statements)
isDescribedBy (1 statement)
hasProperty (5 statements)
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
Human Disease Ontology cancer
Experimental Factor Ontology cancer
Gene Ontology dormancy process
Mathematical Modelling Ontology Ordinary differential equation model
Curation status
Curated
Modelling approach(es)
Tags
Connected external resources
SBGN view in Newt Editor
| Name | Description | Size | Actions |
|---|---|---|---|
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.cps | COPASI 4.24 (Build 197) file for the model | 70.47 KB | Preview | Download |
| Malinzi2018 - tumour-immune interaction model.sedml | Sedml L1V2 file producing figure 2 | 2.24 KB | Preview | Download |
| call_mvb.m | Correction MATLAB file sent by the author | 2.63 KB | Preview | Download |
| figure 2.png | PNG plot of the model simulation Figure 2 | 47.03 KB | Preview | Download |
| mvb.m | Correction MATLAB file sent by the author | 565.00 Bytes | Preview | Download |
- Model originally submitted by : Szeyi Ng
- Submitted: Sep 9, 2019 9:29:21 AM
- Last Modified: Sep 11, 2019 2:43:08 PM
Revisions
-
Version: 8
- Submitted on: Sep 11, 2019 2:43:08 PM
- Submitted by: Szeyi Ng
- With comment: Edited model metadata online.
-
Version: 4
- Submitted on: Sep 9, 2019 9:29:21 AM
- Submitted by: Szeyi Ng
- With comment: Automatically added model identifier BIOMD0000000809
(*) You might be seeing discontinuous
revisions as only public revisions are displayed here. Any private revisions
of this model will only be shown to the submitter and their collaborators.
Legends
: Variable used inside SBML models
: Variable used inside SBML models
Species
| Species | Initial Concentration/Amount |
|---|---|
| x Immune Cell |
0.3 mmol |
| y cancer |
0.8 mmol |
| ystar cancer ; Dead |
0.1 mmol |
| u Chemokine ; Concentration |
1.0E-6 mmol |
Reactions
| Reactions | Rate | Parameters |
|---|---|---|
| => x; y | compartment*delta*x*y/(gamma+x) | delta = 3.0218; gamma = 2.02 |
| y => ; x | compartment*nu_2*x*y | nu_2 = 0.7279 |
| ystar => | compartment*myu_2*ystar | myu_2 = 0.24 |
| => x | compartment*phi_1*x*(1-phi_2*x) | phi_2 = 0.25; phi_1 = 1.3398 |
| x => ; y | compartment*nu_1*x*y | nu_1 = 0.00218 |
| => ystar; x, y | compartment*rho*x*y | rho = 0.1 |
| => y | compartment*sigma_1*y*(1-sigma_2*y) | sigma_2 = 0.5; sigma_1 = 0.3 |
| => u; x, y | compartment*nu_3*x*y | nu_3 = 300.0 |
| u => | compartment*myu_1*u | myu_1 = 1.0 |
Curator's comment:
(added: 06 Sep 2019, 17:19:19, updated: 06 Sep 2019, 17:19:19)
(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.