Malinzi2018  tumourimmune interaction model
Model Identifier
BIOMD0000000809
Short description
The paper describes a spatiotemporal 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 spatiotemporal 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 spatiotemporal cases. Stability analysis and numerical simulations of the temporal model replicate experimental observations of immuneinduced tumour dormancy. Travelling wave solutions of the spatiotemporal 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 spatiotemporal model shows a possibility of dynamical stabilization of the tumourfree steady state. Simulation results reveal that the tumour swells to a dormant level.
Format
SBML
(L2V4)
Related Publication
 Mathematical analysis of a tumourimmune interaction model: A moving boundary problem.
 Malinzi J, Amima I
 Mathematical biosciences , 2/ 2019 , Volume 308 , pages: 819 , 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 spatiotemporal 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 spatiotemporal cases. Stability analysis and numerical simulations of the temporal model replicate experimental observations of immuneinduced tumour dormancy. Travelling wave solutions of the spatiotemporal 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 spatiotemporal model shows a possibility of dynamical stabilization of the tumourfree 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
Name  Description  Size  Actions 

Model files 

Malinzi2018  tumourimmune interaction model.xml  SBML L2V4 file for the model  54.70 KB  Preview  Download 
Additional files 

Malinzi2018  tumourimmune interaction model.cps  COPASI 4.24 (Build 197) file for the model  70.47 KB  Preview  Download 
Malinzi2018  tumourimmune 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 
1.0E6 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*(1phi_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*(1sigma_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 01 would give stable solutions.