## Admon2017 - Modelling tumor growth with immune response and drug using ordinary differential equations

Model Identifier
BIOMD0000000904
Short description
Modelling tumor growth with immune response and drug using ordinary differential equations

This is a mathematical study about tumor growth from a different perspective, with the aim of predicting and/or controlling the disease. The focus is on the effect and interaction of tumor cell with immune and drug. This paper presents a mathematical model of immune response and a cycle phase specific drug using a system of ordinary differential equations. Stability analysis is used to produce stability regions for various values of certain parameters during mitosis. The stability region of the graph shows that the curve splits the tumor decay and growth regions in the absence of immune response. However, when immune response is present, the tumor growth region is decreased. When drugs are considered in the system, the stability region remains unchanged as the system with the presence of immune response but the population of tumor cells at interphase and metaphase is reduced with percentage differences of 1.27 and 1.53 respectively. The combination of immunity and drug to fight cancer provides a better method to reduce tumor population compared to immunity alone.
Format
SBML (L2V4)
Related Publication
• Modelling tumor growth with immune response and drug using ordinary differential equations
• Mohd Rashid Admon, Normah Maan
• Jurnal Teknologi , 5/ 2017 , Volume 79 , pages: 49-56 , DOI: 10.11113/jt.v79.9791
• Department of Mathematical Sciences, Faculty of Sciences, 81310, UTM Johor Bahru, Malaysia
• This is a mathematical study about tumor growth from a different perspective, with the aim of predicting and/or controlling the disease. The focus is on the effect and interaction of tumor cell with immune and drug. This paper presents a mathematical model of immune response and a cycle phase specific drug using a system of ordinary differential equations. Stability analysis is used to produce stability regions for various values of certain parameters during mitosis. The stability region of the graph shows that the curve splits the tumor decay and growth regions in the absence of immune response. However, when immune response is present, the tumor growth region is decreased. When drugs are considered in the system, the stability region remains unchanged as the system with the presence of immune response but the population of tumor cells at interphase and metaphase is reduced with percentage differences of 1.27 and 1.53 respectively. The combination of immunity and drug to fight cancer provides a better method to reduce tumor population compared to immunity alone.
Contributors
Submitter of the first revision: Mohammad Umer Sharif Shohan
Submitter of this revision: Mohammad Umer Sharif Shohan

Curation status
Curated

Modelling approach(es)

Tags

#### Connected external resources

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### Model files

Admon2017.cps COPASI version 4.24 (Build 197) Admon2017 - Modelling tumor growth with immune response and drug using ordinary differential equations 79.47 KB Preview | Download
• Model originally submitted by : Mohammad Umer Sharif Shohan
• Submitted: Dec 18, 2019 5:15:16 PM
##### Revisions
• Version: 3
• Submitted on: Jan 2, 2020 9:16:32 AM
• Submitted by: Mohammad Umer Sharif Shohan
• With comment: SBML file edited to add Derived From
• Version: 2
• Submitted on: Dec 18, 2019 5:15:16 PM
• Submitted by: Mohammad Umer Sharif Shohan
• With comment: Automatically added model identifier BIOMD0000000904

(*) 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

Species
Species Initial Concentration/Amount
u 0.0 mmol
Tm

Neoplastic Cell
1.2 mmol
Ti

Neoplastic Cell
1.3 mmol
I

immune response
0.9 mmol
Reactions
Reactions Rate Parameters
u => compartment*gamma*u gamma = 0.0
=> Tm; Ti compartment*a1*Ti a1 = 1.0
Tm => ; I, u compartment*(d3*Tm+a4*Tm+c3*Tm*I+k1*(-exp((-k2)*u))*Tm) c3 = 0.9; k1 = 0.0; a4 = 0.8; k2 = 0.57; d3 = 0.4
=> Ti; Tm compartment*2*a4*Tm a4 = 0.8
Ti => ; I compartment*((c1*I+d2)*Ti+a1*Ti) a1 = 1.0; c1 = 0.9; d2 = 0.11
I => ; Tm, u, Ti compartment*(c2*I*Ti+c4*Tm*I+d1*I+k3*(1-exp((-k4)*u))*I) c2 = 0.085; d1 = 0.29; k3 = 0.0; c4 = 0.085; k4 = 0.061
=> I; Ti, Tm compartment*(k+p*I*(Ti+Tm)^n/(alpha+(Ti+Tm)^n)) k = 0.029; n = 3.0; p = 0.1; alpha = 0.2
Curator's comment:
(added: 18 Dec 2019, 17:15:06, updated: 18 Dec 2019, 17:15:06)
The model has been encoded in COPASI 4.24 (Build197) and the figure 4 of the publication has been reproduced using COPASI