Solis-perez2019 - A fractional mathematical model of breast cancer competition model
Model Identifier
BIOMD0000000903
Short description
A fractional mathematical model of breast cancer competition model Author links open overlay panelJ.E.Solís-PérezaJ.F.Gómez-Aguilar bA.Atanganac a Tecnológico Nacional de México/CENIDET. Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, México b CONACyT-Tecnológico Nacional de México/CENIDET. Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, México c Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa Abstract In this paper, a mathematical model which considers population dynamics among cancer stem cells, tumor cells, healthy cells, the effects of excess estrogen and the body’s natural immune response on the cell populations was considered. Fractional derivatives with power law and exponential decay law in Liouville–Caputo sense were considered. Special solutions using an iterative scheme via Laplace transform were obtained. Furthermore, numerical simulations of the model considering both derivatives were obtained using the Atangana–Toufik numerical method. Also, random model described by a system of random differential equations was presented. The use of fractional derivatives provides more useful information about the complexity of the dynamics of the breast cancer competition model.
Format
SBML
(L2V4)
Related Publication
- A fractional mathematical model of breast cancer competition model
- J.E.Solís-Pérez a J.F.Gómez-Aguilar b A.Atangana c
- Chaos, Solitons & Fractals , 10/ 2019 , Volume 127 , pages: 38-54 , DOI: 10.1016/j.chaos.2019.06.027
- a Tecnológico Nacional de México/CENIDET. Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, México b CONACyT-Tecnológico Nacional de México/CENIDET. Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, México c Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa
- In this paper, a mathematical model which considers population dynamics among cancer stem cells, tumor cells, healthy cells, the effects of excess estrogen and the body’s natural immune response on the cell populations was considered. Fractional derivatives with power law and exponential decay law in Liouville–Caputo sense were considered. Special solutions using an iterative scheme via Laplace transform were obtained. Furthermore, numerical simulations of the model considering both derivatives were obtained using the Atangana–Toufik numerical method. Also, random model described by a system of random differential equations was presented. The use of fractional derivatives provides more useful information about the complexity of the dynamics of the breast cancer competition model. Volume 127, October 2019, Pages 38-54
Contributors
Submitter of the first revision: Mohammad Umer Sharif Shohan
Submitter of this revision: Mohammad Umer Sharif Shohan
Modellers: Mohammad Umer Sharif Shohan
Submitter of this revision: Mohammad Umer Sharif Shohan
Modellers: Mohammad Umer Sharif Shohan
Metadata information
is (2 statements)
hasInstance (3 statements)
hasTaxon (1 statement)
hasProperty (1 statement)
isDescribedBy (2 statements)
isDerivedFrom (1 statement)
hasInstance (3 statements)
Taxonomy
Homo sapiens
Mathematical Modelling Ontology Ordinary differential equation model
NCIt Breast Carcinoma
Mathematical Modelling Ontology Ordinary differential equation model
NCIt Breast Carcinoma
hasTaxon (1 statement)
hasProperty (1 statement)
isDescribedBy (2 statements)
isDerivedFrom (1 statement)
Curation status
Curated
Modelling approach(es)
Tags
Connected external resources
Name | Description | Size | Actions |
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Model files |
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Solis-perez2019.xml | SBML L2V4 representation of Solis-perez2019 - A fractional mathematical model of breast cancer competition model | 53.56 KB | Preview | Download |
Additional files |
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Solis-perez2019.cps | COPASI version 4.24 (Build 197) Solis-perez2019 - A fractional mathematical model of breast cancer competition model | 102.41 KB | Preview | Download |
Solis-perez2019.sedml | SEDML L1V2 Solis-perez2019 - A fractional mathematical model of breast cancer competition model | 3.61 KB | Preview | Download |
- Model originally submitted by : Mohammad Umer Sharif Shohan
- Submitted: Dec 18, 2019 2:41:48 PM
- Last Modified: Dec 18, 2019 2:41:48 PM
Revisions
Legends
: Variable used inside SBML models
: Variable used inside SBML models
Species
Species | Initial Concentration/Amount |
---|---|
C BTO:0006293 |
737100.0 mmol |
T Neoplastic Cell |
7616700.0 mmol |
E | 0.0 mmol |
I Immune Cell |
0.0 mmol |
H Healthy |
2.5E7 mmol |
Reactions
Reactions | Rate | Parameters |
---|---|---|
=> C; E | compartment*(k1*C*(1-C/M1)+p1*C*E/(a1+C)) | p1 = 600.0; M1 = 2270000.0; k1 = 0.75; a1 = 1135000.0 |
T => ; I | compartment*(n1*T+gamma2*I*T) | gamma2 = 3.0E-6; n1 = 0.01 |
=> E | compartment*tau | tau = 2700.0 |
E => ; C, T, H | compartment*(mu+d1*C/(a1+C)+d2*T/(a2+T)+d3*H/(a3+H))*E | a2 = 1.135E7; mu = 0.97; a3 = 1250000.0; a1 = 1135000.0; d1 = 0.01; d2 = 0.01; d3 = 0.01 |
I => ; T, E | compartment*(gamma3*I*T+n2*I+u*I*E/(v+E)) | gamma3 = 1.0E-7; v = 400.0; u = 0.2; n2 = 0.29 |
=> I; T | compartment*(s+p*I*T/(w+T)) | s = 13000.0; w = 300000.0; p = 0.2 |
C => ; I | compartment*gamma1*I*C | gamma1 = 3.0E-7 |
H => ; T, E | compartment*(delta*H*T+p3*H*E/(a3+H)) | a3 = 1250000.0; p3 = 100.0; delta = 6.0E-8 |
=> H | compartment*q*H*(1-H/M3) | q = 0.7; M3 = 2.5E7 |
=> T; C, E | compartment*(k2*C*C/M1*(1-T/M2)+p2*T*E/(a2+T)) | p2 = 0.0; M2 = 2.27E7; a2 = 1.135E7; M1 = 2270000.0; k2 = 0.514 |
Curator's comment:
(added: 18 Dec 2019, 14:41:36, updated: 18 Dec 2019, 14:41:36)
(added: 18 Dec 2019, 14:41:36, updated: 18 Dec 2019, 14:41:36)
The model has been encode in COPASI 4.24 (Build 197) and the Figure 1 of the publication has been reproduced using COPASI