Solis-perez2019 - A fractional mathematical model of breast cancer competition model

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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

Metadata information

is (2 statements)
BioModels Database MODEL1912180005
BioModels Database BIOMD0000000903

hasInstance (3 statements)
Taxonomy Homo sapiens
Mathematical Modelling Ontology Ordinary differential equation model
NCIt Breast Carcinoma

hasTaxon (1 statement)
Taxonomy Homo sapiens

hasProperty (1 statement)
Mathematical Modelling Ontology Ordinary differential equation model

isDescribedBy (2 statements)
isDerivedFrom (1 statement)
Curation status
Curated
Modelling approach(es)
ordinary differential equation model
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Model files
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
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
  • Version: 2 public model Download this version
    • Submitted on: Dec 18, 2019 2:41:48 PM
    • Submitted by: Mohammad Umer Sharif Shohan
    • With comment: Automatically added model identifier BIOMD0000000903
Legends
: 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)
The model has been encode in COPASI 4.24 (Build 197) and the Figure 1 of the publication has been reproduced using COPASI