dePillis2003 - The dynamics of an optimally controlled tumor model: A case study

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Model Identifier
BIOMD0000000909
Short description
<notes xmlns="http://www.sbml.org/sbml/level2/version4"> <body xmlns="http://www.w3.org/1999/xhtml"> <pre>The dynamics of an optimally controlled tumor model: A case study L.GDe Pillisab ARadunskayaa https://doi.org/10.1016/S0895-7177(03)00133-X Abstract We present a phase-space analysis of a mathematical model of tumor growth with an immune response and chemotherapy. We prove that all orbits are bounded and must converge to one of several possible equilibrium points. Therefore, the long-term behavior of an orbit is classified according to the basin of attraction in which it starts. The addition of a drug term to the system can move the solution trajectory into a desirable basin of attraction. We show that the solutions of the model with a time-varying drug term approach the solutions of the system without the drug once traatment has stopped. We present numerical experiments in which optimal control therapy is able to drive the system into a desirable basin of attraction, whereas traditional pulsed chemotherapy is not.</pre> </body> </notes>
Format
SBML (L2V4)
Related Publication
  • The dynamics of an optimally controlled tumor model: A case study
  • L.GDe Pillis , Radunskaya
  • Mathematical and Computer Modelling , 6/ 2003 , Volume 37 , Issue 11 , pages: 1221-1244 , DOI: 10.1016/S0895-7177(03)00133-X
  • Harvey Mudd College, Claremont, CA 91711, U.S.A. Pomona College, Claremont, CA 91711, U.S.A.
  • Abstract We present a phase-space analysis of a mathematical model of tumor growth with an immune response and chemotherapy. We prove that all orbits are bounded and must converge to one of several possible equilibrium points. Therefore, the long-term behavior of an orbit is classified according to the basin of attraction in which it starts. The addition of a drug term to the system can move the solution trajectory into a desirable basin of attraction. We show that the solutions of the model with a time-varying drug term approach the solutions of the system without the drug once traatment has stopped. We present numerical experiments in which optimal control therapy is able to drive the system into a desirable basin of attraction, whereas traditional pulsed chemotherapy is not. Volume 37, Issue 11, June 2003, Pages 1221-1244
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

Curation status
Curated
Modelling approach(es)
ordinary differential equation model
Tags
Immuno-oncology

Connected external resources

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Model files
dePillis2003.xml SBML L2V4 dePillis2003 - The dynamics of an optimally controlled tumor model: A case study 41.07 KB Preview | Download

Additional files
dePillis2003.cps COPASI version 4.24 (Build 197) dePillis2003 - The dynamics of an optimally controlled tumor model: A case study 74.89 KB Preview | Download
dePillis2003.sedml SEDML L1V2 dePillis2003 - The dynamics of an optimally controlled tumor model: A case study 3.13 KB Preview | Download

  • Model originally submitted by : Mohammad Umer Sharif Shohan
  • Submitted: Jan 8, 2020 3:39:16 PM
  • Last Modified: Jan 8, 2020 3:39:16 PM
Revisions
  • Version: 3 public model Download this version
    • Submitted on: Jan 8, 2020 3:39:16 PM
    • Submitted by: Mohammad Umer Sharif Shohan
    • With comment: Automatically added model identifier BIOMD0000000909
Legends
: Variable used inside SBML models


Species
Species Initial Concentration/Amount
N 1.0 mmol
I

C12735 		0.15 mmol
u

C2252 		0.0 mmol
T

Neoplastic Cell 		0.25 mmol
Reactions
Reactions Rate Parameters
N => ; T, u compartment*(c4*T*N+a3*(1-exp(-u))*N) a3 = 0.1; c4 = 1.0
I => ; T, u compartment*(c1*I*T+d1*I+a1*(1-exp(-u))*I) d1 = 0.2; c1 = 1.0; a1 = 0.2
=> N compartment*r2*N*(1-b2*N) b2 = 1.0; r2 = 1.0
u => compartment*d2*u d2 = 1.0
=> u compartment*v v = 0.0
=> T compartment*r1*T*(1-b1*T) b1 = 1.0; r1 = 1.5
=> I; T compartment*(s+p*I*T/(alpha+T)) alpha = 0.3; s = 0.33; p = 0.01
T => ; I, N, u compartment*(c2*I*T+c3*T*N+a2*(1-exp(-u))*T) c2 = 0.5; c3 = 1.0; a2 = 0.3
Curator's comment:
(added: 08 Jan 2020, 15:39:03, updated: 08 Jan 2020, 15:39:03)
The model has been encoded in COPASI 4.24 (Build 197) and Figure 10 has been generated using COPASI