dePillis2007 - Chemotherapy for tumors An analysis of the dynamics and a study of quadratic and linear optimal controls

  public model
Model Identifier
MODEL2001160001
Short description
Abstract We investigate a mathematical model of tumor–immune interactions with chemotherapy, and strategies for optimally administering treatment. In this paper we analyze the dynamics of this model, characterize the optimal controls related to drug therapy, and discuss numerical results of the optimal strategies. The form of the model allows us to test and compare various optimal control strategies, including a quadratic control, a linear control, and a state-constraint. We establish the existence of the optimal control, and solve for the control in both the quadratic and linear case. In the linear control case, we show that we cannot rule out the possibility of a singular control. An interesting aspect of this paper is that we provide a graphical representation of regions on which the singular control is optimal. 2006 Elsevier Inc. All rights reserved.
Format
SBML (L2V4)
Related Publication
  • Chemotherapy for tumors: an analysis of the dynamics and a study of quadratic and linear optimal controls.
  • de Pillis LG, Gu W, Fister KR, Head T, Maples K, Murugan A, Neal T, Yoshida K
  • Mathematical biosciences , 9/ 2007 , Volume 209 , Issue 1 , pages: 292-315 , PubMed ID: 17306310
  • Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, United States. depillis@hmc.edu
  • We investigate a mathematical model of tumor-immune interactions with chemotherapy, and strategies for optimally administering treatment. In this paper we analyze the dynamics of this model, characterize the optimal controls related to drug therapy, and discuss numerical results of the optimal strategies. The form of the model allows us to test and compare various optimal control strategies, including a quadratic control, a linear control, and a state-constraint. We establish the existence of the optimal control, and solve for the control in both the quadratic and linear case. In the linear control case, we show that we cannot rule out the possibility of a singular control. An interesting aspect of this paper is that we provide a graphical representation of regions on which the singular control is optimal.
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

isDescribedBy (1 statement)
PubMed 17306310

hasTaxon (1 statement)
Taxonomy Homo sapiens

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

isDerivedFrom (1 statement)
isPropertyOf (1 statement)
Mathematical Modelling Ontology Ordinary differential equation model

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

Connected external resources

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Model files
dePillis2007.xml SBML L2V4 dePillis2007 - Chemotherapy for tumors An analysis of the dynamics and a study of quadratic and linear optimal controls 40.63 KB Preview | Download

Additional files
dePillis2007.cps COPASI version 4.24 (Build 197) dePillis2007 - Chemotherapy for tumors An analysis of the dynamics and a study of quadratic and linear optimal controls 81.68 KB Preview | Download

  • Model originally submitted by : Mohammad Umer Sharif Shohan
  • Submitted: Jan 16, 2020 12:29:36 AM
  • Last Modified: Jan 16, 2020 12:29:36 AM
Revisions
  • Version: 2 public model Download this version
    • Submitted on: Jan 16, 2020 12:29:36 AM
    • Submitted by: Mohammad Umer Sharif Shohan
    • With comment: Edited model metadata online.
Legends
: Variable used inside SBML models


Species
Species Initial Concentration/Amount
T

neoplasm 		1.0E7 mmol
N

Immune Cell 		500000.0 mmol
C

C120462 		4.17E10 mmol
M

Combination Chemotherapy 		0.0 mmol
I

Interleukin-2 		2000.0 mmol
L

cytotoxic T-lymphocyte 		2000.0 mmol
Reactions
Reactions Rate Parameters
=> T compartment*a*T*(1-b*T) a = 0.002; b = 1.02E-9
=> N; T compartment*(alpha_1+g*T^eta/(h+T^eta)*N) alpha_1 = 13000.0; h = 600.0; g = 0.025; eta = 1.0
N => ; T, M compartment*(f*N+p*N*T+K_N*M*N) p = 1.0E-7; f = 0.0412; K_N = 0.6
C => ; M compartment*(beta*C+K_C*M*C) beta = 0.012; K_C = 0.6
M => compartment*gamma*M gamma = 0.9
=> I; T, L compartment*(p_T*T/(g_T+T)*L+w*L*I+V_I) V_I=0.0; w = 2.0E-4; g_T = 100000.0; p_T = 0.6
L => ; T, M compartment*(m*L+q*L*T+u*L*L+K_L*M*L) K_L = 0.6; q = 3.42E-10; u = 3.0; m = 0.02
=> L; C, T, I compartment*(r2*C*T+p_I*L*I/(g_I+I)+V_L) r2 = 3.0E-11; p_I = 0.125; V_L=0.0; g_I = 2.0E7
T => ; N, M compartment*(c1*N*T+D*T+K_T*M*T) D = 6.6666657777779E-7; K_T = 0.8; c1 = 3.23E-7
=> M compartment*V_M V_M=0.0
=> C compartment*alpha_2 alpha_2 = 5.0E8
I => compartment*mu_I*I mu_I = 10.0