dePillis2007 - Chemotherapy for tumors An analysis of the dynamics and a study of quadratic and linear optimal controls
Model Identifier
MODEL2001160001
Short description
Abstract
We investigate a mathematical model of tumorâ€“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
Submitter of this revision: Mohammad Umer Sharif Shohan
Modellers: Mohammad Umer Sharif Shohan
Metadata information
isDescribedBy (1 statement)
hasTaxon (1 statement)
hasProperty (1 statement)
isDerivedFrom (1 statement)
isPropertyOf (1 statement)
hasTaxon (1 statement)
hasProperty (1 statement)
isDerivedFrom (1 statement)
isPropertyOf (1 statement)
Curation status
Non-curated
Modelling approach(es)
Tags
Connected external resources
Name | Description | Size | Actions |
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Model files |
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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 |
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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
Legends
: Variable used inside SBML models
: 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 |