Khajanchi2015 - The combined effects of optimal control in cancer remission

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Model Identifier
BIOMD0000000897
Short description 
The combined effects of optimal control in cancer remission
SubhasKhajanchi
DibakarGhosh
Abstract

We investigate a mathematical model depicting the nonlinear dynamics of immunogenic tumors as envisioned by Kuznetsov et al. [1]. To understand the dynamics under what circumstances the cancer cells can be eliminated, we implement the theory of optimal control. We design two types of external treatment strategies, one is Adoptive Cellular Immunotherapy and another is interleukin-2. Our aim is to establish the treatment regimens that maximize the effector cell count and minimize the tumor cell burden and the deleterious effects of the total amount of drugs. We derive the existence of an optimal control by using the boundedness of solutions. We characterize the optimality system, in which the state system is coupled with co-states. The uniqueness of an optimal control of our problem is also analyzed. Finally, we demonstrate the numerical illustrations that the optimal regimens reduce the tumor burden under different scenarios.
Format
SBML (L2V4)
Related Publication
  • The combined effects of optimal control in cancer remission
  • SubhasKhajanchi a,b, DibakarGhosh c
  • Applied Mathematics and Computation , 11/ 2015 , Volume 271 , pages: 375-388 , DOI: 10.1016/j.amc.2015.09.012
  • a Department of Mathematics, Indian Institute of Technology Roorkee, Uttaranchal - 247667, India b Department of Mathematics, Bankura University, Bankura - 722146, India c Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata - 700108, India
  • We investigate a mathematical model depicting the nonlinear dynamics of immunogenic tumors as envisioned by Kuznetsov et al. [1]. To understand the dynamics under what circumstances the cancer cells can be eliminated, we implement the theory of optimal control. We design two types of external treatment strategies, one is Adoptive Cellular Immunotherapy and another is interleukin-2. Our aim is to establish the treatment regimens that maximize the effector cell count and minimize the tumor cell burden and the deleterious effects of the total amount of drugs. We derive the existence of an optimal control by using the boundedness of solutions. We characterize the optimality system, in which the state system is coupled with co-states. The uniqueness of an optimal control of our problem is also analyzed. Finally, we demonstrate the numerical illustrations that the optimal regimens reduce the tumor burden under different scenarios.
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
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Khajanchi2015.cps COPASI version 4.24 (Build 197) representation of Khajanchi2015 - The combined effects of optimal control in cancer remission 50.82 KB Preview | Download
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  • Model originally submitted by : Mohammad Umer Sharif Shohan
  • Submitted: Dec 17, 2019 10:09:12 AM
  • Last Modified: Jan 2, 2020 10:34:14 AM
Revisions
  • Version: 4 public model Download this version
    • Submitted on: Jan 2, 2020 10:34:14 AM
    • Submitted by: Mohammad Umer Sharif Shohan
    • With comment: SBML edited to add isDerivedFrom
  • Version: 2 public model Download this version
    • Submitted on: Dec 17, 2019 10:09:12 AM
    • Submitted by: Mohammad Umer Sharif Shohan
    • With comment: Automatically added model identifier BIOMD0000000897

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Legends
: Variable used inside SBML models


Species
Species Initial Concentration/Amount
T

Neoplastic Cell 		8286380.0 mmol
E

Effector Immune Cell 		1708110.0 mmol
Reactions
Reactions Rate Parameters
T => ; E compartment*(n*E*T+e2*T) n = 1.101E-7; e2 = 0.0
=> E; T compartment*(s*e1+p*E*T/(g+T)) s = 13000.0; e1 = 1.0; p = 0.1245; g = 2.019E7
=> T compartment*a*T*(1-b*T) b = 2.0E-9; a = 0.18
E => ; T compartment*(m*E*T+d*E) m = 3.422E-10; d = 0.0412
Curator's comment:
(added: 17 Dec 2019, 10:09:04, updated: 17 Dec 2019, 10:09:04)
The model has been encoded in COPASI 4.24 (Build 197) and the figure 1 a and figure 1b of the publication has been reproduced using COPASI.