Trisilowati2018 - Optimal control of tumor-immune system interaction with treatment

  public model
Model Identifier
BIOMD0000000880
Short description 
This is a mathematical model of a growing tumor and its interaction with the immune system. The model consists of four populations: tumor cells, dendritic cells (representing the innate immune system), cytotoxic T cells, and helper T cells (as the specific immune system). The model is comprised of a system of ordinary differential equations.
Format
SBML (L2V4)
Related Publication
  • Optimal control of tumor-immune system interaction with treatment
  • Trisilowati, T.
  • AIP Conference Proceedings , 10/ 2019 , Volume 2021 , DOI: 10.1063/1.5062816
  • Mathematics Department, Faculty of Mathematics and Natural Sciences, Brawijaya University, Jalan Veteran Malang, East-Java, 65145, Indonesia
  • This paper concerns the optimal control of a mathematical model of a growing tumor and its interaction with the immune system. This model consists of four populations - tumor cells, dendritic cells (as an innate immune system), cytotoxic T cells, and helper T cells (as a specific immune system) - in the form of a system of ordinary differential equations. Some tumors present dendritic cell and such cells have a potential role in regulating the immune system. In this model, we assume that dendritic cells can activate cytotoxic T cells and, in turn, can clear out tumor cells. Furthermore, by adding controls as a treatment to the model, we minimize both the tumor cell population and the cost of treatment. We do this by applying the optimal control for this problem. First, Pontryagin's Principle is used to characterize the optimal control. Then, the optimal system is solved numerically using the Forward-Backward Runge- Kutta method. Finally, the effect of each treatment is investigated. The numerical results show that these controls are effective in reducing the number of tumor cells.
Contributors
Submitter of the first revision: Johannes Meyer
Submitter of this revision: Johannes Meyer
Modellers: Johannes Meyer

Metadata information

hasTaxon (1 statement)
Taxonomy Homo sapiens

hasProperty (2 statements)
Mathematical Modelling Ontology Ordinary differential equation model
Gene Ontology immune response

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

Connected external resources

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Model files
Trisilowati2018.xml SBML L2V4 Representation of Trisilowati2018 - Optimal control of tumor-immune system interaction with treatment 47.74 KB Preview | Download

Additional files
Trisilowati2018.cps COPASI file of Trisilowati2018 - Optimal control of tumor-immune system interaction with treatment 79.67 KB Preview | Download
Trisilowati2018.sedml SED-ML file of Trisilowati2018 - Optimal control of tumor-immune system interaction with treatment 3.58 KB Preview | Download

  • Model originally submitted by : Johannes Meyer
  • Submitted: Nov 28, 2019 3:41:28 PM
  • Last Modified: Nov 28, 2019 3:41:28 PM
Revisions
  • Version: 2 public model Download this version
    • Submitted on: Nov 28, 2019 3:41:28 PM
    • Submitted by: Johannes Meyer
    • With comment: Automatically added model identifier BIOMD0000000880
Legends
: Variable used inside SBML models


Species
Species Initial Concentration/Amount
L CD8 T Cells

cytotoxic T cell 		10.0 item
T Tumor Cells

neoplastic cell 		1000000.0 item
D Dendritic Cells

dendritic cell 		10.0 item
H CD4 T Cells

helper T cell 		5.0 item
Reactions
Reactions Rate Parameters
L_CD8_T_Cells => ; T_Tumor_Cells compartment*alpha_2*T_Tumor_Cells*L_CD8_T_Cells alpha_2 = 8.0E-10
=> T_Tumor_Cells compartment*a_1*T_Tumor_Cells*(1-b_1__1*T_Tumor_Cells) b_1__1 = 1.02E-9; a_1 = 0.431
D_Dendritic_Cells => ; L_CD8_T_Cells compartment*beta_2*D_Dendritic_Cells*L_CD8_T_Cells beta_2 = 2.0E-5
=> D_Dendritic_Cells compartment*a_2*D_Dendritic_Cells*(1-b_2__1*D_Dendritic_Cells) b_2__1 = 1.25E-5; a_2 = 0.234
T_Tumor_Cells => ; L_CD8_T_Cells compartment*alpha_1*T_Tumor_Cells*L_CD8_T_Cells alpha_1 = 4.2E-8
L_CD8_T_Cells => compartment*e*L_CD8_T_Cells e = 1.04E-8
=> H_CD4_T_Cells compartment*a_3*H_CD4_T_Cells*(1-b_3__1*H_CD4_T_Cells) b_3__1 = 5.0E-4; a_3 = 0.017
T_Tumor_Cells => compartment*u_1*T_Tumor_Cells u_1 = 0.0
H_CD4_T_Cells => ; L_CD8_T_Cells compartment*beta_3*H_CD4_T_Cells*L_CD8_T_Cells beta_3 = 2.0E-5
Curator's comment:
(added: 28 Nov 2019, 15:41:19, updated: 28 Nov 2019, 15:41:19)
Reproduced plots of Figure 1(a,c,d) in the original publication. Model simulated and plots produced using COPASI 4.24 (Build 197).