Trisilowati2018 - Optimal control of tumor-immune system interaction with treatment
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
Submitter of this revision: Johannes Meyer
Modellers: Johannes Meyer
Metadata information
hasTaxon (1 statement)
hasProperty (2 statements)
hasProperty (2 statements)
Curation status
Curated
Modelling approach(es)
Tags
Connected external resources
Name | Description | Size | Actions |
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Model files |
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Trisilowati2018.xml | SBML L2V4 Representation of Trisilowati2018 - Optimal control of tumor-immune system interaction with treatment | 47.74 KB | Preview | Download |
Additional files |
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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
Legends
: Variable used inside SBML models
: 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)
(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).