An evolutionary differential game for regulating the role of monoclonal antibodies in treating signaling pathways in esophageal cancer
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Jul 30, 2024 version files 20.55 KB
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Archive.zip
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README.md
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Abstract
This work presents a new framework for a competitive evolutionary game between monoclonal antibodies and signaling pathways in esophageal cancer. The framework is based on a novel mathematical model that takes into account the dynamic progression of signaling pathways, resistance mechanisms, and monoclonal antibody therapies. The analysis and computation of two game-theoretic strategies, Stackelberg and Nash's equilibria, are conducted within this framework to ascertain the most favorable outcome for the patient. By comparing Stackelberg equilibria to Nash equilibria, numerical experiments show that the Stackelberg equilibria are superior for treating signaling pathways and are critical for the success of monoclonal antibodies in improving esophageal cancer patient outcomes.
Codes for finding Nash and Stackelberg equilibria for a competitive evolutionary game between monoclonal antibodies and signaling pathways in esophageal cancer. The codes are versatile and can be easily adjusted for any differential game that usually requires identifying Nash and Stackelberg equilibria.
Description of the file structure
- Stack.m: The main file to run the algorithm for computing Stackelberg equilibrium.
- Nash.m: The main file to run the algorithm for computing Nash equilibrium.
- Soptm.m: Solves the optimization problem of signaling pathways in esophageal cancer to find the optimal responses to the administered treatments.
- APoptm.m: Solves the optimization problem of monoclonal antibodies to find the optimal doses of Pembrolizumab to stimulate T cells to attack the signaling pathways.
- ABoptm.m: Solves the optimization problem of monoclonal antibodies to find the optimal doses of Brentuximab to deliver chemotherapy.
- Forward.m: Solves the forward the ODE Evolutionary mathematical model for signaling pathways in EC.
- Adjoint.m: Solves the adjoint ODE associated with Brentuximab.
- Adjoint2.m: Solves the adjoint ODE associated with Pembrolizumab.
- Adjoint3.m: Solves the adjoint ODE associated with the signaling pathways.
- J_A.m: The functional objective of mAbs.
- J_S.m: The functional objective of the signaling pathways.
- Gradient.m: Computes the gradient of J_A with respect to the Pembrolizumab strategies (u_p).
- Gradient2.m: Computes the gradient of J_A with respect to the Brentuximab strategies (u_b).
- Gradient3.m: Computes the gradient of J_S with respect to the signaling pathways strategies (u_c).
- Paramter.m: Contains two test datasets of parameter values for the ODE model.
- ABrmijolinsearch.m: Armijo line search algorithm for the gradient step size of solving the optimization problem of mAbs to find the optimal doses of Brentuximab.
- APrmijolinsearch.m: Armijo line search algorithm for the gradient step size of solving the optimization problem of mAbs to find the optimal doses of Pembrolizumab.
- Sarmijolinsearch.m: Armijo line search algorithm for the gradient step size of solving the optimization problem of signaling pathways in esophageal cancer to find the optimal responses to the administered treatments.