DOI: 10.5061/dryad.8kprr4xvg
title: An evolutionary differential game for regulating the role of monoclonal antibodies in treating signaling pathways in esophageal cancer

description: 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.
description: # An evolutionary differential game for regulating the role of monoclonal
 antibodies in treating signaling pathways in esophageal cancer 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.