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This work presents a new framework for a competitive evolutionary game between monoclonal antibodies and signalling pathways in oesophageal cancer. The framework is based on a novel dynamical model that takes into account the dynamic progression of signalling pathways, resistance mechanisms and monoclonal antibody therapies. This game involves a scenario in which signalling pathways and monoclonal antibodies are the players competing against each other, where monoclonal antibodies use Brentuximab and Pembrolizumab dosages as strategies to counter the evolutionary resistance strategy implemented by the signalling pathways. Their interactions are described by the dynamical model, which serves as the game’s playground. The analysis and computation of two game-theoretic strategies, Stackelberg and Nash equilibria, are conducted within this framework to ascertain the most favourable outcome for the patient. By comparing Stackelberg equilibria with Nash equilibria, numerical experiments show that the Stackelberg equilibria are superior for treating signalling pathways and are critical for the success of monoclonal antibodies in improving oesophageal cancer patient outcomes. 

Nonstandard finite-difference (NSFD) methods, pioneered by R. E. Mickens, offer accurate and efficient solutions to various differential equation models in science and engineering. NSFD methods avoid numerical instabilities for large time steps, while numerically preserving important properties of exact solutions. However, most NSFD methods are only first-order accurate. This paper introduces two new classes of explicit second-order modified NSFD methods for solving n-dimensional autonomous dynamical systems. These explicit methods extend previous work by incorporating novel denominator functions to ensure both elementary stability and second-order accuracy. This paper also provides a detailed mathematical analysis and validates the methods through numerical simulations on various biological systems. 

Abstract On 3 February 2022, SpaceX launched 49 Starlink satellites, 38 of which unexpectedly de‐orbited. Although this event was attributed to space weather, definitive causality remained elusive because space weather conditions were not extreme. In this study, we identify solar sources of the interplanetary coronal mass ejections that were responsible for the geomagnetic storms around the time of launch of the Starlink satellites and for the first time, investigate their impact on Earth's magnetosphere using magnetohydrodynamic modeling. The model results demonstrate that the satellites were launched into an already disturbed space environment that persisted over several days. However, on performing comparative satellite orbital decay analyses, we find that space weather alone was not responsible but conspired together with a low‐altitude insertion and low satellite mass‐to‐area ratio to precipitate this unusual loss. Our work bridges space weather causality across the Sun–Earth system—with relevance for space‐based human technologies.