This article uses computational mathematics to investigate the dynamics of cooperative occurrences in chemical reactions inside living organisms. We study the dynamics of complex systems using mathematical models based on ordinary differential equations, paying special attention to chemical equilibrium and reaction speed. Explanations of cooperation, non-cooperation, and positive cooperation are presented in our study. We analyze the stabilities of equilibrium points by a systematic analysis that makes use of the Jacobian matrix and the threshold parameter R0. We next extend our investigation to evaluate global stability and the probability of the model. Variations in k3 have a notable effect on substrate concentration probabilities, indicating that it plays an important role in reaction kinetics. Reducing k3 highlights the substrate's critical contribution to the system by extending its presence in the concentration. We find that different results were obtained for cooperative behavior: higher reaction rates at different binding sites are correlated with positive cooperativity, while slower reactions are induced by negative cooperativity. The Adams–Bashforth method is used to show numerical and graphical solutions with the help of MATLAB. Tables and graphs are used to further explain the effects of the parameters. This study underlines how well ordinary differential equations may represent the complicated system dynamics found in chemical reactions. It also provides elusive insights into cooperative occurrences, which develops our understanding of the phenomenon and serves as a foundation for future research.