Pairwise network models in epidemiology: a review of approximations, dynamics, and applications

The theory of complex networks provides a powerful and versatile framework for analyzing the structure, behavior, and evolution of interconnected systems. In this review, we provide a historical development of pairwise network models in epidemiology, focusing on their ability to capture local interaction dynamics in networks. We investigate the main approximation methods used to capture higher-order correlations that emerge in the early phase of an epidemic and analyze how network clustering influences the epidemic threshold. Finally, we highlight potential future research directions.