Analysis, Prediction, and Control of Epidemics: A Survey from Scalar to Dynamic Network Models

During the ongoing COVID-19 pandemic, mathematical models of epidemic spreading have emerged as powerful tools to produce valuable predictions of the evolution of the pandemic, helping public health authorities decide which intervention policies should be implemented. The study of these modelsÑgrounded in the systems theory and often analyzed using control-theoretic toolsÑis an extremely important area for many researchers from different fields, including epidemiology, engineering, physics, mathematics, computer science, sociology, economics, and management. In this survey, we review the history and present the state of the art in the modeling, analysis, and control of epidemic dynamics. We discuss different approaches to epidemic modeling, either deterministic or stochastic, ranging from the first implementations of scalar systems of differential equations, which describe the epidemic spreading at the population level, to the most recent models on dynamic networks, which capture the spatial spread and the time-varying nature of human interactions.