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

TL;DR

This survey reviews the evolution of epidemic modeling from simple scalar differential equations to complex dynamic network models, emphasizing control strategies and interdisciplinary applications during pandemics like COVID-19.

Contribution

It provides a comprehensive overview of epidemic models, highlighting recent advances in dynamic network approaches and control methods for epidemic management.

Findings

Dynamic network models better capture spatial and temporal spread.

Control strategies are crucial for effective epidemic mitigation.

Recent models incorporate time-varying human interactions.

Abstract

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 models -- grounded in the systems theory and often analyzed using control-theoretic tools -- is an extremely important research 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 to describing the epidemic spreading at the population level, and to more recent models on dynamic networks, which capture the spatial spread and the time-varying nature of human interactions.