Analysis and Control of Epidemics: A Survey of Spreading Processes on Complex Networks

This article reviews and presents various solved and open problems in the development, analysis, and control of epidemic models. The proper modeling and analysis of spreading processes has been a long-standing area of research among many different fields, including mathematical biology, physics, computer science, engineering, economics, and the social sciences. One of the earliest epidemic models conceived was by Daniel Bernoulli in 1760, which was motivated by studying the spread of smallpox [1]. In addition to Bernoulli, there were many different researchers also working on mathematical epidemic models around this time [2]. These initial models were quite simplistic, and the further development and study of such models dates back to the 1900s [3]-[6], where still-simple models were studied to provide insight into how various diseases can spread through a population. In recent years, there has been a resurgence of interest in these problems as the concept of "networks" becomes increasingly prevalent in modeling many different aspects of the world today. A more comprehensive review of the history of mathematical epidemiology can be found in [7] and [8].