IEEE Circuits and Systems Magazine - Q4 2021 - 4

Feature
Analysis, Prediction,
and Control of Epidemics:
A Survey from Scalar to
Dynamic Network Models
Lorenzo Zino, Member, IEEE and
Ming Cao, Senior Member, IEEE
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 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.
I. Brief History of 260 Years of Mathematical
Models of Epidemics
S
4
ince the beginning of human history, pandemics
have posed deadly threats, which often decimated
our species. Hence, it was not surprising
that, in parallel with the theoretical development of calculus,
mathematicians started to apply their theoretical
paradigms to describe, study, and unveil the mechanisms
of spreading of infectious diseases. In this vein, the first
milestone can be found in the work on smallpox by
Digital Object Identifier 10.1109/MCAS.2021.3118100
Date of current version: 12 November 2021
IEEE CIRCUITS AND SYSTEMS MAGAZINE
Daniel Bernoulli [1], published in 1760. In the 18th century,
there was an ongoing public debate about variolation,
i.e., inoculation of infectious material from smallpox
cases to induce a mild infection and lifelong immunity. In
Bernoulli's work, the Dutch-born Swiss mathematician
built a mathematical theory to support the effectiveness of
1531-636X/21©2021IEEE
FOURTH QUARTER 2021

IEEE Circuits and Systems Magazine - Q4 2021

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