IEEE Circuits and Systems Magazine - Q4 2021 - 19

V. The Current Challenges with COVID-19
Since its inception in December 2019, the COVID-19
outbreak has rapidly spread, becoming a worldwide
pandemic with over 108 million reported cases as of
February 16, 2021. In response to this unprecedented
health crisis, we witnessed an extraordinary mobilization
of the scientific community toward better understanding
the novel disease and combating its spread.
Within this joint effort, the systems and control communities
are playing a key role in developing accurate
mathematical models to predict the evolution of the
pandemic and assess the effect of diverse intervention
policies that have been enacted or that may be implemented
[136]-[138].
A first, important contribution comes from the formulation
and analysis of more complex models for
the epidemic progression in fully-mixed populations.
These models allow to capture the specific features of
COVID-19, including a latency period before the symptoms
onset, the presence of asymptomatic individuals,
and the implementation of intervention policies such
as hospitalization of severe cases and testing. Among
these models, we should mention the SIDARTHE model
proposed in [18] (see Fig. 11), which takes into consideration
also the imperfect reporting of infected individuals.
In this work, the epidemic model is studied in a fullymixed
population framework by seeing it as a positive
linear system under feedback, and the stability of the
disease-free equilibrium is thus characterized in terms
of the H3
norm of its transfer function, which interestingly
coincides with the basic reproduction number R .0
Using this model, an open-loop fast switching strategy
to control and suppress the spread of the disease, consisting
in intermittent lockdown phases, has been proposed
and studied in [139].
Once the epidemic model has been tailored to
capture the epidemic progression of COVID-19, its
implementation on a network structure (extensively
discussed in this survey) is key to predict the spatial
spread of the disease, as highlighted in [136]. The
time-varying nature of human mobility as well as the
implementation of intervention policies through different
sequential phases have put epidemic models
on dynamic network at the forefront of the stage. In
this vein, we mention several data-informed analyses
of the outbreak in different countries, using models
with regional granularity. These studies include Italy
[140], [141], Ontario, Canada [142], Western Australia
[143], and Kazakhstan [144]. Based on these network
models, nonlinear MPC has been used to understand
the impact of intervention policies and plan their optimal
implementation. We mention the works in [145]
and in [146], with case studies based on the outbreak
FOURTH QUARTER 2021
in Italy and Germany, respectively. The impact of local,
time-varying lockdown measures and mobility restrictions
is analyzed in [147], where feedback control
laws coordinated by a centralized controller are used
to design an intermittent and differentiated regional
intervention scheme that outperforms nationwide
measures. Dynamic networks also enable modeling
the individual behavioral response to the pandemic in
terms of the adoption of self-protective behaviors and
social-distancing measures, which has a huge impact
on disease spreading [148].
At the moment of writing this survey, effective pharmaceutical
treatments for COVID-19 were unfortunately
still not available, while the research for a vaccine has
recently led to some promising findings, and extensive
vaccination campaigns are getting started. In this delicate
phase, in which only a very limited amount of the
vaccine is available, public health authorities need to
carefully plan the distribution of vaccines. The control
problems described and discussed in this survey (e.g.,
how to optimally modify the recovery rates by distributing
a fixed amount of antidote) will be precious tools to
help inform vaccination campaigns and distribution of
pharmaceutical treatments.
VI. Directions of Current and Future Research
In this survey, we went through 260 years of progresses
in mathematical models of epidemics. Starting from the
very first intuition that mathematics, and in particular
systems theory, can provide effective tools toward better
understanding the spread of infectious diseases,
we reviewed the recent developments and the state of
the art in the analysis and control of epidemic models
on networks. Alongside, we outlined some of the most
promising avenues of current and future research, which
SI DA
E
H
T
R
Figure 11. Schematic of the SIDARTHE model, proposed in
[18] to capture the epidemic progression of COVID-19. The
modeled is obtained from an SIR model, in which the health
state " infected " is substituted by five states, representing all
the four possible combinations of whether the individual has
symptoms and is detected, and a state for individuals seriously
ill; two states are used instead of the " removed " state
to account for individuals that are healed (H) or extinct (E),
respectively. The arrows illustrate all the possible transitions,
which are governed by 16 different parameters.
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