IEEE Computational Intelligence Magazine - August 2022 - 55

intervention efforts are required to
reconcile health and economy optimally.
A hypothetical pandemic scenario,
similar to the one presented in [7],
is used for the experiments, which
allows
the compar ison of results
between these papers.
II. Background and Related Work
NPIs try to minimize the exposure to
the pathogen, with the goal to reduce
the infection risk. Increased hygiene,
social distancing, lockdowns, and contact
tracing are examples for typical NPIs
[1], [10]. Despite NPIs being very effective
at containing pandemics, they
impose limitations on the economic system,
e.g., social-distancing rules burden
the food-service industry, and border
closures shut down large parts of the
travel industry. Hence, decision-makers
face the challenge of choosing containment
strategies that prevent the pathogen
from spreading without burdening
the economy more than necessary.
This can be modeled by the health
economy dilemma (HED), which can
be formulated as a multi-objective optimization
problem. In the literature, several
mathematical diffusion models are
used either to estimate the model
parameters for a real-world fit, or to find
better containment strategies. Various
works focus on optimization or prediction
of the pandemic's variables [11],
while a minority of the works model
decision-making for containment strategies
as a multi-objective problem (e.g.,
[6], [7], [12], [13]). For their optimization,
control strategies have to be represented
within the diffusion models with
adjustable parameters. Usually, the interventions
are picked using secondary data
[6], determined by machine learning [4],
or estimated using real-world proxy
measures [14]. Either way, the resulting
strategies are based on interventions
already known. Hence, novel strategies
are unlikely to be found, a challenge that
this paper addresses.
Depending on the level of analysis,
various diffusion models have been
studied in the literature. On a finegrained
level, agent-based models,
which respect stochastic interactions
between individuals, are common [15],
[16]. These models integrate at least
one random variable, such as the transmission
probability. Using these models
to study large populations is a big challenge,
as the data availability for largescale
applications is poor, which
diminishes the advantages of the
approach. Long-lasting pandemics
exhibit dynamic behavior that is difficult
to capture in a fine-grained model
without compromising the accuracy of
predictions [16]. In large-scale studies,
decision-makers usually rely on compartment
models, e.g., deterministic
differential equations like variants of
the SIR compartment model [2], [8].
The SIR (susceptible, infectious, recovered)
model contains several compartments
into which the population is
divided. Similarly, the SEIR variant
(susceptible, exposed, infectious, recovered)
adds the exposed compartment
that contains individuals who came
into contact with a pathogen, but are
not yet infected. Due to the simplicity
of this model, it is often used for realworld
simulations [7], [17].
III. Methodology
The presented approach for the pandemic
compartment model is fundamentally
close to the common SEIR
model [9]. The main compartments are:
S (susceptible) for individuals who are
vulnerable to being infected. E
(exposed) for those who came into
contact with infected individuals and
will become infected. I (infected) for
the spreaders of the virus. R (recovered)
indicates those who have gained
immunity. Typically, the population
starts in S and then transitions over to
E, I, and eventually R. The relative
compartment
sizes
and equation
parameters, such as the transmission
probability, determine how fast this
process happens and how the curves for
each compartment will look like.
Often, individuals in R will lose immunity
over time and go back to S, in
which case the virus will never fully
disappear in these models. In addition,
compartments for quarantined individuals
were added analogous to the basic
compartments: Sq, Eq, Iq, and Rq
respectively. It is an assumption in this
study that measures leading to quarantine
of individuals are the most significant
problem for the economy.
Therefore, the inclusion of these specialized
compartments allows modeling
of this property. Additionally, the SEIR
model is extended to include a compartment
D (deaths) for individuals
who succumbed to the virus. The
economy is represented by a virtual
compartment (see Section III-A). Figure
1 illustrates
the links between
compartments and highlights the most
important driving forces between
them. The population in each compartment
is relative to the total population.
As such, the total population is denoted
by 1 (representing 100% of the population)
and is equal to the sum of all pandemic
compartments, with each being
$ 0 and
#1 :
NS SE EI
IR RD
== ++ ++
++ ++ (1)
1 qq
qq
The differential equations which link
the pandemic compartments are given
by the following:
dt
dS
dt
dS
q
=- -- -
-- -+
+
rp
lr
=- +
+ct
cISp S
iR pS
rp dp
()
1
lr qqer q
dE
dt
dEq
dt
=- +
-=+
ct
cISp E
pE iE
rp dp
rp 1 dp
qr
r
-ct
cISp E
pE iE
+ qr
qerq rq
(5)
AUGUST 2022 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 55
()
qerq
(4)
qr
(3)
ct cISctc IS
ct cISp Sv Sp S
iR
rp dp() ()
rp dp
11 dp
qr rqer q
(2)
It is a major challenge to find an appropriate strategy that
simultaneously considers health, economy and social
aspects, which are known to be in conflict with each other.
IEEE Computational Intelligence Magazine - August 2022

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