Estimation of monkeypox spread in a nonendemic country considering contact tracing and self-reporting: A stochastic modeling study

Abstract

In May 2022, monkeypox started to spread in non-endemic countries. To investigate contact tracing and self-reporting of the primary case in the local community, a stochastic model is developed. An algorithm based on Gillespie's stochastic chemical kinetics is used to quantify the number of infections, contacts, and duration from the arrival of the primary case to the detection of the index case (or until there are no more local infections). Different scenarios were set considering the delay in contact tracing and behavior of infectors. We found that the self-reporting behavior of a primary case is the most significant factor affecting outbreak size and duration. Scenarios with a self-reporting primary case have an 86% reduction in infections (average: 5 to 7, in a population of 10,000) and contacts (average: 27 to 72) compared to scenarios with a non-self-reporting primary case (average number of infections and contacts: 27 to 72 and 197 to 537, respectively). Doubling the number of close contacts per day is less impactful compared to the self-reporting behavior of the primary case as it could only increase the number of infections by 45%. Our study emphasizes the importance of the prompt detection of the primary case. This article is protected by copyright. All rights reserved.

Full text

Received: 31 August 2022
|
Accepted: 13 October 2022
DOI: 10.1002/jmv.28232
RESEARCH ARTICLE
Estimation of monkeypox spread in a nonendemic country
considering contact tracing and self‐reporting: A stochastic
modeling study
Youngsuk Ko
1
|Victoria May Mendoza
1,2
|Renier Mendoza
1,2
|Yubin Seo
3
|
Jacob Lee
3
|Eunok Jung
1
1
Department of Mathematics, Konkuk
University, Seoul, South Korea
2
Institute of Mathematics, University of the
Philippines Diliman, Quezon City, Philippines
3
Department of Internal Medicine, Division of
Infectious Disease, Kangnam Sacred Heart
Hospital, Hallym University College of
Medicine, Seoul, South Korea
Correspondence
Eunok Jung, Konkuk University, 120
Neungdong‐ro, Gwangjin‐gu, Seoul 05029,
South Korea.
Email: junge@konkuk.ac.kr
Funding information
National Research Foundation of Korea
Abstract
In May 2022, monkeypox started to spread in nonendemic countries. To investigate
contact tracing and self‐reporting of the primary case in the local community, a
stochastic model is developed. An algorithm based on Gillespie's stochastic chemical
kinetics is used to quantify the number of infections, contacts, and duration from the
arrival of the primary case to the detection of the index case (or until there are no
more local infections). Different scenarios were set considering the delay in contact
tracing and behavior of infectors. We found that the self‐reporting behavior of a
primary case is the most significant factor affecting outbreak size and duration.
Scenarios with a self‐reporting primary case have an 86% reduction in infections
(average: 5–7, in a population of 10 000) and contacts (average: 27–72) compared
with scenarios with a non‐self‐reporting primary case (average number of infections
and contacts: 27–72 and 197–537, respectively). Doubling the number of close
contacts per day is less impactful compared with the self‐reporting behavior of the
primary case as it could only increase the number of infections by 45%. Our study
emphasizes the importance of the prompt detection of the primary case.
KEYWORDS
monkeypox, primary case, stochastic modeling
1|INTRODUCTION
Monkeypox is a zoonotic disease caused by the monkeypox virus.
Two possible means of transmission are animal‐to‐human and
human‐to‐human. Animal‐to‐human transmission, also known as
zoonotic transmission, is possible upon contact with or consumption
of an infected natural host animal, such as rats, squirrels, and prairie
dogs.
1,2
Human‐to‐human transmission can be caused by respiratory
droplets or contact with lesions and bodily fluids. Contact with
contaminated materials such as clothing, bedding, or eating utensils
can also cause infections.
3
The signs and symptoms of monkeypox
are similar to smallpox but are less severe. In the current outbreak,
symptoms are described as flu‐like, followed by a rash starting in the
genital and perianal areas, which may or may not spread to the other
parts of the body.
4,5
The monkeypox virus was first reported in 1970.
6
It is commonly
found in Central and West Africa and occasionally identified in other
countries.
1
If undetected, transmission in nonendemic countries is
possible, triggering outbreaks.
7,8
Since May 2022, an unprecedented
outbreak of human monkeypox cases has been observed in Australia
and several countries in Europe and North America.
9,10
On July 23,
the World Health Organization (WHO) declared a global health
emergency as the number of confirmed cases reached more than
16 000.
11
As of August 11, 2022, the United States recorded the
highest number of cumulative cases (10 360), followed by Spain
(5482) and Germany (3025).
12
J Med Virol. 2022;95:e28232. wileyonlinelibrary.com/journal/jmv © 2022 Wiley Periodicals LLC.
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The social media coverage about monkeypox spread directly or
indirectly generates racist and homophobic stereotypes that worsen
stigma.
9
Stigma can discourage people from seeking medical help,
which may impede the efforts in identifying cases.
13,14
Self‐reporting
plays an important role in mitigating the spread of infections. Once a
suspected case is identified, the WHO recommends that contact
identification and contact tracing be initiated.
15
In this study, we are
interested in understanding the dynamics of monkeypox infection in
nonendemic settings. we would like to discuss the following relevant
questions:
1. Upon the arrival of a primary case in a nonendemic country, how
many infections may occur?
16
2. Depending on when the index case is found, how many contacts
would the infector have already made?
3. How long is the duration of the outbreak?
4. What happens if the primary case does not self‐report?
The basic reproductive number of monkeypox was estimated to
be 2.13 (uncertainty bounds 1.46–2.67).
17
Although it is less than
the basic reproductive number of coronavirus disease of
2019 (COVID‐19), monkeypox has a potential to become an
epidemic.
18
Hence, understanding the transmission dynamics of the
disease is essential to mitigate its spread.
Numerous mathematical models have been proposed to under-
stand the transmission dynamics of infectious diseases and evaluate
the impact of different control measures.
19–21
Since the COVID‐19
has become a pandemic, epidemiological models have been widely
used to propose strategies to control its spread.
22–26
However, there
are only a few works on monkeypox transmission models. Bankuru
et al.
27
have shown that vaccination may be able to control
monkeypox transmission in a semiendemic setting (with the disease
existing only on humans). Peter et al.
28
suggested that isolation of
infected individuals can reduce disease transmission. Bhunu et al.
29
showed that increased contact between the host animal and human
can lead to an increase in the number of monkeypox cases, especially
in HIV‐infected individuals. Han et al.
30
investigated the mechanisms
in the macroecology of pathogen transmission and the risk of
spillover infection to humans by combining data mining with
theoretical models. Tchuenche and Bauch
31
emphasized the impor-
tance of empirical data aggregation about the wild animal in
formulating a model. They have shown that depending on the
animal‐to‐human contact rate, culling may have the counter‐intuitive
outcome of increasing the transmission of monkeypox among
children. All the above‐mentioned monkeypox models consider both
human and animal‐host compartments. However, since the disease
had spread in nonendemic countries where natural animal hosts are
not present, these may not be applicable in this study. Furthermore,
these models focused on the long‐term dynamics of the disease and
not on initial countermeasures to preventing an outbreak in a
community. Notably, all these models are deterministic.
Tothebestofourknowledge,thisstudyisthefirsttousestochastic
modeling to show the dynamics of monkeypox spreading in a
nonendemic country. Stochastic models have been extensively used in
other infectious diseases. For example, Hao et al.
32
showed that multiple
epidemic waves in Kansan, Japan may not be necessarily caused by
infected individuals but by the stochastic nature of epidemic events. A
stochastic model was formulated to investigate the impact of contact
tracing in the control of infectious diseases.
33
It has also been widely used
in evaluating control measures for COVID‐19 such as lockdown, social
distancing, vaccination, contact tracing, and testing.
34–38
Srivastav et al.
39
compared deterministic and stochastic models and showed that for small
populations, stochasticity plays a significant role. Deterministic models
also do not account for fluctuations. Furthermore, transmission and
recovery from infection are intrinsically stochastic processes.
40
Since the
focusofthestudyisontheeffectsofcontacttracingandself‐reporting of
the primary case in the local community, we use a stochastic model to
understand the dynamics of monkeypox transmission in a nonendemic
setting. We focus on the early phase of the outbreak rather than the long‐
term view and consider essential factors such as contact tracing, which is
a standard nonpharmaceutical intervention, and behavior of the primary
case and infectees, whether self‐reporting or not.
The rest of the article is organized as follows. Section 2details
the methodology used in this study. Section 3presents the model
simulations and hypothesis test results. Section 4provides the
discussions, limitations, and strengths of our research. Lastly,
Section 5contains the conclusions and policy implications.
2|METHODS
A stochastic model that assumes a nondelayed Markovian frequency‐
dependent disease transmission and incorporates delayed non‐
Markovian reactions is developed. The flow diagram of the model
is displayed in Figure 1. The transmission rate consists of the number
of contacts per unit time (
c
) and probability of successful disease
transmission (
p
).
41
Contact is made between infectors (I1or I2) and
susceptible hosts (
S
), formulated as the term
c
S
II
N
(+)
12, where
N
indicates the total population except isolated hosts
(
S
CEI I
R
+++++
12
) and subscripts 1 or 2 denote self‐reporting
or non‐self‐reporting, respectively. Here are the nondelayed
reactions, which are also displayed in Figure 1as solid arrow lines:
⎯→⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ ⎯ →⎯⎯⎯⎯⎯
r
SI CrSI E:+ ,:+ ,
cpN cpN
11
(1−)
21
−1−1
⎯→⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ ⎯ →⎯⎯⎯⎯⎯
r
SI CrSI E:+ ,:+
.
cpN cpN
32
(1−)
42
−1−1
The parameters
r
2
and
r
4
indicate successful disease transmission
reactions by I1and I2, respectively, in contrast to
r
1
and
r
3
. Depending
on
p
, a susceptible host who had contact with an infector can either
be uninfected (
C
) or in latent stage (E). Except for these four
reactions, the other reactions in our model are delayed non‐
Markovian through the epidemiological process, which are shown
in Figure 1as dashed arrows.
The probability that an infectee will later self‐report is denoted by
ρ
.
When an infectee in the latent stage becomes an infector (I1or I2), the
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host can spread the disease. If the infector self‐reports (I1), then the host
is isolated (
Q
I
) and contact tracing events are generated once the case is
confirmed. The duration from self‐reporting of an infector to isolation is
denoted by
t
inf 1
. Hosts who had contact with the confirmed host (
C
,E,I1,
I2) within contact tracing time (
t
unt , 14 days, assumed) will be tracked. An
infector in I2will stay in I2until the host is naturally recovered (R)in
t
inf 2
days,oruntiltrackedandisolated.Note that contact tracing events are
also generated if a traced host is infected (E,I1,I2). A host in
C
can be
traced and isolated (QC) even if the host is not infected or go back to
S
after
t
unt . We assumed the isolation time
t
iso
is 21 days.
Aggregating the values from Prem's study, the average number
of contacts per day (
c
) in Korea is estimated as 12.74 (3.20 household
contacts, 9.54 others).
42
Combining these contacts with the
probability of a successful disease transmission through a household
contact and other contacts, 25.25% and 9.56%, respectively, the
adjusted probability of a successful disease transmission through a
contact (
p
) is estimated as 13.51%.
43
Denoting by
c
hh
and
c
other (phh
and pother ) the daily number of (probability of infection through)
household and other contacts, respectively, the probability of
infection through a contact is calculated as follows,
pc
cc pc
cc p=+×++×
.
hh
hh
hh
hhother
other
other
other
We assume uniform distributions for the infectious period of
non‐self‐reporting infector,
t
inf 2
(range: 14–28 days), and contact
tracing time,
t
trace
.
44,45
Latent period (
t
lat
) and infectious period of
self‐reporting infector (
t
inf 1
) are generated from log‐normal distribu-
tion and aggregated from previous studies.
46,50
The average values of
t
lat
and
t
inf 1
are 8.5 and 2.96 days, respectively. We assume that the
delay for a host with monkeypox from self‐reporting to isolation
(
t
inf 1
) is similar to the period from symptom onset to diagnosis of a
known case of COVID‐19 exposure. The delays
t
unt and
t
iso
are fixed
to constant values and not generated from a distribution.
The definition of the primary case and index case are as follows.
16
✓Primary case: the person who brings the disease to a community.
✓Index case: the first patient identified by health authorities with
the disease.
Considering whether the primary case self‐reports or not (initial
condition of the simulation is I1or I2), self‐report rate of infectees in the
local community (
ρ
, 0.5 or 1), and delay for contact tracing (
t
trace
,1–4or
4–7 days), we set up eight scenarios, ran 100 000 simulations for each
scenario, and observed the number of infections, contacts, duration of
primary case arrival to index case detection (P1), and duration of primary
case arrival to the end of the simulation (P2). End of the simulation means
that all who were infected in the local community (except isolated) are
removed, that is,
EI I++=
0
12
. The exact stochastic simulation
algorithm for systems with delays was adopted to express the delayed
events. A detailed description of the algorithm, which was developed
based on Gillespie's stochastic chemical kinetics, is presented by Cai.
47
Figure 2illustrates the simulation process of two different scenarios
FIGURE 1 Flow diagram of the stochastic modeling. Arrows with a solid line indicate nondelayed (Markovian) reaction while arrows with
dashed curve are delayed (non‐Markovian) reaction. Susceptible hosts (
S
) can become infected with probability
p
upon contact with an infector
(I1or I2). Once an infector self‐reports (I1), the host is isolated (
Q
I
) and contact tracing events are generated. Hosts (
C
,E,I1,I2) who had contact
with the confirmed host within contact survey time
t
survey
will be traced. If there is no contact tracing, the infector who does not report can
spread the disease for a significantly longer period, as the average duration of
t
inf 2
and
t
trace
are 21 and 2.5 days, respectively.
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depending on whether the primary case self‐reports or not. In (A), the
primary case is the same as the index case and the simulation ends when
all infected contacts of the primary case are isolated. In (B), contact
tracing was generated later resulting to secondary infections and a longer
simulation process. We simply set the population size as 10 000.
We also performed a statistical hypothesis test comparing two
different scenarios to assess the significance of contact tracing time,
and self‐reporting of the primary case and infectees. Since it was
observed that the number of infections does not follow the shape of
a normal distribution, we performed the Wilcoxon signed‐rank test.
48
FIGURE 2 The stochastic simulation process illustrating the possible mitigation or spread of infection depending on whether the primary
case self‐reports or not. In (A), the primary case (red, with yellow edge) arrives and makes contact with hosts. One of them gets infected (orange)
and the others remain uninfected (gray). Later, when the primary case self‐reports, contact tracing is generated and hosts who had contact with
the primary case are isolated and the simulation ends. In (B), the primary case who does not self‐report (red, with purple edge) infects one host,
which would later become an infector. Contact tracing is generated later than in (A) when the secondary infected host self‐reports. The
simulation keeps going since infectors are still present in the local community. Note that each event is simulated individually in the numerical
implementation.
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The null hypothesis is that two paired scenarios with different
settings are the same, while the alternative hypothesis says that the
two scenarios are different.
3|RESULTS
The different scenarios are labeled S‐1–S‐8, according to the
setting of the simulation. The setting of each scenario and
corresponding simulation results, illustrated as boxplots, are
shown in Figure 3. Note that P1 and P2 denote the duration of
the primary case arrival to index case detection and end of the
simulation, respectively. Numerical results are summarized in
Table 1.
We observe that if the primary case does not self‐report (S‐5–S‐
8), then the simulations are worse than in the scenarios where the
primary case self‐reports (S‐1–S‐4). The average number of infec-
tions, contacts, and duration from primary case arrival to the end of
simulation for scenarios S‐1–S‐4 are 6.12, 45.35, and 7.25 days,
respectively, which are 7.40, 7.39, and 2.46 times higher than those
of scenarios S‐5–S‐8 (45.29, 333.33, and 17.81 days, respectively).
Considering the number of contacts per day and the probability
of successful disease transmission, the expected number of infections
per day is 1.72 (Number of contacts per day
×
× probability of
FIGURE 3 Scenario‐based simulation results. (A) Boxplots showing the total numbers of infections and contacts, and duration of P1 and P2
corresponding to each scenario. The scenarios vary according to whether the primary case self‐reports or not, self‐report rate of infectee (50%
or 100%), and duration from reporting to the start of contact tracing (1–4or4–7 days). (B) Timeline illustrating the two phases P1 and P2. The
size and duration of the outbreak in scenarios S‐5–S‐8 are greater than those in scenarios S‐1–S‐4.
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infection by contact). This means that in scenarios S‐5–S‐8, where
the primary case is not the index case, the primary case would already
have made dozens of secondary infections until the index case is
detected, which takes (incubation period) + (duration from self‐report
to isolation) days. The average duration of P1 in scenarios S‐1–S‐4is
slightly less than 3 days since the primary case is most likely identical
to the index case, while in S‐5–S‐8, it takes 8–10 days on average
until the index case is detected.
Figure 4shows the probability density of the total number of
infections and contacts, and durations of P1 and P2 for scenarios S‐1,
S‐4, S‐5, and S‐6. Scenario S‐6 shows the worst outcome, with a 25%
increase on the number of infections compared with S‐5 as contact
tracing was delayed longer. We observe skewed distributions for S‐1
and S‐4, suggesting that the outbreak which may result from these
settings would most likely be on a small scale. The average number of
infections until the end of the simulation in S‐5 (26.66) is
approximately four times higher than in S‐1orS‐4 (5.36 or 7.3,
respectively). Scenario S‐4 shows a slightly higher average number of
infections compared with S‐1 due to the more delayed contact
tracing.
Figure 5shows the results of the Wilcoxon signed‐rank test. We
observe that all the paired scenarios were significantly different,
except for S‐1 and S‐2(p‐value: 0.25), in which all infected cases have
been reported but with different values for the contact tracing delay
(1–4or4–7 days). The p‐values of the tests comparing S‐3 and S‐4,
and S‐1 and S‐3 were second and third highest (0.03 and 0.01),
respectively, but both are below significant level (0.05).
To investigate what happens if the average number of household
contacts is higher, such as in a potential super‐spreader event, we
considered doubling the number of household contacts for scenarios
S‐1 and S‐5. We denote these scenarios by S‐1x and S‐5x. The plots
in Figure 6show the simulation results. As the number of household
contacts doubled from 3.20 to 6.41, the average number of contacts
and probability of disease transmission through a contact increased
to 15.94% and 15.87% (from 12.74% and 13.51%, respectively). The
average number of infections and contacts in S‐1x (S‐5x), compared
with S‐1(S‐5), increased by 50.43% (44.96%) and 28.10% (23.35%),
respectively. There were no significant changes in the durations of P1
and P2.
4|DISCUSSION
In Korea, the first monkeypox case had self‐reported right after
arrival.
49
As a result, there were no recorded secondary infections,
which would be similar to a “good”scenario (S‐1–S‐4) in our
simulation setting. However, if the primary case was in the incubation
stage and did not self‐report after symptom onset, then hundreds of
contacts and dozens of infections could be expected to have
occurred in the local community once the index case was found. In
TABLE 1 Numerical results of the scenarios
Time phase
Behavior of a
primary case
Self‐report
rate of
infected (%)
Contact
tracing
delay
Number of infections Number of contacts Duration (day)
Mean Median 95% CI Mean Median 95% CI Mean Median 95% CI
From primary
case
arrival to
index case
Self‐report 100 1–4 day 5 3 (0–20) 37.01 26 (4–139) 2.68 2 (0.37–8.25)
4–7 day 5.01 3 (0–20) 37.05 26 (4–138) 2.69 2 (0.37–8.28)
50 1–4 day 5.42 3 (0–24) 40.19 26 (4–173) 2.75 2 (0.37–9.01)
4–7 day 5.44 3 (0–24) 40.27 26 (4–175) 2.76 2 (0.36–9)
No self‐
report
100 1–4 day 19.67 18 (8–39) 145.67 136 (69–279) 8.2 8 (4.73–12.16)
4–7 day 19.7 18 (8–39) 145.96 136 (69–279) 8.21 8 (4.75–12.15)
50 1–4 day 31.11 26 (9–83) 230.26 191 (77–605) 9.58 9 (5.24–14.68)
4–7 day 31.12 26 (9–82) 230.33 192 (77–603) 9.58 9 (5.25–14.62)
From primary
case
arrival to
end of the
simulation
Self‐report 100 1–4 day 5.36 3 (0–24) 39.7 26 (4–172) 5.72 5 (0.46–13.05)
4–7 day 5.56 3 (0–27) 41.14 26 (4–192) 8.53 8 (0.46–17.78)
50 1–4 day 6.26 3 (0–33) 46.46 26 (4–241) 5.87 5 (0.45–14.63)
4–7 day 7.3 3 (0–46) 54.09 26 (4–331) 8.86 8 (0.46–20.97)
No self‐
report
100 1–4 day 26.66 24 (11–56) 197.3 179 (96–398) 13.59 14 (9.51–18.18)
4–7 day 33.18 30 (15–67) 245.72 223 (134–481) 19.65 20 (15.88–23.98)
50 1–4 day 48.87 39 (13–143) 361.66 284 (106–1051) 15.64 15 (10.15–22.07)
4–7 day 72.46 54 (18–235) 536.65 398 (145–1734) 22.37 22 (16.52–30.12)
Abbreviation: CI, confidence interval.
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this scenario, more efforts would have been needed to control the
disease.
We observed that more cases occurred when contact tracing
was delayed. The increment was small if the primary case self‐
reports, in which the average number of infections increased only by
11% (5.81–6.43) if contract tracing was delayed from 1–4to4–7
days. However, if the primary case does not self‐report, then the
difference is greater as the average number of infections increased
by 40% (37.77–52.82). The statistical hypothesis test emphasized the
importance of case finding (self‐report of the primary case and
secondary cases), as the result of the test showed that if all cases self‐
report, then the delay in contact tracing does not affect the outcome
significantly.
We investigated the effects of doubling the number of
household contacts per day (which can be referred to as close
contact). The results illustrated in Figure 6warn of the potential
FIGURE 4 Probability distributions of simulation results for scenarios S‐1 (blue solid), S‐4 (green dashed), S‐5 (red solid), and S‐6 (orange
dashed). (A) Total number of infections. (B) Total number of contacts. (C) Duration from primary case arrival to the identification of index case.
(D) Duration from primary case arrival to the end of the simulation. The self‐reporting behavior of the primary case significantly changed the
shape of the distributions of the number of infections and contacts, as S‐1 and S‐4 show a higher probability of a smaller number of infections
compared with S‐5 and S‐6. The delay in contact tracing does not affect the duration of P1, as contact tracing is generated once a case is
confirmed, but the delay causes more total infections.
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significant increase in the number of monkeypox infections when
unreported initial cases have contact with more people, or if the
community where the primary case belongs to has more close
contacts.
This study focused on the early stageofanoutbreakconsideringthe
behavior of the primary cases and infectees, and possible delay of contact
tracing. This approach is more intuitive than a theoretical analysis and
may guide healthcare authorities in the planning and management of
possible monkeypox outbreaks in nonendemic countries. For instance, it
was shown that the delay in the detection of the index case is related to
thenumberofcontactsmadeandknowingthescaleofcontacttracing
efforts to be performed is crucial in managing workforce once the index
case is found. In the simulations, we have used the average number of
contacts per day suited for Korea, but this can easily be adapted to other
countries' contact patterns. If the average household size is bigger or the
number of contacts is more, then the probability of disease transmission
increases.
There were limitations to our study. Contact tracing was applied
to the model through a randomized sampling and not based on one's
personal contacts. It is expected that using an individual‐based
network would realistically represent contact tracing and behavior
(contact and self‐report) of specific individuals. Also, we assumed
that contact tracing is perfect, that is, all infectors are found if 100%
coverage is in effect. The probability of successful infection after
contact might be overestimated since the concept of contact from
the cited literature might differ from the definition of contact used in
this study.
25
Finally, we did not consider sexual contact in this study
due to the lack of data. These limitations can be considered in the
next study.
5|CONCLUSION
In this study, the potential risk of monkeypox spread in a nonendemic
country was studied using a stochastic model. We simulated
outbreaks caused by a primary case that either self‐reports or not
and considered different coverage rates of contact tracing and self‐
reporting rates of infectees.
Stigma, which may result in an increase in hidden cases and
negatively impact disease control, can be avoided by implementing
FIGURE 5 Results of the Wilcoxon signed‐rank test comparing two scenarios in terms of contact tracing time and reporting rate of infectees
and the primary case. The bars indicate the p‐value of each test, and the red dashed line indicates the significance level, 0.05. Only the p‐value of
the paired scenarios S‐1 and S‐2 resulted to the rejection of the alternative hypothesis, i.e., the number of infections in S‐1 and S‐2 is not
significantly different.
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evidence‐based and rights‐based approaches.
13
Scientists have
emphasized that knowledge about the epidemiology of the disease
and awareness of its risks are important ways to prevent transmis-
sion.
7,14
Therefore, to encourage self‐reporting, healthcare authori-
ties must ensure confidentiality of confirmed cases and individuals
under investigation, and access to health services. Moreover, prompt
case finding and information campaigns must be conducted.
Our simulation results strongly emphasize the importance of
border control to find the primary case. If the primary case self‐
reports, then despite having a low self‐reporting rate of infectees and
FIGURE 6 Probability distributions of simulation results if the number of household contacts is doubled. (A) Total number of infections.
(B) Total number of contacts. (C) Duration from primary case arrival to the identification of the index case. (D) Duration from primary case arrival
to the end of the simulation. (E) Boxplots illustrating the results in (A), including the number of infections from P1, the duration from primary case
arrival to the identification of the index case. (F) Boxplots illustrating the results in (B), including the number of contacts from P1, the duration
from primary case arrival to the identification of the index case. (G) Boxplots illustrating the results in (C) and (D). Results show that if the primary
case does not self‐report (S‐5 and S‐5x), then the increase in outbreak size caused by the doubling of household contacts (or close contacts) can
become higher.
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delayed contact tracing, the situation does not become worse
compared with the scenarios where the primary case does not self‐
report (in Figure 3).
AUTHOR CONTRIBUTIONS
Eunok Jung acquired funding for this study. Youngsuk Ko, Jacob Lee,
and Eunok Jung conceived and designed the study. Youngsuk Ko,
Renier Mendoza, and Victoria May Mendoza analyzed the data and
wrote the first draft. Eunok Jung, Jacob Lee, and Yubin Seo gave
suggestions on improving the quality of the analysis and monitored
the study progress. All authors contributed to the data collection,
checking, and processing. All authors reviewed the final version of
the manuscript. All authors read and approved the final manuscript.
ACKNOWLEDGMENT
This article is supported by the Korea National Research
Foundation (NRF) grant funded by the Korean government (MEST)
(NRF‐2021M3E5E308120711). This paper is also supported by
the Korea National Research Foundation (NRF) grant funded by
the Korean government (MEST) (NRF‐2021R1A2C100448711).
We appreciate professor Jaekyoung Kim from the Korea
Advanced Institute of Science & Technology for introducing
Non‐Markovian process during the Korean Society for Industrial
and Applied Mathematics tutorial program. Thanks should also go
to the Korean Society for Industrial and Applied Mathematics for
organizing the tutorial program.
CONFLICT OF INTEREST
The authors declare no conflict of interest.
DATA AVAILABILITY STATEMENT
No new data were generated or analyzed in support of this study.
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SUPPORTING INFORMATION
Additional supporting information can be found online in the
Supporting Information section at the end of this article.
How to cite this article: Ko Y, Mendoza VM, Mendoza R, Seo
Y, Lee J, Jung E. Estimation of monkeypox spread in a
nonendemic country considering contact tracing and self‐
reporting: a stochastic modeling study. J Med Virol.
2022;95:e28232. doi:10.1002/jmv.28232
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