The impact of multiple non-pharmaceutical interventions for China-bound travel on domestic COVID-19 outbreaks

Abstract

Objectives
Non-pharmaceutical interventions (NPIs) implemented on China-bound travel have successfully mitigated cross-regional transmission of COVID-19 but made the country face ripple effects. Thus, adjusting these interventions to reduce interruptions to individuals’ daily life while minimizing transmission risk was urgent.

Methods
An improved Susceptible-Infected-Recovered (SIR) model was built to evaluate the Delta variant’s epidemiological characteristics and the impact of NPIs. To explore the risk associated with inbound travelers and the occurrence of domestic traceable outbreaks, we developed an association parameter that combined inbound traveler counts with a time-varying initial value. In addition, multiple time-varying functions were used to model changes in the implementation of NPIs. Related parameters of functions were run by the MCSS method with 1,000 iterations to derive the probability distribution. Initial values, estimated parameters, and corresponding 95% CI were obtained. Reported existing symptomatic, suspected, and asymptomatic case counts were used as the training datasets. Reported cumulative recovered individual data were used to verify the reliability of relevant parameters. Lastly, we used the value of the ratio (Bias²/Variance) to verify the stability of the mathematical model, and the effects of the NPIs on the infected cases to analyze the sensitivity of input parameters.

Results
The quantitative findings indicated that this improved model was highly compatible with publicly reported data collected from July 21 to August 30, 2021. The number of inbound travelers was associated with the occurrence of domestic outbreaks. A proportional relationship between the Delta variant incubation period and PCR test validity period was found. The model also predicted that restoration of pre-pandemic travel schedules while adhering to NPIs requirements would cause shortages in health resources. The maximum demand for hospital beds would reach 25,000/day, the volume of PCR tests would be 8,000/day, and the number of isolation rooms would reach 800,000/day within 30 days.

Conclusion
With the pandemic approaching the end, reexamining it carefully helps better address future outbreaks. This predictive model has provided scientific evidence for NPIs’ effectiveness and quantifiable evidence of health resource allocation. It could guide the design of future epidemic prevention and control policies, and provide strategic recommendations on scarce health resource allocation.

Full text

Frontiers in Public Health 01 frontiersin.org
The impact of multiple
non-pharmaceutical interventions
for China-bound travel on
domestic COVID-19 outbreaks
LichaoYang
1, MengzhiHu
1, HuatangZeng
2, WannianLiang
1,3*
and JimingZhu
1,3*
1 Vanke School of Public Health, Tsinghua University, Beijing, China, 2 Shenzhen Health Development
Research and Data Management Center, Shenzhen, Guangdong, China, 3 Institute for Healthy China,
Tsinghua University, Beijing, China
Objectives: Non-pharmaceutical interventions (NPIs) implemented on China-bound
travel have successfully mitigated cross-regional transmission of COVID-19 but
made the country face ripple eects. Thus, adjusting these interventions to reduce
interruptions to individuals’ daily life while minimizing transmission risk was urgent.
Methods: An improved Susceptible-Infected-Recovered (SIR) model was built
to evaluate the Delta variant’s epidemiological characteristics and the impact of
NPIs. To explore the risk associated with inbound travelers and the occurrence
of domestic traceable outbreaks, we developed an association parameter
that combined inbound traveler counts with a time-varying initial value. In
addition, multiple time-varying functions were used to model changes in the
implementation of NPIs. Related parameters of functions were run by the MCSS
method with 1,000 iterations to derive the probability distribution. Initial values,
estimated parameters, and corresponding 95% CI were obtained. Reported
existing symptomatic, suspected, and asymptomatic case counts were used as
the training datasets. Reported cumulative recovered individual data were used to
verify the reliability of relevant parameters. Lastly, weused the value of the ratio
(Bias2/Variance) to verify the stability of the mathematical model, and the eects
of the NPIs on the infected cases to analyze the sensitivity of input parameters.
Results: The quantitative findings indicated that this improved model was highly
compatible with publicly reported data collected from July 21 to August 30, 2021.
The number of inbound travelers was associated with the occurrence of domestic
outbreaks. A proportional relationship between the Delta variant incubation period
and PCR test validity period was found. The model also predicted that restoration
of pre-pandemic travel schedules while adhering to NPIs requirements would
cause shortages in health resources. The maximum demand for hospital beds
would reach 25,000/day, the volume of PCR tests would be8,000/day, and the
number of isolation rooms would reach 800,000/day within 30 days.
Conclusion: With the pandemic approaching the end, reexamining it carefully helps
better address future outbreaks. This predictive model has provided scientific evidence
for NPIs’ eectiveness and quantifiable evidence of health resource allocation.
It could guide the design of future epidemic prevention and control policies, and
provide strategic recommendations on scarce health resource allocation.
KEYWORDS
China-bound travel, COVID-19, non-pharmaceutical interventions, time-varying, health
resource allocation
OPEN ACCESS
EDITED BY
Reza Lashgari,
Shahid Beheshti University, Iran
REVIEWED BY
Wiriya Mahikul,
Chulabhorn Royal Academy, Thailand
Seba Contreras,
Max Planck Society, Germany
*CORRESPONDENCE
Jiming Zhu
jimingzhu@tsinghua.edu.cn
Wannian Liang
liangwn@tsinghua.edu.cn
RECEIVED 10 April 2023
ACCEPTED 01 June 2023
PUBLISHED 13 July 2023
CITATION
Yang L, Hu M, Zeng H, Liang W and
Zhu J (2023) The impact of multiple
non-pharmaceutical interventions for China-
bound travel on domestic COVID-19
outbreaks.
Front. Public Health 11:1202996.
doi: 10.3389/fpubh.2023.1202996
COPYRIGHT
© 2023 Yang, Hu, Zeng, Liang and Zhu. This is
an open-access article distributed under the
terms of the Creative Commons Attribution
License (CC BY). The use, distribution or
reproduction in other forums is permitted,
provided the original author(s) and the
copyright owner(s) are credited and that the
original publication in this journal is cited, in
accordance with accepted academic practice.
No use, distribution or reproduction is
permitted which does not comply with these
terms.
TYPE Original Research
PUBLISHED 13 July 2023
DOI 10.3389/fpubh.2023.1202996

Yang et al. 10.3389/fpubh.2023.1202996
Frontiers in Public Health 02 frontiersin.org
1. Introduction
COVID-19 has created a global challenge that demands
researchers, policymakers, and governments address multiple
dimensions which go far beyond the implications of human health
and well-being (1–4). Scientic evidence has indicated that
non-pharmaceutical interventions (NPIs) are eective measures to
contain a pandemic and ease pressures on healthcare systems (5–7).
NPIs are actions, apart from getting vaccinated and taking medicine,
that people can take to help slow the spread of illnesses, also known
as mitigation strategies (8–10). It includes travel restrictions, contact
tracing, PCR tests, measures in social distancing, personal protection,
and quarantines (6, 11, 12). e implementation of such interventions
while maintaining social stability is a challenge to all countries. As a
country consisting of more than 1.4 billion or 18% of the world’s
population, China’s high population density, high volume, speed, and
non-locality of human mobility would provide perfect conditions for
the virus to spread (13, 14). When highly transmissible Delta and
Omicron variants resulted in massive surges in COVID-19 cases from
December 2021 (15, 16), China saw the largest spike for the past
2 years, despite determinedly pursuing one of the world’s strictest virus
elimination policies. When a local COVID-19 case occurred,
mandatory interventions would betaken to cut o the transmission
chain and terminate the outbreak in time to achieve maximum
eectiveness with minimum cost. Aer years of exploration, such
strategies’ implementation received remarkable results in containing
regional cases (17, 18). However, it required extensive community
involvement, government funding guarantees, application of new
technology, motivation, and constraint mechanisms. Such a strategy
created indenable impacts on regional social development (19, 20).
us, knowing how to maximize the advantages of strategy in
outbreak control while avoiding damaging the development of the
country was critically important. Due to the combined use of NPIs in
the strategy, wedecided to quantify the impact of dierent NPIs.
Extensive research was conducted by using a time-varying modeling-
informed approach and focusing on the following three interventions
in this paper: inbound ight restrictions, PCR tests, and centralized
quarantine measures.
Severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2)
viral spread patterns were shaped by the high volume of cross-country
mobility networks (21). In response to the pandemic, China reduced
inbound ight schedules from 10,000 per week in 2019 to 500 per
week in recent years (22), and international arrivals were reduced
from approximately 162.5 million in 2019 to 30.4 million in 2020 (23).
In July 2021, the aviation authority updated requirements—passengers
were required to complete a PCR test within 5 days of embarkation
and provide negative test results before boarding, as the government
tried to further reduce the risk of imported cases (24). However, from
July 1 to July 31, 2021, 1,213 conrmed COVID-19 cases were
reported across the country, compared with 1,893 cases in August and
1,264 cases in September (25). Although travel restrictions and PCR
tests were proven as useful practices (26), the theoretical basis of those
strategies and how to strategically align them with a country’s
development was not studied.
ere was a high level of agreement that the adoption of travel
measures led to important changes in the dynamics of the early phases
of the COVID-19 pandemic (27). Flight restrictions may have led to
additional reductions in the number of exported and imported cases
on the international scale, but such limitations (up to 90% of trac)
had only a modest eect unless combined with a 50% or higher
reduction of transmission in the community (28). With the occurrence
of domestic COVID-19 outbreaks, the association between
international travel and the implementation of NPIs has not been
identied. NPIs such as centralized hospitalization for mild and
moderate patients could reduce disease transmissions and enhance
protection for healthy and unhealthy individuals (29, 30).
Nevertheless, the ecacy of mandatory isolation for international
travelers at a designated place in a given period was not discussed.
Research on Hong Kong-bound air passengers indicated that home
quarantine was less eective than a centralized quarantine strategy
initially but showed similar ecacy in the later phase (31). However,
the eectiveness of self-isolation, transmission rate within the family
cluster, related disease burden, and consumption of public health
resources were not mentioned. According to a study published by
United States Centers for Disease Control and Prevention, the
transmission of SARS-CoV-2 among household members was
common, and secondary infection rates were higher and occurred
rapidly, with approximately 75% of infections identied within 5 days
of the index patient’s illness onset (32). Substantial transmission
occurred whether the index patient was an adult or a child, leaving no
one healthy enough to help other family members.
Mathematical models and time series analyses have been widely
used to study the pandemic and predict the trend. Researchers used a
time-dependent SIR model to track the transmission and recovery rate
at time
t
and presented less than 3% of one-day prediction errors (33).
But the eects of NPIs were not discussed in the research. Another
time-varying SIRD model was also developed to capture possible
changes in the epidemic behavior, due for example to containment
measures enforced by authorities or modications of the epidemic
characteristics and to the eect of advanced antiviral treatments in
Italy (34). However, the research team did not take the interaction
eects between containment measures and international travel bans
into consideration. To infer more accurate parameter estimates and
reduce uncertainties, scholars used real datasets of COVID-19 cases
via an SEIR model with time-varying transmission and reporting rates
to perform 1-week ahead predictions and generated more realistic
interpretations (35). Despite that, this model was designed to predict
the number of under-reported active cases not for NPIs evaluation,
strategic planning, and resource allocation.
us, wewould develop epidemiological models to simulate the
domestic spread of SARS-CoV-2 sparked by passengers who had
followed NPIs, such as inbound travel restrictions, quarantine
measures, and PCR tests. However, the traditional epidemiological
models fail to show the real-time implications of NPIs
implementations, delayed symptoms, and test results. To present
the time-varying eects, we developed a homogenous hybrid
dynamic Susceptible-Infectious-Recovered (SIR) model to quantify
such implications. e model can capture multiple data resources
rather than a single dataset and generate a more robust estimation
of the underlying dynamics of transmission from noisy data.
Furthermore, it clearly described the synergistic eects of multiple
interventions, such as face masks and social distancing. By
combining an improved SIR model with four datasets collected
from July 21 to August 30, 2021, weexplored the sustained human-
to-human transmission relationship between the inbound travelers
and the domestic outbreaks under eective NPIs. Based on the

Yang et al. 10.3389/fpubh.2023.1202996
Frontiers in Public Health 03 frontiersin.org
simulation results, weformed a comprehensive model to quantify
the impact of each NPIs and predicted the trend of future outbreaks
based on the implementation of these NPIs. e goal was to ①
explore the relationship between the imported cases and the
development of the domestic epidemic, ② discuss how to adjust
existing prevention and control strategies based on our ndings,
and ③ prepare sucient health resources in advance while
preventing health systems become overwhelmed. Moving forward,
wewould like to explore the balance point in epidemic prevention
and international travel restrictions that could minimize the
disruptions to social development.
2. Materials and methods
2.1. Model assumptions for consideration
e total population was 1,411,478,724 except for Hong Kong,
Macau, Taiwan, and about 300,000 who are naturally immune (36).
• Assuming that the population is closed, meaning that there are
no births and deaths. Population migration status change is
considered during the study period, but they are dynamically
stable, then
St Ct Qt It It
Lt Lt Rt Dt Nt N
as
ie
()
+
()
+
()
+
()
+
()
+
()
+
()
+
()
+
()
=
()
==
.
• Assuming the population is homogeneously distributed and
individuals mix uniformly.
• Assuming that the infectiousness of symptomatic and
asymptomatic individuals is the same in a real-world
scenario (37).
• Assuming that the recovered patients are negligible during the
early stage of the pandemic and their presence will likely not
aect the disease transmission (38–40).
• Assuming that symptomatic and asymptomatic cases will
be moved into convalescence aer rehabilitation due to
COVID-19 immunity aer infection.
• Assuming the eect of vaccines, average delays between symptom
onset and test results are constant.
• Assuming all inboard and abroad travelers have performed the
PCR tests, centralized quarantine, and completed treatments at
designated hospitals.
2.2. A homogenous hybrid network-based
model of SARS-CoV-2 transmission
e SIR model was used to model the spread of infectious diseases
among a xed population. is classic compartment model divided
the population into susceptible (S), infected (I), and recovered (R)
individuals and track the transitions of individuals among these states.
It is a deterministic model of a homogeneous population with well-
mixed interactions. Since China is continually updating its prevention
and control measures, weextend the SIR modeling framework to nine
classes: susceptible (
S
), carried (
C
), asymptomatic infected (
Ia
),
symptomatic infected (
Is
), recovered (
R
), quarantined (
Q
), dead (
D
),
immigrated (
Li
), and emigrated (
Le
) to study the SARS-CoV-2
transmission on dynamic networks. Especially asymptomatic infected
(
Ia
) are individuals who show no symptoms but PCR test positive, and
virus-carrier compartment (
C
) represents individuals who show no
symptoms and PCR test negative but infectivity. Furthermore,
quarantined (
Q
), immigrated (
Li
), and emigrated (
Le
) compartments
are designed to analyze the eectiveness of NPIs, such as the inbound
ight restriction, PCR test, and centralized quarantine.
In the system of improved SIR model (Figure1),
α
0t
()
represents
the percentage of inbound passengers. ey are required to stay in a
designated place for X days upon arrival and receive closed-loop care.
A portion
λ
of
Q
will move to
S
, a portion
δ
i
of
Q
will move to
Is
, and
a portion
δ
q
of
Q
will move to
Ia
. Once they entered into the
susceptible group
S
, there is a risk ratio
β
of
S
to move some of them
into
C
and diagnosed as
Is
or
Ia
by the transfer rate of
ε
and
eq
respectively. In addition, a portion
p
of
S
determined by close contact
and sub-close contact tracing will move to quarantined
Q
. In the
meantime, a portion of
qi
and
qr
represent the
Ia
will move to
Is
and
R. With the above, since population fraction in compartments
SCQI ILLRD
as ie
,,,,,,,,
varies with time
t
(in days), weassume S(t) +
C(t) + Q(t) + Ia(t) + Is(t) + Li(t) + Le(t) + R(t) + D(t) = N(t)==N, the
following kinetic equation is obtained. Initial values, conditions, and
descriptions are presented in Table1.
( ) ( ) ( ) ( )
()
1 1212 1as
dS
pStC tI tI SQ
dt
βθ θθθθ αλ
=−+ +∗+∗−+
dC
dt
StCtIt
IeC
as q
=
()
+
()
∗+
()
∗
()
−++
()
βθ θθθθ αε
1121 22
( ) ( ) ( )
()
( )
1 1212 0a s i qi
dQ
pStC tI tI tL Q
dt
θ θθθθ α λδδ

= +∗+∗+ −++

dI
dt
QeCq
qI
aqq
ir
a
=+−+
()
δ
dI
dt
CQIr
dI
siiai
is
=+ +−+
()
εδ
q
dR
dt
rI qI R
is ra
=+ −
α
3
dD
dt
dI
is
=
dL
dt
SC
R
e=+ +
αα α
12 3
dL
dt tL
ii
=−
()
α
0
2.3. The designed functions are related to
fitted parameters
Multipronged interventions have considerable positive eects on
minimizing the spread of outbreaks, decreasing the reproduction
number, and reducing total infections. To further clarify the

Yang et al. 10.3389/fpubh.2023.1202996
Frontiers in Public Health 04 frontiersin.org
mechanism of interventions and additive eect on epidemic,
parameters
α
0t
()
,
λ
,
δ
i
, and
δ
q
related to the NPIs implemented for
China travelers are constructed in the improved SIR model. Especially
α
0t
()
is a comprehensive parameter determined by the parameter
τ
t
()
related to interventions PCR test and the parameter
ϑ
t
()
related
to inbound ight restrictions. e parameters
λ δ
,i
, and
δ
q
are
dependent on centralized quarantine measures. ose four dependent
variables are mainly changed by the independent variables, i.e.,
x0
,
x1
,
x2
, and
γ
.
x0
represents the validity period of the PCR test,
x1
is the
number of international ights,
x2
is the strength of the centralized
quarantine measure,
γ
is the weight parameter related to the
incubation period of SARS-CoV-2.
α
0t
()
as the main explanatory variable, signies the proportion of
the population migrating to China from other countries. We have
modeled the population entry rate via the contribution of the validity
period of the PCR test and the restrictions on international ights
according to the characteristic of immigration by actual data tracing,
shown as the formula (1):
ατϑ
0ttt
()
=
()
+
()
(1)
To simulate the number of international ights, weset parameters
τ
t
()
and
ϑ
t
()
varying with time
t
.
τ
t
()
represents the contribution of
the eective duration of the PCR test and
ϑ
t
()
represents the
contribution of the number of inbound ights on population entry
rate at time
t
. en wend
τ
t
()
is linear to the weight parameter
e1
(43), and the weight portion is
e
times the reciprocal relationship with
the number of inbound ights
x1
and is logarithmic with the eective
duration of nucleic acid testing
x0
(44).
ϑ
t
()
is linear to the weight
parameter
l1
, and the weight portion is
l
times reciprocal relationship
with the eective duration of the PCR test by tting to the data (45):
τ γ
texxet
()
=∗ ∗
()
+/log
101
(2)
ϑ
tl xlt
()
=
()
+/log 11
(3)
γ
is the weight parameter only aected by the eective duration
of the PCR test
x0
. Aer wedraw a curve of best t, wend the
eects of PCR test validity period setting are in line with the
logarithmic function. is means the virus incubation period could
inuence the test validity period (46). When the test validity period
is shorter than the incubation period, the eect of the validity
period of the PCR test conforms to the signicant variation part of
the logarithmic function, so set
γ
=1
. If the test validity period is
longer than the incubation period, the eect of the validity period
of the PCR test conforms to the gently part of the logarithmic
function, so set
γ
=100000
0
x
.
γ
=≤10
,if xthe length of theaverage incubation period
γ
=>100000 0
0
xif xthe length of theaverage incubation perio, dd
(4)
e parameter
λ
is the release ratio at the end of the quarantine,
which follows an exponential distribution with parameters
c1
and
c
(47):
12
cx
ce
λ
−∗
= ∗ (5)
e parameter
δ
i
is the probability of the quarantine measure to
the symptomatic infectious individuals, and the parameter
δ
q
is the
probability of the quarantine measure to the asymptomatic infectious
individuals (48). Additionally,
0
∆
,
ρ
0
,
η
0
,
1
∆
,
ρ
1
, and
η
1
are all the
FIGURE1
Improved SIR model on SARS-CoV-2 transmission. Dashed lines are influence parameters refer to a real-world scenario where the untraceable
infections were reported. For example, untraceable infections that caused by contaminated cold-chain products θ2 and infections rate θ1(t) that trigger
local outbreaks. Solid lines are transition probability of compartments. Parameters α0(t), λ, δi and δq are related to the NPIs implemented for China-
bound travelers and α1, α2, and α3 are the outbound parameters; ri,di are the recovery rate and qr is the death rate; p, β, ε, eq, qi are the transition
probability. Furthermore, the arrows represent the direction of transition/influence between compartments. With above, the initial values and detailed
values are presented in Tables 1, 2.

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TABLE1 Initial conditions description for models.
Parameter Meaning Value Source
p
Isolation rate of susceptible class 0.00000015 Ref (40)
1
α
Exit rate of the susceptible class
0.00000011 1
x∗
Reported data
2
α
Exit rate of the carried class
0.0001 1
x∗
Reported data
3
α
Exit rate of the recovered class
0.0000057 1
x∗
Reported data
( )
1
t
θ
Relative transmission strength of carried class to the susceptible class - See formula (8)
2
θ
e probability of local outbreak 0.1194 See formula (9)
β
e transmission parameter of Delta variant
0.000000001
Ref (41)
ε
Transfer rate of carried class to the symptomatic class 0.1515 = 1/4.4*2/3 Ref (42)
r
i
Recovery rate of the symptomatic infected individuals [0.0357,0.0714] Reported data
d
i
Death rate due to infection 0 Reported data
eqTransfer rate of concentration quarantine susceptible individuals to the
symptomatic infected class
0.0758 = 1/4.4*1/3 Ref (42)
( )
0
t
α
Entry rate from foreign region to the mainland China - See formula (1)
( )
t
τ
e initial weigh value of eective duration of PCR test - See formula (2)
( )
t
ϑ
e initial weigh value of number of immigration ights - See formula (3)
λ
Release rate of concentration quarantine susceptible individuals to the
susceptible class
- See formula (5)
i
δ
Transfer rate of concentration quarantine susceptible individuals to the
symptomatic infected class
- See formula (6)
q
δ
Transfer rate of concentration quarantine susceptible individuals to the
asymptomatic infected class
- See formula (7)
q
r
Recovery rate of the asymptomatic infected individuals [0.0357,0.0714] Reported data
( )
0SInitial value of susceptible individuals in the free environment 1.41007756e+09−Li(t)Reported data
( )
0CInitial value of existing carried cases 6 Reported data
( )
0I
s
Initial value of existing symptomatic cases 638 Reported data
( )
0RInitial value of cumulative recovered individuals 87,140 Reported data
( )
0DInitial value of cumulative deaths 4,346 Reported data
( )
0QInitial value of existing suspected cases 8,577 Reported data
( )
0I
a
Initial value of existing asymptomatic cases 456 Reported data
( )
0L
i
Initial value of cumulative immigration
211 41/ 0.68
1
x∗∗
Reported data
( )
0L
e
Initial value of existing emigration 0 Reported data
N
Total population in the mainland China 1,411,478,724 Reported data
0
xe eective duration of PCR test [2,3,4,5,6,7,8,9,10,11,12,13,14] Reported data
1
xe number of immigration ights [20,40,60,79,100,120,140,160,180,320,640,1,000,1,366] Reported data
2
xe strengths of centralized isolation and quarantine [10,14,17,21,24,28,31,35,38,42,45,49,52] Reported data
γ
e weight parameter of incubation period - See formula (4)

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tting parameters, wealso derive the 95% condence interval (CI),
which is shown in Table2:
δρη
ix=∆
+∗
()
00
02
log (6)
δρη
qx=∆
+∗
()
11
12
log (7)
In the context of infectious disease control, curtailing interactions
between infected and susceptible populations, reducing the
infectiousness of symptomatic patients, reducing the susceptibility of
susceptible individuals, and scaling up such intervention coverage to
accommodate rapid increases in the number of suspected cases are
well-known strategies for minimizing pandemic spread (49). China
has adopted measures conforming to China’s conditions based on the
strategic theory, i.e., local management. When an outbreak occurs, a
local management strategy will beimplemented in that particular city.
To model the local management policy concretely, dynamic parameter
θ
1t
()
varying with time is introduced to the improved model. e
parameter is determined by the number of cities with infected cases
and the population of each city. To enhance the generation ability of
the model, weset the city size equal to 4,000,000 residents (50). Since
the centralized quarantine strategy of inbound ights is managed in a
closed loop, and researches show the majority of domestic outbreaks
were caused by contaminated imported cold-chain food (51, 52)
which was less traceable, weset
θ
2
as the probability of infection
caused by cold-chain propagation.
θ
1t
Thepopulationsizeofoutbreakcity
N
()
=
(8)
θ
2=
−Thefrequency of outbreakscausedbycoldchain
Thefreque
nncyoftotal outbreaks
(9)
2.4. Data resource
July 21, 2021, was set as the starting date of this study. e initial
value of
S0
()
was collected from the Seventh National Population
Census. e initial values of existing symptomatic cases
Is0
()
, existing
asymptomatic cases
Ia0
()
, existing suspected cases
Q0
()
, cumulative
recovered individuals
R0
()
, and cumulative deaths
D0
()
were captured
from July 21, 2021, based on the National Health Commission of China
reports.
Le0
()
and
Li0
()
were collected from VariFlight since July 21,
2021. Since the incubation period is around 4 days, the existing virus-
carried cases
C0
()
were set to equal to the new domestic case count
aer (0 + 4) days, i.e., July 25, 2021. Based on VariFlight data and travel
requirements, all international ights’ capacity were set to equal to 50%
of the original capacity. For better versatility, the average population for
medium-sized cities in China was set as 4,000,000 (53).
2.5. Parameters setting and parameters
estimation
According to VariFlight, there were an average of 16,707 inbound
immigrants and 12,310 outbound emigrates per day. Deidentied
aggregated data collected from July 21, 2021, to August 30, 2021, was
used to t the inbound parameter
α
0t
()
, the outbound parameters
α α
12
,
, and
α
3
(54). To study the impact of the scenario with the
normal inbound ights on the domestic outbreaks and economic
TABLE2 Estimated parameters description for models.
Parameter Meaning 95%CI Value Source
0
∆Minimum conversion rate (0.00000881, 0.000011) 0.00001 Estimated
0
ρ
Adjustment coecient (0.00021, 0.00024) 0.00023 Estimated
0
η
Adjustment coecient (990,1,011) 1,000 Estimated
1
∆Minimum conversion rate (0.0000009,0.0000011) 0.000001 Estimated
1
ρ
Adjustment coecient (0.00015, 0.00016) 0.00016 Estimated
1
η
Adjustment coecient (2.89, 3.11) 3 Estimated
q
i
Transfer rate (0.008, 0.011) 0.01 Estimated
c
Weight parameter of controlling increasing rate (0.66, 0.72) 0.68 Estimated
1
cExponential decline rate (0.00008,0.00012) 0.0001 Estimated
e
Logarithmic increment rate (0.009,0.011) 0.01 Estimated
l
Logarithmic increment rate (0.0235, 0.0265) 0.025 Estimated
1
eLinear increasing rate (0.00214,0.00216) 0.00216 Estimated
1
lLinear increasing rate (0.000018,0.0000219) 0.00002 Estimated

Yang et al. 10.3389/fpubh.2023.1202996
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development, wecollected the historical data from July 1 to 14, 2019,
to simulate the future ow trend of inbound travelers, observe the
development trend of COVID-19 and summarize recommendations.
eoretically, without considering the epidemiological
characteristics of SARS-CoV-2, this generic improved SIR model
could provide estimation with the above parameters (
prdeq
iiqr
,,,, ,,
βε
).
Parameters
p
and
β
were dened via reference (40). However, as the
Delta variant continued to mutate, the early transmission rate
β
was
lower than the current variation (Table3). In addition, the average
incubation period of the Delta virus was about 4.4 days and about
two-thirds of those infectious cases were symptomatic (55),
corresponding to
ε
+=eq1
, as a result, weset the transfer rate
ε
as
1/4.4*2/3. Furthermore, according to the study report (53), the average
recovery period was between 14 and 28 days, thus weset
ri
and
qr
equal to (1/28, 1/14). Lastly, historical data has shown zero deaths
during the selected period, so
di
was set as zero.
To investigate how NPIs implementation impacts the outbreak
duration or the turning point, the logic parameters (
0
∆
,
ρ
0
,
η
0
,
1
∆
,
ρ
1
,
η
1
,
e
,
l
,
e1
,
l1
,
qi
,
c
,
c1
) associated with tting functions were estimated
by Monte Carlo Stochastic Simulation (MCSS) approach. To get the
probability distribution for variables related to population behaviors,
a large number of simulation repetitions were needed to stabilize the
frequency distributions. Parameters were randomly generated within
a range equal to their best t to the observed data or literature via
ecient Python soware, then weran the MCSS method with 1,000
iterations to derive the probability distribution of those variables.
Finally, weobtained the initial values and estimated parameters of the
model, and listed parameters, initial values, as well as corresponding
95% CI in Table2.
We further compared the prediction results with three training
datasets to determine their nal parameters solution aiming to
minimize RMSE. To verify the validation of the SIR model and
estimated parameters, we compared the model with the testing
dataset. Predictive results indicated that the estimated values were in
very good agreement with real reported data and that the estimated
parameter values can beused to predict the future development trend
of COVID-19in mainland China.
3. Results
3.1. Model verification of reliability, stability,
and sensitivity
Figures 2A–D were simulated based on existing symptomatic,
suspected, and asymptomatic cases and cumulative recovered individual
datasets, reported by the National Health Commission of China from
July 21, 2021, to August 30, 2021. e reported existing cases were set as
training datasets to generate (Figures 2A–C). Reported cumulative
recovered individuals were used as a testing dataset to generate
(Figure2D). To verify the model’s reliability, root mean square error
(RMSE) was adopted to cross-validate the predicted results and the real-
world results. Since a smaller RMSE result refers to a better tting result,
by putting the weight vector quantity (1,0.1,1) to training datasets to
reach a goal of minimum RMSE, weobtained the optimal parameters
solution. Finally, for reliability verication, the optimal parameters were
assigned to the target model to obtain the predicted results and compare
it with the trend of cumulative recovered individuals.
To verify the model’s stability while generating the best model
tting result, weidentied the equilibrium point between variance
and bias, and set the value of ratio (Bias
2
/Variance) in the interval
[0.5,1.3], based on bias-variance dilemma theory (Table3).
e sensitivity of NPIs on infected cases was tested in this section.
Since the amount of three intervention combinations was 2,197, it was
unrealistic to observe the eect of simultaneous changes on infected
cases. In this paper, the changing inuence of each NPIs on infected
cases was observed while the other two NPIs maintain normal.
Especially, Based on July 21, 2021, to August 30, 2021, NPIs
requirements (
xxx
01 2
27917= = =,,
), We completed sensitivity
analysis on each travel-related intervention with input parameters, for
example, the parameters
e
，
e1
of validity period setting of PCR test,
the parameters
l
,
l1
of the control of inbound ights, and the parameters
c
,
1
c
,
0
∆
,
ρ
0
,
η
0
,
1
∆
,
ρ
1
, and
η
1
of the strength of centralized
quarantine. To quantify the parameter sensitivity of each intervention,
we set the number of infected cases caused by current travel
interventions as N*. en the intensity of each intervention was set to
vary around its mean 20%, to derive N
i
. Wecalculated the relative error
of input parameters of each intervention according to the formula [abs
(N
*
−N
i
)/N
*
], as listed here (Table4). Wecould observe that the input
parameters sensitivity of the validity period setting of the PCR test was
the highest, and the sensitivity of the control of inbound ights was the
lowest. us, the results showed the input parameters of the PCR test
were more stable than the other two types of input parameters.
3.2. Demand for health resources
e prevalence of COVID-19 worldwide will increase the risk of
local transmission. Our model has described a scenario on how to
allocate health resources in preparation for possible outbreaks when
international ights have been reduced from 1,366 to 79. Figure3
showed the predictive demand for hospital beds, PCR test volume, and
centralized isolation rooms.
Firstly, Figures3A,D,G showed how the number of international
ights impacts hospital bed demand. Westipulated the number of
beds in use was congured to beequal to the number of infected
individuals to visualize hospital bed occupancy based on the China
CDC’s requirements (56).
TABLE3 SIR model stability analysis.
Datasets
Training datasets Testing dataset
Existing symptomatic
cases
Existing suspected
cases
Existing
asymptomatic cases
Cumulative
recovered individuals
Bias2
177701.8000 205784670.7000 1724.8290 327447.3000
Variance 210671.1451 165107018.8000 3089.3700 648821.8800
Bias / Variance
2
0.8435 1.2463 0.5583 0.5046

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FIGURE2
(A–D) Model fitting and real-world data comparison. Panels (A–D) were the verification results of model parameters inputting, compared existing
symptomatic cases, existing suspected cases, existing asymptomatic cases, and cumulative recovered individual datasets, from July 21, 2021 to August
30, 2021 based on the National Health Commission of China reports. Additionally, dotted lines were the 95%CI of prediction results, solid lines were
the prediction results by model inputting, and original points were the statistical data from the National Health Commission of China reports. Moreover,
the RMSE of (A) is equal to 194.35; the RMSE of (B) is equal to 6733.59; the RMSE of (C) is equal to 46.54; and the RMSE of (D) is equal to 283.57.
TABLE4 SIR model sensitivity analysis.
The window of related
parameters/multiple
proportions
Relative error of the validity
period setting of PCR test
Relative error of the
control of inbound flights
Relative error of the
strength of the centralized
quarantine
0.8 0.0794 0.0133 0.0380
1 0 0 0
1.2 0.0692 0.0137 0.0299
Figures3B,E,H simulated the demand for PCR tests, which was
achieved by the product of the obtained number of virus carriers and
their highest transmission coecient. Lastly, Figures3C,F,I indicated
the isolation rooms demand varies with the number of inbound
ights. Based on the current quarantine requirements, one person per
private hotel room, wecould congure the isolation rooms in unit
proportion with the isolated population.
Based on the analysis, wefound that when the number of
international flights was doubled (x
1
= 160), the number of
hospital beds in use would increase by 83%, the PCR test volume
would increase by 44%, and the number of isolation rooms in
need was doubled. The results showed that the growth in the
number of international flights had the greatest impact on
isolation room demand. When the number of international
flights increased from 79 to 1,366, the demand for hospital beds
raised to 25,000/day, the PCR test volume was up to about 8,000/
day, and 800,000/day isolation rooms within 30 days were in need
in preventing the spread of the epidemic. Our simulation results
indicated that, under those epidemic prevention and control
strategies, China was not ready to fully resume pre-pandemic
international travels due to excessive demand for health
resources. Additionally, the prevalence of COVID-19 in the
surrounding countries would increase the probability of a sizable
domestic outbreak. To prevent excess demand for health
resources, the implementation of an aggressive disease prevention
and control strategy was recommended.
As the virus continues to evolve, China is likely to readjust its
preventive policies, wewill discuss how these future modications
would impact the spread of disease and demand for health resources
in the follow-up study.

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3.3. Eectiveness of NPIs and risk warning
of domestic outbreaks
Our retrospective model has indicated that NPIs on travel
requirements have successfully contained the spread of the virus. In
this section, wewill discuss the control of the number of inbound
ights, the validity period setting of PCR tests, and the strength of
centralized quarantine. By observing and analyzing changes in the
number of infected cases and level of intervention implementation,
the result will show the eectiveness of NPIs and risk warning of
future domestic outbreaks.
3.3.1. The validity period setting of PCR test
Figure4 shows that with the increase of validity period setting
of PCR test, the number of symptomatic and asymptomatic
infected cases will continue to grow until converging to a stable
state presenting no eect of the intervention. Figure4 shows there
are no major uctuations in the number of infected cases when the
validity period of the PCR test is in a 4-day window. However,
when weadjust the validity period to 7 days and more, the number
of infected cases will bein a stable state. Our results show it is
necessary and urgent to set a PCR test time requirement before
travelers’ arrival. Secondly, the simulation shows that the validity
period of the PCR test is closely related to the incubation period of
the Delta variant, thus, the test validity period is suggested to beset
within 4 days. To maximize impacts, the validity period should not
exceed 7 days.
3.3.2. The control of inbound flights
Figure5 reveals the relationship between the number of inbound
ights and the infected case count. As the number of international
ights increases, the number of infected cases would grow
exponentially. In this part, weadjust the inbound ight number from
20 to 180 with arithmetic progression and proportional sequence. e
simulation results show when the inbound ight number equals 79 per
day, there will be approximately 2,411 infected cases. When the
inbound ight number exceeds 180 per day, the number of infected
cases would rise to 4,715. When the number of inbound ights equals
1,366 per day, the daily infected cases would achieve 30,501. ese
results supported the following conclusions: rst, the simulation results
show that the change in ight numbers has a greater impact than other
interventions, thus, limiting the number of inbound ights is the most
eective intervention in preventing local transmissions. As a result, the
adjustment of the intervention should beconsidered carefully, because
the change in 3–4 infected cases count could trigger a local outbreak
under the current severe international situation (47).
3.3.3. The strength of centralized quarantine
Figure6 shows how centralized quarantine inuences the number
of infected cases. With the extension of the quarantine period, the
number of infected cases will continue to grow. It can beobserved that
the impact of the intervention is still remarkable within threshold 35
on preventing the spread of the epidemic and the number of infected
cases is converging to a stable situation when exceeding threshold 35.
e model also indicates that 17 days of centralized quarantine would
FIGURE3
(A–I) Health resource demand prediction based on number of inbound flights. Panels (A–C) show the demand for hospital beds, PCR tests, and
isolation rooms in a real-world scenario where the daily inbound flight is equal to 79. Panels (D–F) simulate the changes when inbound flights are 160,
a scenario where the current requirements have been slightly lifted. Panels (G–I) present results when the number of inbound flights is 1,366, a
scenario with no inbound flight restrictions.

Yang et al. 10.3389/fpubh.2023.1202996
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FIGURE4
The validity period setting of PCR test vs. infected cases count.
FIGURE5
The number of inbound flights vs. infected cases count.
eectively prevent disease spread. e quarantine benet will diminish
aer 17 days benchmark and reach a stable state aer 35 days.
3.3.4. Comprehensive review of all interventions
Figure 7A simulated the interaction of the strength of
centralized quarantine and the validity period setting of PCR test
on the development of domestic epidemic in the current number
of inbound ights scenario. Under two scenarios, where the
number of restricted inbound ights was equal to 79 and the
number of recovered normal inbound ights was 1,366, the 3-day
of validity period setting would cause more local infected cases
compared with the 2-day setting, especially in the recovered
normal inbound ights scenario in Figure7B. To quantify the
dierence in the infected cases between 2(79)- and 3(79)-day in
the restricted scenario, weused RMSE to measure the gap, deriving
about 53.431. For the small dierence between 2(1366) and

Yang et al. 10.3389/fpubh.2023.1202996
Frontiers in Public Health 11 frontiersin.org
3(1366)-day in the recovered scenario, RMSE is 1.0377. us, the
2(79)-day PCR test was recommended for the ight-restricted
scenario and the 2(1,366) or 3(1,366)-day test was recommended
for a normal schedule.
4. Discussion
4.1. Application of the improved SIR model
from a macro perspective
Studies performed in the United Kingdom and the
UnitedStates indicated that the effectiveness of any single NPIs
was likely to belimited, combining multiple interventions was
worthy of further study (57). Scholars also indicated that the
effectiveness of travel bans in reducing the spread of infectious
diseases, and the relative effectiveness of NPIs for controlling the
pandemic has gone largely unstudied (58, 59). Therefore, our
proposed model played a significant role in estimating the
combined effects of NPIs implementation and predicting the
demand for isolation rooms, PCR test volume, and hospital beds.
The results could provide scientific guidance for nationwide
strategic planning and policy implementation and also bridge the
theoretical gaps between international travel controls and related
effectiveness of the NPIs.
On one hand, weanalyzed how inbound flights would impact
the distribution of health resources in response to a possible local
outbreak. The model quantified the impact of local virus carriers
FIGURE6
The strength of centralized quarantine vs. infected cases count.
FIGURE7
(A,B) The strength of centralized quarantine and the validity period setting of PCR test.

Yang et al. 10.3389/fpubh.2023.1202996
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that supported PCR testing arrangements for community
screening. The number of infected cases and quarantined
population could support the allocation of hospital beds and the
configuration of isolation rooms. Thus, werecommended that
the government should restore inbound flight numbers
appropriately with sufficient medical supply in response to the
increase in daily infected cases.
On the other hand, our model and related results provided
scientific evidence that supported the design and implementation
of existing interventions. The results indicated that
comprehensive interventions of a two-day PCR test, 79 inbound
flights per day, and 17 days of centralized quarantine were
effective in stabilizing domestic disease transmission. In addition,
the modeling effort also provided theoretical advice for future
adjustment. When the epidemic prevention and control goal is to
treat and monitor the health status of all infected individuals,
limiting the inbound flight number to a small scale is
recommended. When the priority is to treat severe and critical
cases in hospitals and monitor the health status of individuals
who have mild or no symptoms at home, resuming a regular
inbound flight schedule is recommended.
4.2. Application of the improved SIR model
from a micro perspective
The risk estimation of COVID-19 importation can beapplied
to identify the effectiveness of travel-related control measures
(60). However, the connection between imported cases and local
outbreaks was not studied. In our model, parameters
θ
1
and
θ
2
were key factors to understand and mitigate domestic outbreak
risks, and also represented mathematical logic interaction
associated with the domestic outbreak and global pandemic
status. Going further, the current improved SIR model provided
more heuristic thinking for constructing new models for
domestic outbreaks affected by various factors.
4.3. Application of the improved SIR model
at other variants of SARS-CoV-2, such as
omicron
e new variant SARS-CoV-2 Omicron demonstrated partial
vaccine escape and high transmissibility, with early reports indicating
lower severity of infection (47) and reduced risk of hospitalization
(61) than pre-existed variants. Wewould like to extend the delta-
focused simulation model and related control strategy parameters to
Omicron and discuss the applicability and sustainability of the
continued implementation of such strategies in combating the new
variants in our future research.
4.4. Limitations
Our study has several limitations. First, our model did not
consider individuals’ preventative behaviors. Secondly, weonly
considered the nationwide prevention strategies and did not dive
into detailed strategies enacted at the province and city levels. To
minimize such impacts, we adopted reasonable assumptions
about epidemiological parameters and aspects of human
behaviors that contributed to disease transmission. Although the
results showed that our conclusions were remarkably robust, this
model was highly sensitive to the quality of input parameters.
Thus, wecautiously selected parameters and values based on
literature research results and research data. In the proposed
homogeneous hybrid model, the population and individuals were
distributed and mixed homogeneously and uniformly.
Disturbances, such as economic status, political environments,
living environments, cultural influences, etc. remained the same.
In the meantime, the transmission coefficient, and average delay
between symptom onset and test results were constant, and the
effect analysis of vaccines, the reporting delays, and testing delays
were not captured, which would lead to the requiring
hospitalization or developing severe COVID-19 stochastic by
nature. Since the purposed model was set to make conservative
predictions, when a new variant presents different severity,
infectiousness, and immune escape features, weneed to convert
the purposed model with updated parameters and generate
up-to-date predictions. Finally, the model neglected the
stochastic effects at low-case numbers. When imported infections
were reported, especially when testing was required, having or
not a population-scale outbreak was a matter of probabilities;
differential equation models cannot capture this accurately.
Furthermore, for a disease like COVID-19 with such an over-
dispersed individual variation of infectiousness (62), outbreaks
were likely to die out if very few cases were introduced (63).
4.5. Conclusion
Our nding indicated that restriction on inbound ight numbers
played a key role in preventing and controlling the epidemic, but the
combined use of other NPIs would maximize the eect in preventing
additional transmission. Centralized quarantine days should beset
in between 17 to 35 days for the Delta variant. e validity period of
the PCR test was related to the disease incubation period, and the
valid time should beless than 7 days. In addition, when the disease
incubated, the PCR test period did not have a signicant impact on
epidemic control. More importantly, the model estimated that if
recovering the pre-pandemic inbound travel strategy in 2019, the
number of hospital beds would reach 25,000 per day, the volume of
PCR tests would be8,000 per day, and the isolation capacity would
be nearly 800,000 per day within 30 days to maintain the same
achievement of preventing outbreaks. All in all, our improved model,
which can robustly generate scenarios, will help understand the
tradeos between dierent strategies, and further guide the health
resources preparation and allocation.
Data availability statement
e original contributions presented in the study are included in
the article/supplementary material, further inquiries can bedirected
to the corresponding authors.

Yang et al. 10.3389/fpubh.2023.1202996
Frontiers in Public Health 13 frontiersin.org
Author contributions
LY, MH, HZ, WL, and JZ developed this project and created the
manuscript concept. LY designed the model, interpreted the results,
and wrote and edited the manuscript. MH contributed to the literature
research, data collection, manuscript writing, and editing. All authors
contributed to the article and approved the submitted version.
Funding
is was funded by the National Natural Science Foundation of
China (grant number 72091514); the Sanming Project of Medicine in
Shenzhen (grant number 20212001132); and the Bill & Melinda Gates
Foundation (grant number INV-018302).
Conflict of interest
e authors declare that the research was conducted in the
absence of any commercial or nancial relationships that could
beconstrued as a potential conict of interest.
Publisher’s note
All claims expressed in this article are solely those of the
authors and do not necessarily represent those of their affiliated
organizations, or those of the publisher, the editors and the
reviewers. Any product that may be evaluated in this article, or
claim that may be made by its manufacturer, is not guaranteed or
endorsed by the publisher.
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