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Lockdown Strategy Worth Lives: The SEIRD Modelling in COVID-19 Outbreak in Indonesia

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Lockdowns, despite their conflicting restrictions and consequences they might offer when enforced as a national strategy, are deemed to be suggestive for a prompt conquer to the Coronavirus Disease-19 (COVID-19) outbreak. There have been some success stories such as in China, South Korea and our ASEAN member fellow, Vietnam, which exhibited extremely fallen numbers of COVID-19 cases post the enforcement of lockdown. Indonesia, however, remains in the crux of dispute whether or not the lockdown is opted to force COVID-19 transmission down under control. We, in this respect, employ the most popular model which has been broadly applied in the field of epidemiology, referred as SEIRD (Susceptible, Exposed, Infectious, Recovered, and Death), the extension form of an age-structured SEIR, where the Death (D) is included to provide more factual situation. We modify the I (Infectious) fraction as symptomatic (Is) and asymptomatic (Ia) infectives. There are three lockdown scenarios simulated in our modified SEIRD with the starting date are 26 April 2020 when the immediate lockdown was enacted-and a-week and two-week-gaps, respectively. We figured out that by stipulating the lockdown without delay (26 April 2020), the new cases could be kept below 10,000. A week delay escalates case number to 5,000 and delay for one more week results in beyond 20,000 new cases. Furthermore, when the intervention is delayed following the delayed lockdown, normalization would demand a longer period within which dealing with more critical and dying patients is unavoidable and should be more anticipated.
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Lockdown strategy worth lives: The SEIRD modelling in COVID-19
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International Conference on Biospheric Harmony Advanced Research 2020
IOP Conf. Series: Earth and Environmental Science 729 (2021) 012002
IOP Publishing
doi:10.1088/1755-1315/729/1/012002
1
Lockdown strategy worth lives: The SEIRD
modelling in COVID-19 outbreak in Indonesia
I Nurlaila1,2,, A A Hidayat2, B Pardamean2,3
1Information Systems Department, BINUS Online Learning, Bina Nusantara University,
Jakarta, Indonesia 11480
2Bioinformatics and Data Science Research Center, Bina Nusantara University, Jakarta,
Indonesia 11480
3Computer Science Department, BINUS Graduate Program - Master of Computer Science,
Bina Nusantara University, Jakarta, Indonesia 11480
E-mail: ika.nurlaila@binus.edu
Abstract. Lockdowns, despite their conflicting restrictions and consequences they might offer
when enforced as a national strategy, are deemed to be suggestive for a prompt conquer to the
Coronavirus Disease-19 (COVID-19) outbreak. There have been some success stories such as in
China, South Korea and our ASEAN member fellow, Vietnam, which exhibited extremely fallen
numbers of COVID-19 cases post the enforcement of lockdown. Indonesia, however, remains in
the crux of dispute whether or not the lockdown is opted to force COVID-19 transmission down
under control. We, in this respect, employ the most popular model which has been broadly
applied in the field of epidemiology, referred to as SEIRD (Susceptible, Exposed, Infectious,
Recovered, and Death), the extension form of an age-structured SEIR, where the Death (D)
is included to provide more factual situation. We modify the I (Infectious) fraction as symp-
tomatic (Is) and asymptomatic (Ia) infectives. There are three lockdown scenarios simulated in
our modified SEIRD with the starting date are 26 April 2020 when the immediate lockdown was
enacted- and a-week and two-week-gaps, respectively. We figured out that by stipulating the
lockdown without delay (26 April 2020), the new cases could be kept below 10,000. A week delay
escalates case number to 5,000 and delay for one more week results in beyond 20,000 new cases.
Furthermore, when the intervention is delayed following the delayed lockdown, normalization
would demand a longer period within which dealing with more critical and dying patients is
unavoidable and should be more anticipated.
Keywords: Contact matrices, COVID-19, Epidemiological modelling, Lockdown, SEIRD
equation,
1. Introduction
The Coronavirus Disease-19 (COVID-19) has been the most frightening outbreak in the last
few months after the first case was identified in Wuhan, China, in December 2019 [1]. It did
not take a while for the viruses to spread across the globe, leaving no nation without any
infection cases. Despite the lower frequency of mortality compared to that seen for two previous
major pandemics: Middle East Respiratory Syndrome (MERS) and Severe Acute Respiratory
Syndrome (SARS) [2], the impacts of the pandemic affect almost all aspects in life [3].
Southeast Asian Countries, where geographically situated adjacent to the epicentre of the
pandemic, are combating the hit in their own finest ways. Although the countries unite under an
International Conference on Biospheric Harmony Advanced Research 2020
IOP Conf. Series: Earth and Environmental Science 729 (2021) 012002
IOP Publishing
doi:10.1088/1755-1315/729/1/012002
2
umbrella called Association of Southeast Asian Nations (ASEAN), they cope with the COVID-
19 almost individually. Taking into account the nations under ASEAN share a lot of similarities
in terms of natural resources and involved in such intense trading and political relationships, we
presumed that the national intervention should reflect those similarities. Instead, we figured out
that discrepancies among them were considerably huge. It is, simply, manifested through how as
nations they strive to manage the impacts, which in majority are bad ones, and take a thorough
control on the COVID-19 transmission and mitigation. Vietnam, for an instance, has lifted its
lockdown since no more new cases surfaces [4] and being the first country in the ASEAN that
officially ended the social distancing when another ASEAN’s members are still struggling [5].
Malaysia also showed an excellent performance in handling COVID-19 by successfully controlling
its accumulative fatality rate to only 1.67% [6]. In contrary, Indonesia appeared to be far
left behind by its most adjacent neighbor country, Malaysia. To date Indonesia exhibits no
satisfying outcome neither post 14-day-nationwide self-quarantine nor post 2-week-large scale
social-restriction (popular as PSBB, pembatasan sosial berskala besar) [7]. This big gap of
inequality has left us thinking of substances that might be very key for either the success or the
failure in respect with the COVID-19-impact managements. A mathematical model is deemed
to serve a prominent assistance to grasp the interplay of lockdowns as the primary strategy
in the outbreak handling and the COVID-19 itself. In addition, by plotting several plausible
lockdown-scenarios we could as well produce a predictive model. In this study, we employed
and modified the SEIRD (Susceptible, Exposed, Infectious Recovered, and Death) model. The
model has been widely used for epidemiology studies [8]. Regarding COVID-19, the model was
used in a study by Prem et al, to measure the progression of COVID-19 and resulted in it was
a reduced median of infection numbers in Wuhan, China, by exceed 92% and 24% in mid-2020
and end-2020, respectively [9]. The model, however, did not take into account the demography
features that might alter the increment of infection dissemination. We are keen to fulfil the gap
and broaden scope of measurement to Indonesia. This is critical to avoid ineffectiveness in the
strategy implementation during the pandemic that might cause unnecessary damages we could
hardly afford.
Up to date, in Indonesia COVID-19 is mainly reported as numbers: numbers of new positive
cases, numbers of deaths and recovered rates. Mathematical model which incorporates aspects
related to the case is barely presented rendering it arduous to orchestrate strategy or intervention
which might fittest to control and manage the impacts. In the present study, we expand our
horizon by striving measuring possible outcomes of COVID-19-handling strategies in Indonesia,
mainly is lockdown. To do so we employed a modified SEIRD model with age structure and
to allow our dataset which comprises susceptible, exposed, symptomatic and asymptomatic
infectives, recovery rates and death toll, to be comprehensively measured. We found them to be
important to evaluate to thoroughly weigh if consequences on the huge restriction system aimed
at suppressing new incidences of COVID-19 is affordable.
2. Related Works
Given the situation where the global concerns are primarily concentrated on COVID-19,
mathematical models are helpful tools for public health policy makers to formulate effective
control strategies to manage the spread of the disease. Hitherto, SEIR model is considered
to be the widely used mathematical model adopted to address queries in the epidemiology
studies [10]. To the most recent was the work by Prem et al. that employed and modified
SEIR model to simulate age-specific and location-specific transmission of COVID-19 at different
stages in Wuhan as well as mitigation strategies [9]. Meanwhile, the use of age-structured SIR
model with the same formulation of the social contact matrices was used to study the effect
of social distancing and different lockdown scenarios affect the control strategies to combat the
pandemic in India [11]. The age-specific contact matrices is important to reflect the vulnerability
International Conference on Biospheric Harmony Advanced Research 2020
IOP Conf. Series: Earth and Environmental Science 729 (2021) 012002
IOP Publishing
doi:10.1088/1755-1315/729/1/012002
3
characteristics for national mitigation policy as suggested by Kaban et al in their study for
Indonesia population [12]. Separately in the same time, Gupta et al, were able to generate
a prediction that from 31st March-13th April 2020 the new case of COVID-19 in India rose
from 5,000-6,000 by employing both SEIR model and regression [10]. Both, however, were
contradicted by the study of Grant where the SEIR model was observed to be underestimating
peak infection rates and on the other hand overestimating epidemic persistence after the peak
elapsed [13]. In addition, a extension of SEIR model called SIDARTHE (Susceptible, Infected,
Diagnosed, Ailing, Recognised, Threatened, Healed, and Extinct (dead)) used to simulate the
COVID-19 pandemic that differentiate between the diagnosed and non-diagnosed population as
well as severity of the symptoms was proposed in Italian population by Giordano et al [14].
3. Methods
3.1. Data
The data of COVID-19 pandemic in Indonesia used in this work is publicly available from the
official website of Indonesia COVID-19 task force [15]. The reporting period from 2 March 2020
to 26 April 2020. However, we only analyzed the data with the starting date of 9 March 2020 as
the number of reported case became more consistent after that date for our model. The social
contact matrices of 152 countries provided Prem et al. is also available from the supplementary
in their paper [9]. The data of the age structure is obtained from PopulationPyramid.net website
[16].
3.2. SEIRD Model
In this work, we assume that the number population is constant, since the number of births
and deaths during the pandemic is much smaller than the number of total population. We
studied the spread of an infectious disease within a population with a categorization into
six states/compartments to: susceptibles (S), exposed (E), symptomatic infectives (Is),
asymptomatic infectives (Ia), recovered individuals (R), and deaths (D), which is depicted
in figure 1. Susceptibles are the healthy subpopulation that are susceptible to the disease.
The number of susceptible population decreases with the infection rate given by a time
dependent quantity denoted as λ(t). The exposed individuals are the infected population
but not yet infectious and will eventually become infected either with clear symptoms/clinical
or asymptomatic/subclinical. The incubation period denotes the period before the exposed
individuals contracting with the disease become infectious. Our proposed model is a direct
extension of an age-structured SEIR model developed by Singh et al. [11] in which we include
the death compartment into the original model to provide a slightly more realistic situation.
The population is categorized into 16 age groups with an age interval of 5 year, thus the total
population can be written as N=P16
i=1 Ni. Our compartment model then can be written as
the following system of ordinary differential equations (ODEs) for a particular age group ias
International Conference on Biospheric Harmony Advanced Research 2020
IOP Conf. Series: Earth and Environmental Science 729 (2021) 012002
IOP Publishing
doi:10.1088/1755-1315/729/1/012002
4
dSi
dt =λi(t)Si
dEi
dt =λi(t)SiγEEi
dIA
i
dt = (1 αi)γEEiγIAIA
i
dIS
i
dt =αiγEEi(1 pi)γsIIS
iγDpiIIS
i
dRi
dt =γAIA
i+γSIs
i
dDi
dt =γDpiIS
i.
(1)
The infection rate for age i,λi(t), with age-aggregated population is defined as
λi(t) = β
16
X
j=1 Cij (t)IA
j
Nj
+Cij (t)IS
j
Nj!.(2)
The public health interventions are encapsulated in the time dependent contact matrices
Cij (t). The matrices describe the structure of social mixing between different age groups. We
employed location-specific contact social matrices denoted by Cl
ij computed by Prem et al.[17]
for 152 countries, including Indonesia. The matrices describe the average number of interactions
per day between an individual in age group iwith an individual in age group jin a specific
location. The matrices have been computed in home (l=H), school (l=S), workplace (l=W),
and other unspecified locations (l=O). Therefore, the time dependent contact matrices can be
written as a linear combination of Cl
ij as
Cij (t) = CH
ij +fSCS
ij +fWCW
ij +fO(t)CO
ij .(3)
Constant fldescribe the extent of the closure of the corresponding location to minimize social
mixing and may be time-dependent functions. Meanwhile, other parameters in equation 1 except
αiand pi:β,γE,γIA,γIS, and γDare fit parameters describing the rate of progression into the
corresponding states. The proportion of a case belongs to clinical/symptomatic case is denoted
by αi. Following the parameters used in [9], we utilized conservative proportions in different age
groups: we put αi= 0.4 for i4 and αi= 0.8 for i > 4. Meanwhile, the fraction of mortality,
pi, denote the proportions of critical cases to die due to the infection for a certain age group
i. As the proportions are not available publicly in Indonesia, as a rough estimate, we employed
the death proportions used by website Worldometer from a report from New York City Health
[18]. The proportions are multiplied by a common factor γDto represent death rate for age i.
We define a rate δ=d1
Dwhere dDis the number of days between the onset of symptoms and
deaths that we assumed to be 14 days [18]. In addition, we utilized the formulation detailed by
Diekmann et al.[19] and Singh et al. [11] to compute the basic reproduction number, R0, which
is defined as the maximum eigenvalue of the next generation matrix (NGM).
We fitted the essential parameters in our model: αi,β,γE,γIA,γIS, and γDby minimizing
the following error function:
n
X
i=1
(Ipred Idata)2+
n
X
i=1
(Dpred Ddata)2
.(4)
International Conference on Biospheric Harmony Advanced Research 2020
IOP Conf. Series: Earth and Environmental Science 729 (2021) 012002
IOP Publishing
doi:10.1088/1755-1315/729/1/012002
5
Figure 1. A SEIRD model for a particular age group with both symptomatic and asymptomatic
infectives are included.
Table 1. Best fit model parameters from the data.
Parameters Value
β0.043
γE0.220
γIA0.118
γIS0.219
γD0.075
Quantities Idata,Ipred ,Dpred, and Ddata are the number of reported positive cases, the number
of simulated cases, number of reported deaths, and the number simulated death cases. We
partially used utilities from PyRoss package for fitting the the parameters [20].
4. Results and Discussion
During our analysis, we employed the calculation of the cumulative cases with the initial date
9 March 2020 because the result of the tests from the previous days became more available (we
observed that the reported cases at that date tripled from the previous day). The progress of
the reported case went relatively smooth from that day forward that might be partially due
to the improved procedures for the tests. By varying the number of days to be included for
fitting the parameters, we found that the daily data from the period 9 March, 2010 to 7 April,
2020 (30 days) produce the best fit parameters. The resulting fit is given in table 1. From
the simulation, we also obtained that the basic reproduction number in the early days of the
pandemic in Indonesia R0= 3.6192. This result excludes the dynamics of the early pandemic
as the data is not available.
As a concrete example, we considered a lockdown scenario that mimics the data of the
infected cases in Indonesia. First of all, from 9 March 2020 until 16 March 2020, without
any interventions, all social mixing across ages in public places still took place, which means
fS=fW=fO= 1. Afterward, Indonesia’s government started to implement a public
intervention at 16 March 2020 by prompting a total school closure, which could be assumed
to be implemented immediately across country, and also only suggested workplace closure and
maintaining physical distance in public spaces. Formulating in our case, this means fS= 0 and
we assumed that only 50% of the workplaces were shut down, fW= 0.75, and the public
suggestion only closed 80% of public spaces, fO= 0.8. As the pandemics worsened, the
government took a more strict measure called PSSB (large scale physical distancing) to stop the
International Conference on Biospheric Harmony Advanced Research 2020
IOP Conf. Series: Earth and Environmental Science 729 (2021) 012002
IOP Publishing
doi:10.1088/1755-1315/729/1/012002
6
Figure 2. Comparison between three different one-half month lockdown scenarios. The right
and left dashed lines indicate the start and the end of the lockdown period.
viruses spread in public spaces and ordered the workplaces to be closed. We assume that 75%
working from home (fW= 0.25) and 50% of other public places were closed (fO= 0.5). We
invent the last stage, a so-called ‘’total lockdown”, which is essential to decrease the number of
infected cases that was implemented in Hubei province, and currently being implemented by half
European countries, including Italy and Spain. This stage ideally closes public spaces (fO= 0)
and only allows for 10% workplaces opened such as hospitals and markets/supermarkets/shops
for essential needs (fW= 0.1).
We simulated three lockdown scenarios based on three different starting date of the lockdown
with a period of 45 days. The bold dashed black line shown in the figure indicates the curve when
no interventions were introduced since the beginning of the day until today, which is untrue but it
provides a baseline information. The first scenario (green line) is the immediate lockdown taken
by the government at 26 April 2020 (the last data point in our data). On the other hand, the
second (blue line) and the third (red line) lockdown scenario take place one week and two weeks
after the first scenario, respectively, corresponding to the delayed interventions. Our results can
be seen in Figure 2. Visually, the data points follow the infection curve until the last date of the
data because we adjusted the magnitude of the contact matrices via f-value as described above
in such way that the choice of percentages leads to the expected trajectory. The first scenario
(green line) is able to keep the number of cases below ten thousands. However, a one-week
delay in the second scenario increases the number by 5,000 cases and further, a two-week delay
results in more than devastating 20,000 infected cases. The delayed interventions clearly imply
a longer lockdown period needed to normalize the situation while the medical system is fully
overwhelmed and thousands more of critical patients die.
We must emphasize that the results from the toy simulation do not reflect the correct
dynamics of COVID-19 pandemic in Indonesia as the number of cases may be underreported
and we mostly estimate the parameters from the preliminary data from another countries. The
result, however, once again resonates the widely existing suggestion made by countless scientific
International Conference on Biospheric Harmony Advanced Research 2020
IOP Conf. Series: Earth and Environmental Science 729 (2021) 012002
IOP Publishing
doi:10.1088/1755-1315/729/1/012002
7
reports involving more advanced and realistic simulations that strict lockdown scenarios are
needed now. The period duration must be adjusted by the government by considering a lot of
multi-aspect constraints.
Our model can be extended to include another compartment/state to provide a more realistic
simulation (i.e predicting hospitalizations, triage, unobserved cases, region-specified cases, and
more) as more data available as developed by Giordano et al [14]. However, the main difficulty
of simulating the data-driven SEIRD model is the lack of clinical and non-clinical information
that may provide clear initial bounds for the parameters since the accurate SEIRD modelling
relies on correct initial values. Nevertheless, agggregating the age groups and social contract
matrices as well as other information such as gender, geospatial location, detailed characters of
the cities, and more may provide a first step for the public health policy maker to plan a decision
mitigating the disease.
5. Conclusion
In our modified SEIRD model, we simulated three different scenarios of lockdown and evaluated
what would be plausible consequences for each option. Our first scenario is when the lockdown
is effectively activated on 26 April 2020. This assists the super limited new case emergences. A
week- and two-week delays cause 5,000 and 20,000 new cases, respectively. Although the model
would not be able to offer an absolute number, it worth a deeper thought especially in the
perspectives of socio-economic consequences which might be unaffordable for a nation given the
damages COVID-19 has caused by far. Therefore, modification in the enacted lockdowns should
have been prior-anticipated with the focus on the mitigation by which normalization could be
feasible within a relatively short time.
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International Conference on Biospheric Harmony Advanced Research 2020
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IOP Publishing
doi:10.1088/1755-1315/729/1/012002
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... All countries are trying to control and restore human life to normal. Governments in various countries carry out social restrictions [7] and communicate to convince the public that COVID-19 is dangerous [8]. Another way to deal with this situation is to detect individuals infected with COVID-19 as early as possible so that they can be quarantined and stop the spread of COVID-19 to others. ...
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Detecting COVID-19 as early as possible and quickly is one way to stop the spread of COVID-19. Machine learning development can help to diagnose COVID-19 more quickly and accurately. This report aims to find out how far research has progressed and what lessons can be learned for future research in this sector. By filtering titles, abstracts, and content in the Google Scholar database, this literature review was able to find 19 related papers to answer two research questions, i.e. what medical images are commonly used for COVID-19 classification and what are the methods for COVID-19 classification. According to the findings, chest X-ray were the most commonly used data to categorize COVID-19 and transfer learning techniques were the method used in this study. Researchers also concluded that lung segmentation and use of multimodal data could improve performance.
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Background: The initial cases of novel coronavirus (2019-nCoV)-infected pneumonia (NCIP) occurred in Wuhan, Hubei Province, China, in December 2019 and January 2020. We analyzed data on the first 425 confirmed cases in Wuhan to determine the epidemiologic characteristics of NCIP. Methods: We collected information on demographic characteristics, exposure history, and illness timelines of laboratory-confirmed cases of NCIP that had been reported by January 22, 2020. We described characteristics of the cases and estimated the key epidemiologic time-delay distributions. In the early period of exponential growth, we estimated the epidemic doubling time and the basic reproductive number. Results: Among the first 425 patients with confirmed NCIP, the median age was 59 years and 56% were male. The majority of cases (55%) with onset before January 1, 2020, were linked to the Huanan Seafood Wholesale Market, as compared with 8.6% of the subsequent cases. The mean incubation period was 5.2 days (95% confidence interval [CI], 4.1 to 7.0), with the 95th percentile of the distribution at 12.5 days. In its early stages, the epidemic doubled in size every 7.4 days. With a mean serial interval of 7.5 days (95% CI, 5.3 to 19), the basic reproductive number was estimated to be 2.2 (95% CI, 1.4 to 3.9). Conclusions: On the basis of this information, there is evidence that human-to-human transmission has occurred among close contacts since the middle of December 2019. Considerable efforts to reduce transmission will be required to control outbreaks if similar dynamics apply elsewhere. Measures to prevent or reduce transmission should be implemented in populations at risk. (Funded by the Ministry of Science and Technology of China and others.).
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The basic reproduction number (0) is arguably the most important quantity in infectious disease epidemiology. The next-generation matrix (NGM) is the natural basis for the definition and calculation of (0) where finitely many different categories of individuals are recognized. We clear up confusion that has been around in the literature concerning the construction of this matrix, specifically for the most frequently used so-called compartmental models. We present a detailed easy recipe for the construction of the NGM from basic ingredients derived directly from the specifications of the model. We show that two related matrices exist which we define to be the NGM with large domain and the NGM with small domain. The three matrices together reflect the range of possibilities encountered in the literature for the characterization of (0). We show how they are connected and how their construction follows from the basic model ingredients, and establish that they have the same non-zero eigenvalues, the largest of which is the basic reproduction number (0). Although we present formal recipes based on linear algebra, we encourage the construction of the NGM by way of direct epidemiological reasoning, using the clear interpretation of the elements of the NGM and of the model ingredients. We present a selection of examples as a practical guide to our methods. In the appendix we present an elementary but complete proof that (0) defined as the dominant eigenvalue of the NGM for compartmental systems and the Malthusian parameter r, the real-time exponential growth rate in the early phase of an outbreak, are connected by the properties that (0) > 1 if and only if r > 0, and (0) = 1 if and only if r = 0.
  • M A Khafaie
  • F Rahim
Khafaie M A and Rahim F 2020 Osong Public Health and Research Perspectives 11 74
  • V P La
  • T H Pham
  • M T Ho
  • M Nguyen
La V P, Pham T H, Ho M T, Nguyen M H et al. 2020 Sustainability 12 2391 URL https://www.mdpi.com/ 2071-1050/12/7/2931
Age-structured impact of social distancing on the covid-19 epidemic in india
  • R Singh
  • R Adhikari
Singh R and Adhikari R 2020 Age-structured impact of social distancing on the covid-19 epidemic in india (Preprint 2003.12055)
  • P A Kaban
  • R Kurniawan
  • R E Caraka
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