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© 2020 Indian Journal of Medical Research, published by Wolters Kluwer - Medknow for Director-General, Indian Council of Medical Research
Prudent public health intervention strategies to control the coronavirus
disease 2019 transmission in India: A mathematical model-based
approach
Sandip Mandal1, Tarun Bhatnagar3, Nimalan Arinaminpathy4, Anup Agarwal1, Amartya Chowdhury1,
Manoj Murhekar†, Raman R. Gangakhedkar2 & Swarup Sarkar1
1Translational Global Health Policy Research Cell (Department of Health Research), 2Division of Epidemiology
& Communicable Diseases, Indian Council of Medical Research, New Delhi, 3ICMR School of Public Health,
†ICMR-National Institute of Epidemiology, Chennai, Tamil Nadu, India & 4Department of Infectious Disease
Epidemiology, School of Public Health, Imperial College, St Mary’s Hospital, London, UK
Received February 27, 2020
Background & objectives: Coronavirus disease 2019 (COVID-19) has raised urgent questions about
containment and mitigation, particularly in countries where the virus has not yet established human-to-
human transmission. The objectives of this study were to nd out if it was possible to prevent, or delay,
the local outbreaks of COVID-19 through restrictions on travel from abroad and if the virus has already
established in-country transmission, to what extent would its impact be mitigated through quarantine of
symptomatic patients?
Methods: These questions were addressed in the context of India, using simple mathematical models
of infectious disease transmission. While there remained important uncertainties in the natural history
of COVID-19, using hypothetical epidemic curves, some key ndings were illustrated that appeared
insensitive to model assumptions, as well as highlighting critical data gaps.
Results: It was assumed that symptomatic quarantine would identify and quarantine 50 per cent of
symptomatic individuals within three days of developing symptoms. In an optimistic scenario of the
basic reproduction number (R0) being 1.5, and asymptomatic infections lacking any infectiousness, such
measures would reduce the cumulative incidence by 62 per cent. In the pessimistic scenario of R0=4, and
asymptomatic infections being half as infectious as symptomatic, this projected impact falls to two per cent.
Interpretation & conclusions: Port-of-entry-based entry screening of travellers with suggestive clinical
features and from COVID-19-aected countries, would achieve modest delays in the introduction of
the virus into the community. Acting alone, however, such measures would be insucient to delay the
outbreak by weeks or longer. Once the virus establishes transmission within the community, quarantine
of symptomatics may have a meaningful impact on disease burden. Model projections are subject to
substantial uncertainty and can be further rened as more is understood about the natural history of
infection of this novel virus. As a public health measure, health system and community preparedness
would be critical to control any impending spread of COVID-19 in the country.
Key words Airport screening - COVID-19 - deterministic model - mathematical model - mitigation - quarantine - transmission
Indian J Med Res, Epub ahead of print
DOI: 10.4103/ijmr.IJMR_504_20
Quick Response Code:
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2 INDIAN J MED RES, 2020
As per the World Health Organization (WHO),
85,403 cases of coronavirus disease 2019 (COVID-19)
were reported globally, as of February 29, 2020,
including 79,394 cases (2838 deaths) from China and
6009 cases (86 deaths) from 53 other countries/territories/
areas1. Initially, all of the cases detected in countries
other than China were linked to infected cases from
China, with subsequent generation of cases in some
of the countries, the latest being Japan, South Korea
and Italy. Considering the high population mobility
through air travel and the documented person-to-person
transmission, the WHO provided an advisory on exit
screening in countries with the ongoing transmission
of COVID-19 and entry screening in countries
without transmission, including screening for the
signs and symptoms of respiratory infection with
focus on temperature screening to detect potential
suspects who would require further laboratory tests
for the conrmation of infection2. As per a stochastic,
worldwide, air transportation network dynamic model,
India ranks 17th among the countries at the highest risk
of importation of COVID-19 through air travel3. The
probability of an infected air traveller to come to India
as the nal destination was 0.209 per cent, with the
highest relative import risk in Delhi (0.064%) followed
by Mumbai, Kolkata, Bengaluru, Chennai, Hyderabad
and Kochi3. This in the context of an epidemic that has
already set in and travel from infected areas continues.
The Ministry of Health and Family Welfare (MoHFW)
of India had initially advised to refrain from travelling
to China and quarantine of those coming from China4.
Those returning from Wuhan, China, after January 15,
2020 were to be tested for COVID-19. Those feeling sick
within a month of return from China were advised to report
to the nearest health facility in addition to maintaining
self-isolation at home5. Initially, thermal entry screening
of passengers from China was established at 21 airports
across the country with universal screening for all ights
from China, Hong Kong, Singapore, Thailand, Japan,
South Korea, Iran and Italy. Symptomatic passengers
were advised to volunteer for screening. Similar screening
was in place at international seaports6. Till February 29,
2020, three cases were reported from India7.
In the absence of a licensed vaccine or effective
therapeutics for COVID-19, in addition to the
non-pharmaceutical measures of hand hygiene and
cough etiquettes, quarantine becomes a critical
strategic containment and mitigation intervention
towards the early detection and isolation of cases to
break the chain of transmission and slow down the
spread of the outbreak. This analysis was done with
the following objectives: (i) is it feasible to prevent, or
delay, the local outbreaks in India through restrictions
on travel from countries with COVID-19 transmission;
and (ii) in the event that COVID-19 transmission
becomes established in India, the extent to which its
impact could be mitigated through quarantine.
Material & Methods
This analysis was based on a simple
Susceptible-Exposed-Infectious-Recovered (SEIR)
model to capture the natural history of COVID-19
and its transmission dynamics. The model structure
is summarised in Fig. 1, with the following governing
equations:
dS S
dt
= −
dE S rE
dt
= −
dI rE I I
dt
=−−
I kE
NN
= +
where the compartments are as follows: susceptible
(S); exposed and infectious but not yet symptomatic
(E); infected and symptomatic (I) and recovered
(R). Model parameters are as follows: among those
Fig. 1. Summary of the model structure used to represent coronavirus
disease 2019 transmission and control in Indian cities. The population
in each metropolitan area is divided into different compartments,
representing states of disease, with ows between compartments
given by the rates shown in the diagram. Thus, susceptible individuals
(S), upon acquiring infection, enter a state of asymptomatic infection
(E) and with some delay develop symptomatic disease (I). It is
assumed that a proportion p of symptomatic cases is subject to
quarantine [I(q)] and the remainder [I(n)] is not. The relative size of
these two populations (p) reects the coverage of quarantine efforts.
Individuals in I(q) are quarantined with an average quarantine delay
(1/δ). Finally, individuals may be cured (R) or die as per recovery
rate (γ) or mortality rate (µ), respectively. Those people who are
successfully quarantined (Q) do not contribute to onward infection.
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MANDAL et al: MATHEMATICAL MODELS FOR COVID-19 INTERVENTIONS IN INDIA 3
exposed, per-capita rate of developing symptoms (r);
among symptomatics, per-capita rates of recovery and
death (γ and µ, respectively) and the average number
of infections caused per day per symptomatic case (β)
and the infectiousness of exposed/asymptomatic cases,
relative to symptomatic (k).
With the evolving understanding of the natural
history of COVID-19 infection, it was assumed that
all infections would go through an asymptomatic
stage lasting three days on an average, followed by
a symptomatic stage, also lasting three days on an
average. Previous work has shown that the extent of
transmission that occurs before symptoms develop can
be an important factor in the feasibility of control8.
The estimates for the basic reproduction number (R0)
range between 1.5 and 4.98-16. In the current study, we
sought to capture a wide range of possible scenarios by
adopting two contrasting scenarios, as listed in Table I.
Containment: Port-of-entry screening model: First,
a deterministic epidemic was simulated in Wuhan,
China, governed by the equations above, to inform
projections for the daily introductions of COVID-19
that would arrive on Indian airports. This simulation
provided estimates for the prevalence of infection
in China, denoted by E(source) (t) and I(source) (t), for the
proportion of the population having asymptomatic and
symptomatic infection, respectively, at time t.
Then the following stochastic process was
simulated for transmission in India: (i) A transmission
process governed by the equations above, using a
simple Gillespie algorithm17 to translate these to
stochastic dynamics, assuming that infection events are
independent of one another; and (ii) Initial conditions
being zero prevalence and universal susceptibility, but
with a time series of ME (τ), MI (τ), introductions of
cases of E and I on day τ into the community, for all τ >
0 (these being arrivals from China who have not been
stopped at the airport).
To calculate the latter, it was assumed that each day,
there were a total of A arrivals from the source region
into Indian airports, ignoring seasonality or secular
temporal trends. Recalling that E(source) (t) and I(source) (t)
are proportions, then on any given day, the proportion
of airport arrivals that is infected and asymptomatic
is E(source) (t). If we assume that symptomatic cases
are m times less likely to travel than those without
symptoms, then the proportion of arrivals being infected
and symptomatic is I(source) (t)/m. Further, assuming
that as a result of airport screening, a proportion pE
of infected and asymptomatic cases is stopped at the
airport before entering the community, and likewise for
a proportion pI of infected and symptomatic cases.
Putting these factors together, the number of cases
of E being introduced into the community in India, per
day would be calculated as:
Introductions of E on day τ ~ Bin (A,q[τ])
where ‘Bin’ denotes a binomial distribution, and
( )
( )
( )
d
q E t dt
=∫
We modelled similarly for the number of
introductions of I on day τ, but with the adjustment m
described above.
For traveller demographics, we assume
conservatively that A=500, meaning that on an average,
500 passengers are arriving per day in Indian airports,
from areas in China where COVID-19 transmission is
established; the prevalence of asymptomatic infection
in international arrivals is the same as in their city of
origin and the prevalence of symptomatic infection
is half as much (m=½), assuming that symptomatics
are half as likely to travel. Airline transportation
data suggested that, on an average, there were
3565 passengers arriving from the entire China per
day, in Indian airports, during the period from October
2018 to March 201918. We expect this number to have
been reduced substantially following recent travel
restrictions, but the relevant data are not yet publicly
available. Thus, we expect our assumption to be an
underestimate.
Under the given scenarios for the proportion of
asymptomatic and symptomatic cases that would go
undetected by screening, we simulated the stochastic
epidemic that would occur in India as a result of the
daily introductions and estimated the average ‘time to
epidemic’ as the number of days to reach a prevalence
of 1000 cases. This threshold, although arbitrary,
Table I. Model parameters for optimistic and pessimistic
scenarios of coronavirus disease-19 transmission in India
Parameters Optimistic
scenario
Pessimistic
scenario
Basic reproduction number (R0)1.5 4
Infectiousness of asymptomatic
cases, relative to symptomatic
case (k)
0 0.5
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4 INDIAN J MED RES, 2020
represents a level at which it is clear that transmission
has been established in India.
Mitigation: Within-country model: In the event that
COVID-19 started spreading in India, we developed a
mathematical model to simulate the transmission dynamics
in the four most populated metropolitan areas (Delhi,
Mumbai, Kolkata and Bengaluru metropolitan areas) in
India, as well as their population connectivity. We chose
to focus on these population centres on the assumption
that the introduction of COVID-19 was most likely to
occur in international transportation hubs, and thus that
these cities were most likely to be the focal points of
initial COVID-19 transmission in the country.
As an intervention, we modelled a ‘quarantine
of symptomatics’ scenario wherein a proportion p of
symptomatic cases was quarantined within an average
of d days of developing symptoms. To incorporate this
intervention, we adapted the model equations above,
as follows:
i
ii
dS S
dt
−=
i
ii i
dE S rE
dt
= −
( )
( ) ( ) ( )
q
q qq
i
ii i i
dI rpE I I I
dt
=−− −
( )
( )
( ) ( )
1
n
nn
i
ii i
dI r pE I I
dt
=− −−
( )
q
i
i ii
dQ
I QQ
dt
= −−
( ) ( )
qn
i
ii i
dR
IIQ
dt
=++
i
I kE
NN
= +
( ) ( )
( )
/
qn
i ij j j j j
ij
c I I kE N= ++
∑
where the subscript i represents city i; I(q) is the number
with symptomatic infection who will self-quarantine after
an average delay of d days; I(n) is the number who are
symptomatic yet do not quarantine and the rate parameter
δ is the inverse of the average quarantine delay, d. The
infectiousness of exposed/asymptomatic cases, relative to
symptomatic cases, is termed as relative infectiousness (k).
Finally, cij is the connectivity between cities i
and j. We used domestic airline transportation data18
as a proxy for cij, while also conducting a sensitivity
analysis to address intercity travel through other
means, including rail and road. These coefcients (cij)
were estimated as a proxy for the frequency of daily
population movement between cities as a proportion
of the population of those cities. In sensitivity analysis,
we assumed ten times the rates shown in Table II, to
address the potential contributions from the lack of rail
and road travel data.
Using this deterministic model, as summarized in
Fig. 1, we simulated the introduction of COVID-19
and the resulting epidemic in one of the metropolitan
areas. We simulated the epidemic in various scenarios
for the proportion of symptomatics being quarantined;
the delay to quarantine and the natural history scenarios
are shown in Table I.
We present the hypothetical scenario for
COVID-19 transmission and interventional effects
in Delhi metropolitan area, as an illustration. We
estimated the time to hypothetical peak epidemic
in days. As an intervention, we modelled a scenario
where a given proportion of symptomatic cases
(50% at most) could self-quarantine, within a given
delay after developing symptoms (at least two days).
The indicators for the impact of intervention on the
hypothetical epidemic scenario were reduction in
cumulative incidence, peak prevalence mitigation
(proportional reduction in the highest number
of prevalent cases) and attack rate mitigation
(proportional reduction in cumulative incidence).
Results
Containment: Airport screening: Fig. 2 shows the
delays that could be achieved in the introduction of
infection within India, as a result of screening airport
arrivals. If symptomatic arrivals alone were screened
(blue curve), the model projections for the time to
epidemic ranged from 45 to 47.7 days. For illustration,
we also examined the impact of screening among
asymptomatic individuals (red curve). Results showed
Table II. Model coefcient for connectivity between cities
Cij Delhi Mumbai Kolkata Bengaluru
Delhi 1 0.00045 0.00029 0.00058
Mumbai 0.00048 1 0.00019 0.00052
Kolkata 0.00032 0.00018 1 0.00025
Bengaluru 0.00058 0.00052 0.00025 1
Cij, connectivity between cities i and j
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MANDAL et al: MATHEMATICAL MODELS FOR COVID-19 INTERVENTIONS IN INDIA 5
that identifying at least 75 per cent of the asymptomatic
individuals was needed, in order to delay the
within-country outbreak by an appreciable amount.
Additional detection of 90 per cent asymptomatic
individuals would delay the average time to epidemic
by 20 days (Table III). These levels of coverage
among asymptomatic cases are practically infeasible,
requiring almost all passengers from the identied
ights to be screened. However, this hypothetical
scenario offers a helpful approach for explaining
the lack of impact from addressing symptomatic
cases alone (Fig. 2, blue curve). Any containment
strategy focused on symptomatic infections, no matter
how comprehensively tends to be negated by the
asymptomatic infections that escape detection and can
go on to cause onward transmission in the community.
Mitigation: Within-country interventions: Fig. 3
illustrates the hypothetical epidemic dynamics that
would result in the four metropolitan areas, from an
outbreak beginning in Delhi metropolitan area, and
under an ‘optimistic’ scenario for transmission. The
Figure illustrates the seeding of transmission in other
cities that could arise, as a result of air transportation
between these populations. The Figure also illustrates
the impact of a hypothetical intervention, wherein 50
per cent of symptomatic cases are quarantined (whether
voluntarily or through screening and testing), within
an average of three days of developing symptoms.
Such measures could reduce the peak prevalence
substantially, thus minimizing the pressure on public
health services. As a consequence, the intervention
has the effect of ‘attening’ the epidemic curve,
distributing cases over a longer duration than in the
absence of intervention. The intervention could reduce
the cumulative incidence by 62 per cent. We next
illustrate how these impacts may vary, under different
transmission and intervention scenarios.
Impact of quarantine of symptomatics: In the
‘optimistic’ scenario, quarantining 50 per cent of
symptomatic cases within three days of developing
symptoms would reduce the cumulative incidence by
62 per cent and the peak prevalence by 89 per cent.
By contrast in a ‘pessimistic’ scenario, the projected
impact on the cumulative incidence falls to two per
cent and the peak prevalence by eight per cent. The
corresponding impact on peak prevalence is similarly
low, as shown in Fig. 4.
Fig. 5 shows that the duration of the outbreak would
be much lower in the scenario of ‘no intervention’
compared to ‘intervention’. As illustrated in Fig. 3, the
overall effect of symptomatic quarantine is to atten the
outbreak and increase the duration of the outbreak.
Table III. Alternate scenarios for the effect of airport entry screening of symptomatic and asymptomatic passengers on the delay in
average time to epidemic (days to reach a prevalence of 1000 cases) in India by R0 and relative infectiousness of asymptomatics
Parameters Delay in average time to epidemic (days)
R0Relative infectiousness,
asymptomatic versus
symptomatic
All symptomatic COVID-19
identied, but zero
diagnosis in asymptomatics
All symptomatic COVID-19
identied, with 50 per cent
diagnosis in asymptomatics
All symptomatic COVID-19
identied, with 90 per cent
diagnosis in asymptomatics
2 0.5 1.2 5.7 16
2 0.1 2.9 7.4 20
4 0.5 0.5 1.9 5.7
4 0.1 0.8 2.9 7.9
COVID-19, coronavirus disease 19
Fig. 2. Model projections for the time to epidemic in India
(the time to reach a prevalence of 1000 cases), under different
scenarios for the intensity of port-of-entry screening. The left half
of the gure illustrates the effect, on epidemic timing, of screening
symptomatic passengers alone; the right half illustrates the additional
effect of diagnosing coronavirus disease-19 amongst asymptomatic
passengers, assuming full screening of symptomatic passengers
(infeasible, but illustrative). Solid lines show central estimates,
whereas dashed lines span 95 per cent of simulated uncertainty
intervals.
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6 INDIAN J MED RES, 2020
Fig. 3. Model projections for the hypothetical epidemic dynamics (symptomatic prevalence over time) with and without intervention under
different scenarios for epidemiologic parameters considering an intervention, in which 50 per cent of the symptomatic cases are isolated
within three days of developing symptoms.
Fig. 4. Model projections for the per cent reduction in hypothetical peak prevalence and per cent reduction in hypothetical cumulative incidence
by initiation of quarantine of symptomatics within two, three and four days under the ‘optimistic’ (A) and ‘pessimistic’ (B) scenarios described
in the main text.
B
A
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MANDAL et al: MATHEMATICAL MODELS FOR COVID-19 INTERVENTIONS IN INDIA 7
Discussion
The focus of our analysis was not towards
predicting the burden of COVID-19 cases but to
identify rational intervention strategies that might
work towards control of the outbreak in India. We
modelled the potential impact of containment strategy
of point-of-entry screening and a mitigation response
through symptomatic screening on hypothetical
COVID-19 transmission scenario in India. Our results
suggest that in order to have an appreciable effect
on delaying the establishment of transmission of
COVID-19 in India, airport arrival screening will need
to have near-complete capture of incoming COVID-19
cases, including asymptomatic cases. Although not
practically feasible using the currently available tools,
our results provide a hypothetical illustration of the
additional benet of identifying asymptomatic cases:
if they escape any containment effort, they would
tend to negate the effects of that effort, by the onward
transmission that they can cause. Presently, there is
no accurate, rapid test for COVID-19 that could be
deployed in this setting, to reach the required levels
of detection among asymptomatic cases; the only way
to reach 90 per cent diagnosis among asymptomatic
arrivals may be through isolation and quarantine of all
arrivals from specied origin airports. Resources may
be better spent on the mitigation of infection in the
community.
Recent studies indicate that airport screening may
not be able to sufciently detect COVID-19-infected
travellers. Quilty et al19 estimated that 46 per cent
(95% condence interval: 36 to 58) of infected
travellers would not be detected by thermal screening at
airport exit and entry, depending on incubation period,
sensitivity of exit and entry screening and proportion
of asymptomatic cases. Gostic et al20 estimated that
travel screening would miss more than half of the
infected travellers on account of being asymptomatic
and being unaware of exposure, emphasizing the
need for post-travel symptom tracking among them.
Our study adds to this by considering the population
implications of such leakages in arrival screening.
Our analysis shows that, even if symptomatic cases
are comprehensively identied and quarantined, the
delay in epidemic timing within India would be in
days and not weeks. According to the data shared by
the Delhi Health Department21, till February 13, 2020,
17 of 5700 (0.3%) passengers, who had arrived from
China and other COVID-19-affected countries prior
to the beginning of airport screening from January 15,
2020, were found symptomatic and hospitalized, while
the rest were advised for home isolation. The status
of another 885 passengers remains unknown21. Entry
screening or travel restrictions may be benecial in
reducing the risk of outbreak in countries with relatively
low connectivity to China, and our study illustrates the
critical importance of community-based measures to
detect potential cases and prevent transmission.
We also examined the potential impact of quarantine
of symptomatics, in controlling transmission within
India, with a focus on four major metropolitan areas.
Our results suggest that it may be possible to interrupt
the transmission of COVID-19 in India, but only in the
most optimistic scenarios (for R0 and for coverage).
Even with high R0 and suboptimal coverage,
symptomatic quarantine can still achieve meaningful
reductions in peak prevalence, resulting in ‘spreading
out’ of the outbreak. This would make it easier to cope
Fig. 5. Projected duration of epidemic (days) for the scenarios with and without symptomatic quarantine at 50 per cent coverage in three days
by R0 and relative infectiousness of asymptomatic cases. Here, the ‘epidemic duration’ is measured as the duration (in days) over which the
prevalence of symptomatic infection is >1 case.
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8 INDIAN J MED RES, 2020
with the peak demand on health services. However,
such measures would have very little effect on the
overall epidemic size. The actual numerical impact will
be highly sensitive to the natural history of COVID-19,
the parameters for which are very uncertain at present.
The WHO Scientic and Technical Advisory Group
for Infectious Hazards has recommended continuation
of the containment strategy and monitoring for
the community transmission of COVID-1922. It
recommends close monitoring of the effectiveness and
social acceptance of public health strategies to control
COVID-19 transmission in the light of its evolving
epidemiological understanding, including engagement
of vulnerable populations, and intensied active
surveillance22.
Continuous follow up of passengers returning
from COVID-19-affected countries and their contact
tracing for the emergence of suggestive symptoms
would put a high strain on the healthcare system, more
so in the eventuality of the introduction of community
transmission. The increasing numbers would make it
impractical to use laboratory testing to conrm each
case, and therefore, use of symptomatic surveillance
should become the primary public health strategy to
detect and respond in the most effective and timely
manner. We could draw examples from the syndromic
surveillance approach for inuenza-like illness in the
context of H1N123. In practice, this could be achieved
either through public advisories for sick individuals
to self-quarantine, along with active engagement with
the community, or through intensive surveillance
for symptoms, followed by testing and quarantine.
A combination of both approaches is likely to be
needed, although promoting self-quarantine is likely
to be more sustainable in the event that transmission
becomes widespread. Engagement of local volunteers
and community-based organizations can provide the
much-needed boost to the efforts of the public health
system. Considering the widespread use of mobile
phones in the country, mobile applications can be
used to self-monitoring and sharing of symptom
information on a real-time basis. The same was done
for monitoring the passengers on the cruise ship off the
Japanese coast24.
With the evolving understanding of COVID-19
epidemiology, especially the proportion of
asymptomatic infected cases, it is difcult to predict
the number of beds required or ventilators necessary
for COVID-19 cases at this stage. As per reports from
other affected countries, we may expect eight to ten
severe and 40-50 non-severe COVID-19 cases for every
death25,26. In a closed setting of similar nature as that
on the cruise ship ‘Diamond Princess,’ we may expect
26 per cent of the entire population to get infected and
one in 450 infected individuals to die27. We deduce
that around ve per cent of the infected patients will
require intensive care and half of those admitted in the
intensive care unit will require mechanical ventilation.
Over time, once the model is validated, appropriate
numbers can be generated for healthcare planning.
It is pertinent that frontline healthcare workers
are identied and trained before the outbreak sets
in. Health and life insurance should be announced
for healthcare workers if they contract COVID-19.
Considering the reports of a high number of infected
healthcare workers, measures should be taken to
build biosecurity wards and prepare for the outbreak
in earnest. Resources should be earmarked; adequate
supplies should be procured before the outbreak gains
momentum. Healthcare workers should be trained in
the use of personal protective equipment, screening
of asymptomatic contacts, isolation measures and
management of COVID-19 cases. Public health
measures should be initiated at multiple levels,
including but not limited to public messaging, and
community health worker-based education.
Limitations of the model: As with any modelling
study, our analysis has some limitations to note. The
mean duration of asymptomatic and symptomatic
stages is very much uncertain. Some infections may
be subclinical and never develop symptoms. In the
port-of-entry screening model, we adopted simple
assumptions on the number of daily arrivals from
non-coronavirus-affected areas due to lack of data.
However, considering that we have only used data
for airport arrivals and in particular from China, these
assumptions are likely to be underestimates in the current
situation where people are travelling from many other
countries that are now reporting COVID-19 cases, and
are thus conservative with respect to our conclusions;
higher numbers of daily arrivals would tend to narrow
the gap in epidemic timing, between baseline and
interventional scenarios. Other important uncertainties
include natural history parameters, for example, the
average duration of infection; the incubation period
and the case fatality rate. Though we have tried to
address some of these uncertainties through examining
different scenarios for transmission, yet we caution that
our model ndings may also be sensitive to these other
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MANDAL et al: MATHEMATICAL MODELS FOR COVID-19 INTERVENTIONS IN INDIA 9
parameters. As more data become available about this
new virus, subsequent modelling work can be rened
accordingly.
For the country-level model, for simplicity, we
created hypothetical scenarios only in four metropolitan
areas that have the highest population density. These
areas cover only about seven per cent of the total
population of India. We ignored the rural population
surrounded by these areas and their connectivity.
Future work to address this gap will benet from more
systematic information on the rates of population ow
between these different settings, data that were not
available for our current study. We have simplied
our meta-population model by considering constant
connectivity between different cities, ignoring
age-dependent mobility among the population. How
seasonality will change the endemicity of COVID-19
is still unknown and hence not considered in the
model. Although there appear to be differences in the
immune responses of children compared to adults, for
simplicity, this model has not accounted the disease
prevalence with age structure.
Comparison of our projected gures with data
from countries such as Japan, the Republic of Korea
and Iran can help to validate our model, assuming
similar transmission dynamics in India. It may be
noted that our analysis is based on the available global
epidemiological parameters from the initial phase of
the outbreak. However, we believe that the predicted
direction of the model-based impact of the proposed
interventions would remain unaffected, although the
onset, magnitude and timing of the simulated epidemic
may change, even with the use of updated parameter
values from the evolving global situation of COVID-19
epidemic. Validation of mathematical models using
real-time data is important to gauge the accuracy of
predicted transmission dynamics of infectious diseases.
While some models for Ebola virus disease27 provided
fairly reasonable estimates, recent COVID-19 models28
were inconsistent in their prediction.
Public health implications: At present, it is not clear to
what extent the COVID-19 epidemic would establish
itself in India. As the introduction of cases may take
anywhere from a minimum of 20 days to a few months to
be visible, we need to enhance surveillance and prepare
the community in a proportionate way that is neither
alarmist nor complacent. The critical concerns are the
efciency and timeliness of quarantine and isolation
and the challenges of detection of COVID-19 with
symptoms similar to many other lower respiratory tract
infections. There is a need to engage community-based
organizations that can take up the work of symptomatic
surveillance, as well as raising awareness of the need
for self-quarantine where possible, and referral to
hospital where necessary, till infection is conrmed.
Till that time, assurance of food and supplies should be
given following examples of such practices in Kerala29.
It is pertinent to engage with the media on a proactive
basis with the provision of facts promptly such that
reporting of these events does not create a picture of the
overwhelming burden of COVID-19 in the country and
lead to undue anxiety among the population that may
negatively inuence self-quarantine. Health authorities
need to be on alert and be prepared to closely monitor
the situation with the establishment of an intensied
surveillance. We advocate for a rational, exible and
resilient approach that is sensitive to the outbreak
stage as the health system prepares for the control of
COVID-19 transmission in India.
Financial support & sponsorship: None.
Conicts of Interest: None.
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For correspondence: Dr Tarun Bhatnagar, ICMR-National Institute of Epidemiology, Ayapakkam, Chennai 600 077, Tamil Nadu, India
e-mail: tarunbhatnagar@nie.gov.in
[Downloaded free from http://www.ijmr.org.in on Monday, March 23, 2020, IP: 59.94.234.25]
