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Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (COVID-19)

Abstract

Background Estimation of the fraction and contagiousness of undocumented novel coronavirus (COVID-19) infections is critical for understanding the overall prevalence and pandemic potential of this disease. Many mild infections are typically not reported and, depending on their contagiousness, may support stealth transmission and the spread of documented infection. Methods Here we use observations of reported infection and spread within China in conjunction with mobility data, a networked dynamic metapopulation model and Bayesian inference, to infer critical epidemiological characteristics associated with the emerging coronavirus, including the fraction of undocumented infections and their contagiousness. Results We estimate 86% of all infections were undocumented (95% CI: [82%-90%]) prior to the Wuhan travel shutdown (January 23, 2020). Per person, these undocumented infections were 52% as contagious as documented infections ([44%-69%]) and were the source of infection for two-thirds of documented cases. Our estimate of the reproductive number (2.23; [1.77-3.00]) aligns with earlier findings; however, after travel restrictions and control measures were imposed this number falls considerably. Conclusions A majority of COVID-19 infections were undocumented prior to implementation of control measures on January 23, and these undocumented infections substantially contributed to virus transmission. These findings explain the rapid geographic spread of COVID-19 and indicate containment of this virus will be particularly challenging. Our findings also indicate that heightened awareness of the outbreak, increased use of personal protective measures, and travel restriction have been associated with reductions of the overall force of infection; however, it is unclear whether this reduction will be sufficient to stem the virus spread.
Substantial undocumented infection facilitates the rapid dissemination of
novel coronavirus (COVID-19)
Authors: Ruiyun Li†,1, Sen Pei†,*,2, Bin Chen†,3, Yimeng Song4, Tao Zhang5, Wan
Yang6, Jeffrey Shaman*,2
Affiliations:
1MRC Centre for Global Infectious Disease Analysis, Department of Infectious
Disease Epidemiology, School of Public Health, Faculty of Medicine, Imperial
College London, London, W2 1PG, United Kingdom
2Department of Environmental Health Sciences, Mailman School of Public Health,
Columbia University, New York, NY 10032, USA
3Department of Land, Air and Water Resources, University of California, Davis, CA
95616, USA
4Department of Urban Planning and Design, The University of Hong Kong, Hong
Kong
5Ministry of Education Key Laboratory for Earth System Modeling, Department of
Earth System Science, Tsinghua University, Beijing, 10084, P. R. China
6Department of Epidemiology, Mailman School of Public Health, Columbia
University, New York, NY 10032, USA
*Correspondence to: S.P. (sp3449@cumc.columbia.edu) J.S.
(jls106@cumc.columbia.edu)
R.L., S.P. and B.C. contributed equally to this work.
Abstract
Background
Estimation of the fraction and contagiousness of undocumented novel coronavirus
(COVID-19) infections is critical for understanding the overall prevalence and
pandemic potential of this disease. Many mild infections are typically not reported
and, depending on their contagiousness, may support stealth transmission and the
spread of documented infection.
Methods
Here we use observations of reported infection and spread within China in
conjunction with mobility data, a networked dynamic metapopulation model and
Bayesian inference, to infer critical epidemiological characteristics associated with
the emerging coronavirus, including the fraction of undocumented infections and
their contagiousness.
Results
We estimate 86% of all infections were undocumented (95% CI: [82%-90%]) prior to
the Wuhan travel shutdown (January 23, 2020). Per person, these undocumented
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infections were 52% as contagious as documented infections ([44%-69%]) and were
the source of infection for two-thirds of documented cases. Our estimate of the
reproductive number (2.23; [1.77-3.00]) aligns with earlier findings; however, after
travel restrictions and control measures were imposed this number falls
considerably.
Conclusions
A majority of COVID-19 infections were undocumented prior to implementation of
control measures on January 23, and these undocumented infections substantially
contributed to virus transmission. These findings explain the rapid geographic spread
of COVID-19 and indicate containment of this virus will be particularly challenging.
Our findings also indicate that heightened awareness of the outbreak, increased use
of personal protective measures, and travel restriction have been associated with
reductions of the overall force of infection; however, it is unclear whether this
reduction will be sufficient to stem the virus spread.
. CC-BY 4.0 International licenseIt is made available under a
is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
(which was not peer-reviewed) The copyright holder for this preprint .https://doi.org/10.1101/2020.02.14.20023127doi: medRxiv preprint
The novel coronavirus that emerged in Wuhan, China (COVID-19) at the end of 2019
quickly spread to all Chinese provinces and, as of February 6, 2020, to 24 other
countries1,2. Efforts to contain the virus are ongoing; however, given the many
uncertainties regarding pathogen transmissibility and virulence, the effectiveness of
these efforts is unknown.
The fraction of undocumented but infectious cases is a critical epidemiological
characteristic that modulates the pandemic potential of an emergent respiratory
virus3−6. These undocumented infections often experience mild, limited or no
symptoms and hence go unrecognised, and, depending on their contagiousness and
numbers, can expose a far greater portion of the population to virus than would
otherwise occur. Here, to assess the full potential of COVID-19, we use a model-
inference framework to estimate the contagiousness and proportion of
undocumented infections in China during the weeks before and after the shutdown of
travel in and out of Wuhan.
Methods
Metapopulation Model
We developed a mathematical model that simulates the spatio-temporal dynamics of
infections among 375 Chinese cities. The model incorporates information on human
movement within the following metapopulation structure:
!"#
!$ % & '"#(#
)
*#
&+'"#(#
,
*#
- .
/
0#1"1
*12(1
)
3& .
/
01#"#
*#2(#
)
3
[1]
!4#
!$ %'"#(#
)
*#
-+'"#(#
,
*#
&4#
5- .
/
0#141
*12(1
)
3& .
/
01#4#
*#2(#
)
3
[2]
!(#
)
!$ % 6 4#
5&(#
)
7
[3]
!(#
,
!$ % 89 & 6: 4#
5&(#
,
7- .
/
0#1(1
,
*12(1
)
3& .
/
01#(#
,
*#2(#
,
3
[4]
;<% ;<- .
/
=<33& .
/
=
3<3
[5]
where
><
,
?<
,
@<
A
,
@<
B
and
;<
are the susceptible, exposed, documented infected,
undocumented infected and total population in city i. Note that we define patients
with symptoms severe enough to be confirmed as documented infected individuals;
whereas other infected persons are defined as undocumented infected individuals.
We specified a rate parameter, β, for the transmission rate due to documented
infected individuals. The transmission rate due to undocumented individuals is
reduced by a factor
C
. In addition,
6
is the fraction of documented infections, Z is the
average latency period and D is the average duration of infection. The effective
reproduction number (
D4
) is calculated as
D4% 6EF -
8
9 & 6
:
CEF
(see
Supplementary Appendix for details). Spatial coupling within the model is
represented by the daily number of people traveling from city j to city i (
=<3
) and a
multiplicative factor,
.
, which is greater than 1 to reflect underreporting of human
movements (see below). We assume that individuals in the
@<
A
group do not move
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between cities. A similar metapopulation model has been used to forecast the spatial
transmission of influenza in the United States7.
Travel Data
Daily numbers of travelers between 375 Chinese cities during the Spring Festival
period (“Chunyun”) were derived from human mobility data collected by the Tencent
Location-based Service (LBS) during the 2018 Chunyun period (February 1 – March
12, 2018) 8. Chunyun is a period of 40 days – 15 days before and 25 days after the
Lunar New Year – during which there are high rates of travel within China. To
estimate human mobility during the 2020 Chunyun period, which began January 10,
we aligned the 2018 Tencent data based on relative timing to the Spring Festival.
For example, we used mobility data from February 1, 2018 to represent human
movement on January 10, 2020, as these days were similarly distant from the Lunar
New Year. During the 2018 Chunyun, a total of 1.73 billion travel events were
captured in the Tencent data; whereas 2.97 billions trips are reported8. To reconcile
these two numbers, we include the parameter
.
in the model system.
Inference and Model Initialization
To infer COVID-19 transmission dynamics during the early stage of the outbreak, we
simulated observations from January 10-23, 2020 (i.e. the period before the initiation
of travel restrictions) using an iterated filter-ensemble adjustment Kalman filter (IF-
EAKF) framework9-11. With this combined model-inference system, we estimated the
trajectories of the four model state variables (
><
,
?<
,
@<
A
,
@<
B
) for all 375 cities, while
simultaneously inferring the six model parameters (Z, D,
C
,
EG 6G .
). The initial prior
ranges of the model parameters were drawn from uniform distributions of the
following ranges:
HIJKLM N O N PIJKLM
,
HIJKLM N F N PIJKLM
,
QRH N C N 9
,
QRS N E N
9RP
,
QRQH N 6 N QRT
,
9 N . N 9RUP
.
For the outbreak origin, Wuhan city, the initial exposed population,
?VBWXY
, and initial
undocumented infected population,
@VBWXY
B
, were drawn from a uniform distribution
ZQG >[[J\X]^
. The documented infected population in Wuhan
@VBWXY
A
on January 10
was set to zero. Although infections were reported prior to January 10, these cases
were sporadic and the EAKF adjustment can account for the effects of these early
infections (by selecting elevated exposed and unreported infection levels). For other
cities, we defined
_<
as the number of travelers from Wuhan to city
`
on the first day
of Chunyun. The initial exposed, documented infected and undocumented infected
populations were set to
?<% _<?VBWXYa;VBWXY
,
@<
A% Q
and
@<
B% _<@VBWXY
Ba;VBWXY
.
To account for delays in infection confirmation, we also defined an observation
model using a Poisson process. Specifically, for each new case in group
@<
A
, a
reporting delay
b!
(in days) was generated from a Poisson distribution with a mean
value of
c!
. In fitting both synthetic and the observed outbreaks, we performed
simulations with the model-inference system using different fixed values of
c!
(
dIJKLM N c!N9HIJKLM
) and
>[[J\X]
(
PQQ N>[[J\X] NSQQQ:
. The best fitting
model-inference posterior was identified by log-likelihood. Full details of the data and
methods, including synthetic testing and sensitivity analyses, are provided in the
Supplementary Appendix.
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Modelling epidemic dynamics after January 23
Finally, we also modelled the transmission of COVID-19 in China after January 23,
when greater control measures were effected. These control measures included
travel restrictions imposed between major cities and Wuhan; self-quarantine and
contact precautions advocated by the government; and more available rapid testing
for infection confirmation12-13. These measures along with changes in medical care-
seeking behaviour due to increased awareness of the virus and increased personal
protective behavior (e.g. wearing of facemasks, social distancing, self-isolation when
sick), likely altered the epidemiological characteristics of the outbreak after January
23. To quantify these differences, we re-estimated the system parameters using the
metapopulation model-inference framework and city-level daily cases reported
between January 24 and February 8. As inter-city mobility was restricted, we set
. %
Q
. In addition, to represent reduced person-to-person contact and increased infection
detection, we updated the initial priors for
E
and
6
to
ZQRHG 9RQ^
and
ZQRHG 9RQ^
,
respectively (see Supplementary Appendix for more details).
Results
Epidemiological Characteristics before January 23, 2020
We first tested the model-inference framework using synthetic outbreaks generated
by the model in free simulation. These simulations verified the ability of the model-
inference framework to simultaneously estimate the six target model parameters
(see Supplementary Appendix, Figures S1-S8).
We next applied the system to the observed outbreak before the travel restrictions of
January 23 – a total of 811 documented cases throughout China. Figure 1 shows
simulations of reported cases generated using the best-fitting model parameter
estimates. The distribution of these stochastic simulations captures the range of
observed cases well. In addition, the best-fitting model captures the spread of
COVID-19 to other cities in China (Figure S9). Our median estimate of the overall
D4
is 2.23 (95% CI: 1.773.00), indicating a high capacity for sustained transmission of
COVID-19 (Table 1). This finding aligns with other recent estimates of the
reproductive number for this time period6,12-14. In addition, the median estimates for
the latent and infectious periods are approximately 3.77 and 3.45 days, respectively.
Further, we find that, during January 10-23, only 14% (95% CI: 9–26%) of total
infections in China were reported. This estimate reveals a very high rate of
undocumented infections: 86%. This finding is independently corroborated by the
infection rate among foreign nationals evacuated from Wuhan (see Supplementary
Appendix). These undocumented infections are estimated to have been half as
contagious per individual as reported infections (µ = 0.52; 95% CI: 0.44 – 0.69).
Other model fittings made using alternate values of
c!
and
>[[J\X]
produced similar
parameter estimates (Figure S10).
The Impact of Undocumented Infections during January 10-23
Using the best-fitting model (Table 1, Figure 1), we estimated 18,829 (95% CI
[3,761, 38,808]) total new COVID-19 infections (documented and undocumented
combined) during January 10-23 in Wuhan city. 86.3% of all infections (95% CI
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[81.9%, 90.1%]) were infected from undocumented cases. Nationwide, the total
number of infections during January 10-23 was 28,898 (95% CI [5,534, 59,491]) with
86.4% (95% CI [82.0%, 90.1%]) infected from undocumented cases.
To highlight further this impact of contagious, undocumented COVID-19 infections on
overall transmission and reported case counts, we generated a set of hypothetical
outbreaks using the best-fitting parameter estimates but with
C % Q
, i.e. the
undocumented infections are no longer contagious (Figure 2). We find that without
transmission from undocumented cases, reported infections during January 10-23
are reduced 66.4% across all of China and 64.0% in Wuhan. Further, there are fewer
cities with more than 8 cumulative documented cases: only 1 city with more than 8
documented cases versus the 10 observed by January 23 (Figure 2). This finding
indicates that contagious, undocumented infections facilitated the geographic spread
of COVID-19 within China.
Epidemiological Characteristics after January 23, 2020
The results of inference for the January 24-February 8 period are presented in Table
2, Figure S11 and Table S1. Control measures are continually shifting, so we show
estimates for both January 24 – February 3 (Period 1) and January 24 – February 8
(Period 2). The best-fitting model for both periods has a reduced reporting
delay,
Ic!
, of 5 days (vs. 10 days before January 23), consistent with more rapid
confirmation of infections. Estimates of both the latency and infectious periods are
relatively unchanged; however,
6G E
and
D4
have all shifted considerably. The
contact rate,
E
, drops to 0.51 (95% CI: 0.39 – 0.69) during Period 1 and 0.34 (95%
CI: 0.270.48) during Period 2, less than half the estimate prior to travel
restrictions. The reporting rate,
6
, is estimated to be 0.71 (95% CI: 0.55 – 0.85), i.e.
71% of infections are documented during Period 1, up from 0.14 prior to travel
restrictions, and is nearly the same in Period 2. The reproductive number is 1.51
(95% CI: 1.17 – 2.10) during Period 1 and 1.00 (95% CI: 0.731.38) during Period
2, down from 2.23 prior to travel restrictions. While the estimate for the relative
transmission rate,
C
, is similar to before January 23, the contagiousness of
undocumented infections, represented by
CE
, is substantially reduced, possibly
reflecting that only very mild and asymptomatic infections remain undocumented.
Discussion
Our findings indicate that a large proportion of COVID-19 infections were
undocumented prior to the implementation of travel restrictions and other heightened
control measures in China on January 23, and that a large proportion of the total
force of infection was mediated through these undocumented infections (Table 1).
This high proportion of undocumented infections, many of whom were likely not
severely symptomatic, appears to have supported the rapid spread of the virus
throughout China. Indeed, suppression of the infectiousness of these undocumented
cases in model simulations reduces the total number of documented cases and the
overall spread of COVID-19 (Figure 2).
Our findings also indicate that a radical increase in the identification and isolation of
currently undocumented infections would be needed to fully control COVID-19.
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Increased news coverage and awareness of the virus in the general population have
already likely prompted increased rates of seeking medical care for respiratory
symptoms. In addition, awareness among healthcare providers, public health officials
and the availability of viral identification assays suggest that capacity for identifying
previously missed infections has increased. Further, general population and
government response efforts have increased the use of face masks, restricted travel,
delayed school reopening and isolated suspected persons, all of which could
additionally slow the spread of COVID-19.
Combined, these measures are expected to increase reporting rates, reduce the
proportion of undocumented infections, and decrease the growth and spread of
infection. Indeed, estimation of the epidemiological characteristics of the outbreak
after January 23, indicate that government control efforts and population awareness
have reduced the rate of spread of the virus (i.e. lower
EG CEG D4
) and increased the
reporting rate. The overall reduction of the effective reproductive number is
encouraging; however, the control efforts have yet to critically and clearly reduce
D4
below 1.
Importantly, the situation on the ground in China is changing day-to-day. New travel
restrictions and control measures are being imposed on new populations in different
cities, and these rapidly varying effects make certain estimation of the
epidemiological characteristics for the outbreak difficult. Further, reporting
inaccuracies and changing care-seeking behavior add another level of uncertainty to
our estimations. While the data and findings presented here indicate that travel
restrictions and control measures have reduced COVID-19 transmission
considerably, whether these controls are sufficient for reducing
D4
below 1 for the
length of time needed to eliminate the disease locally and prevent a rebound
outbreak once control measures are relaxed is unclear. Further, similar control
measures and travel restrictions would have to be implemented outside China to
prevent re-introduction of the virus.
Our findings underscore the seriousness and pandemic potential of COVID-19. The
2009 H1N1 pandemic influenza virus also caused many mild cases, quickly spread
globally, and eventually became endemic. Presently, there are four, endemic,
coronavirus strains currently circulating in human populations (229E, HKU1, NL63,
OC43). If the novel coronavirus follows the pattern of 2009 H1N1 pandemic
influenza, it will also spread globally and become a fifth endemic coronavirus within
the human population.
Many characteristics of the COVID-19 remain unknown or uncertain. Consequently,
care should be taken when interpreting our estimates. For instance, after January
23, we assume a complete travel shutdown with no inter-city human mobility;
however, the degree and initial date of travel restrictions has varied among cities.
Our estimates may therefore represent an upper-bound of the potential impact of
travel restriction on COVID-19 transmission. Further studies accounting for
heterogenous travel interventions are warranted.
Funding
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is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
(which was not peer-reviewed) The copyright holder for this preprint .https://doi.org/10.1101/2020.02.14.20023127doi: medRxiv preprint
This work was supported by US NIH grants GM110748 and AI145883. The content
is solely the responsibility of the authors and does not necessarily represent the
official views of the National Institute of General Medical Sciences, the National
Institute for Allergy and Infectious Diseases, or the National Institutes of Health.
Disclosures
JS and Columbia University disclose partial ownership of SK Analytics. JS also
reports receiving consulting fees from Merck.
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(which was not peer-reviewed) The copyright holder for this preprint .https://doi.org/10.1101/2020.02.14.20023127doi: medRxiv preprint
Tables
Table 1. Best-fit model posterior estimates of key epidemiological parameters for
simulation with the full metapopulation model during January 10-23, 2020 (
>[[J\X] %
PQQQ
,
c!%9Q
days).
Parameter
Median (95% CIs)
Transmission rate (β)
1.10 (0.97, 1.21)
Relative transmission rate (µ)
0.52 (0.44, 0.69)
Latency period (Z)
3.77 (3.31, 4.13)
Infectious period (D)
3.45 (2.91, 3.84)
Reporting rate (α)
0.14 (0.09, 0.26)
Basic reproductive number (RE)
2.23 (1.77, 3.00)
Mobility factor (θ)
1.34 (1.24, 1.44)
Table 2. Best-fit model posterior estimates of key epidemiological parameters for
simulation of the model without travel between cities during January 24 – February 3
and January 24 – February 8 (
>[[J\X] %PQQQ
on January 10,
c!%9QI
days before
January 24,
c!% PI
days between January 24 and February 8).
Parameter
January 24 – February 3
(Median (95% CIs)
January 24 - February 8
(Median (95% CIs)
Transmission rate (β)
0.51 (0.39, 0.69)
0.34 (0.27, 0.48)
Relative transmission rate (µ)
0.49 (0.38, 0.60)
0.43 (0.29, 0.67)
Latency period (Z)
3.49 (3.35, 3.68)
3.50 (3.23, 3.77)
Infectious period (D)
3.50 (3.28, 3.64)
3.51 (3.19, 3.82)
Reporting rate (α)
0.71 (0.56, 0.81)
0.71 (0.56, 0.85)
Effective reproductive number
(RE)
1.51 (1.17, 2.10)
1.00 (0.73, 1.38)
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Figures
Fig. 1. Best-fit model-inference fitting (
>[[J\X] %PQQQ
,
c!%9Q
days) to daily reported
cases in all cities (A), Wuhan city (B) and Hubei province (C). The blue box and whiskers
show the median, interquartial range, and 95% credible intervals are derived from 300
simulations using the best-fit parameters. The red ‘x’s are daily reported cases. The
distribution of estimated
D4
is shown in (D).
Fig. 2. Impact of undocumented infections on the transmission of COVID-19.
Synthetic outbreaks generated using parameters reported in Table 1 are compared
for
C % QRPH
(red) and
C % Q
(blue).
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... Although, due to the significant differences in approach, it is difficult to directly compare our projective model to other contemporary methods, some indirect comparisons may be offered. The susceptible-infectious-recovered (SIR) framework is the basis for many COVID-19 epidemic models [11,22,28,35]. Several websites provide implementations of the SIR framework and present scenarios with different interventions such as social distancing affecting the transmission parameter [11,28], thus allowing for different hypothetical scenarios to be explored. ...
... Unfortunately, they are less suited for forecasts as model parameters are not calibrated based upon case or outcome data. A recent attempt at taking a meta-population approach with SEIR dynamics in each patch, to estimate model parameters (including proportion of asymptomatic infection) based upon case counts from China was given in [22]. This resulted in a spatially explicit model without age-structure. ...
... Another alternative is an agentbased model such as that used in [13]. Similar to [22], [13] forecast a very large number of infections with COVID-19. ...
Preprint
As the Coronavirus 2019 (COVID-19) disease started to spread rapidly in the state of Ohio, the Ecology, Epidemiology and Population Health (EEPH) program within the Infectious Diseases Institute (IDI) at the Ohio State University (OSU) took the initiative to offer epidemic modeling and decision analytics support to the Ohio Department of Health (ODH). This paper describes the methodology used by the OSU/IDI response modeling team to predict statewide cases of new infections as well as potential hospital burden in the state. The methodology has two components: 1) A Dynamic Survival Analysis (DSA)-based statistical method to perform parameter inference, statewide prediction and uncertainty quantification. 2) A geographic component that down-projects statewide predicted counts to potential hospital burden across the state. We demonstrate the overall methodology with publicly available data. A Python implementation of the methodology has been made available publicly. Highlights We present a novel statistical approach called Dynamic Survival Analysis (DSA) to model an epidemic curve with incomplete data. The DSA approach is advantageous over standard statistical methods primarily because it does not require prior knowledge of the size of the susceptible population, the overall prevalence of the disease, and also the shape of the epidemic curve. The principal motivation behind the study was to obtain predictions of case counts of COVID-19 and the resulting hospital burden in the state of Ohio during the early phase of the pandemic. The proposed methodology was applied to the COVID-19 incidence data in the state of Ohio to support the Ohio Department of Health (ODH) and the Ohio Hospital Association (OHA) with predictions of hospital burden in each of the Hospital Catchment Areas (HCAs) of the state.
... Speculation that undocumented infection led to the rapid spread of COVID-19 appeared accurate, and the term 'stealth transmission' was coined. 75,76 On March 10, 2020, President Trump announced that in an attempt to stop the spread of COVID-19 to the US, the US would be closed for 30 days to all flights from Europe, with the exception of flights from the UK. 77 On March 11, 2020, he told the American public, "The virus will not have a chance against us. ...
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In response to COVID-19, many industrialized nations have utilized intentional, consistent strategies with demonstrated efficacy for containment of the pandemic. However, United States COVID-19 policies have been inconsistent with virology and epidemiology data. As the politics surrounding the pandemic have become increasingly contentious, they have all but neutralized efforts to contain it. The lack of media attention to the high rate of long COVID (now estimated at 20%) and the growing list of long-term health consequences (with an increasing list of neurological complications) is also a significant factor contributing to the public's misunderstanding of the disease, and poor compliance with safety protocols. Consequently, COVID-19 remains relatively uncontained in the US, which now has the dubious distinction of the highest number of COVID fatalities in world. Recommendations are made for the intentional use in the US of consistent strategies with demonstrated efficacy for pandemic containment.
... There has been a sudden increase in the patients affected by COVID-19 [6], which has increased the load over healthcare systems across world. But the quantities available for hospital beds and personal protective equipment (PPE) [7] and ventilators are limited in number. ...
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Controlling the spreading of infectious diseases has been shown crucial in the COVID-19 pandemic. Traditional contact tracing is used to detect newly infected individuals by tracing their previous contacts, and by selectively checking and isolating any individuals likely to have been infected. Digital contact tracing with the utilisation of smartphones was contrived as a technological aid to improve this manual, slow and tedious process. Nevertheless, despite the high hopes raised when smartphone-based contact tracing apps were introduced as a measure to reduce the spread of the COVID-19, their efficiency has been moderately low. In this paper, we propose a methodology for evaluating digital contact tracing apps, based on an epidemic model, which will be used not only to evaluate the deployed Apps against the COVID-19 but also to determine how they can be improved for future pandemics. Firstly, the model confirms the moderate effectiveness of the deployed digital contact tracing, confirming the fact that it could not be used as the unique measure to fight against the COVID-19, and had to be combined with additional measures. Secondly, several improvements are proposed (and evaluated) to increase the efficiency of digital control tracing to become a more useful tool in the future.
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Chapter
In this paper, we develop a compartmental model of the COVID-19 epidemic in Burkina Faso by taking into account the compartments of hospitalized, severely hospitalized patients and dead persons. The model exhibits the traditional threshold behavior. We prove that when the basic reproduction number is less than one, the disease-free equilibrium is locally asymptotically stable. We use real data from Burkina Faso National Health Commission against COVID-19 to predict the dynamic of the disease and also the cumulative number of reported cases. We use public policies in our model in order to reduce the contact rate, and thereby to show how the reduction of daily reported infectious cases evolves with a view to assisting decision makers for a rapid treatment of the reported cases.
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A novel coronavirus (2019-nCoV) causing severe acute respiratory disease emerged recently in Wuhan, China. Information on reported cases strongly indicates human-to-human spread, and the most recent information is increasingly indicative of sustained human-to-human transmission. While the overall severity profile among cases may change as more mild cases are identified, we estimate a risk of fatality among hospitalised cases at 14% (95% confidence interval: 3.9-32%).
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Recurrent outbreaks of seasonal and pandemic influenza create a need for forecasts of the geographic spread of this pathogen. Although it is well established that the spatial progression of infection is largely attributable to human mobility, difficulty obtaining real-time information on human movement has limited its incorporation into existing infectious disease forecasting techniques. In this study, we develop and validate an ensemble forecast system for predicting the spatiotemporal spread of influenza that uses readily accessible human mobility data and a metapopulation model. In retrospective state-level forecasts for 35 US states, the system accurately predicts local influenza outbreak onset,—i.e., spatial spread, defined as the week that local incidence increases above a baseline threshold—up to 6 wk in advance of this event. In addition, the metapopulation prediction system forecasts influenza outbreak onset, peak timing, and peak intensity more accurately than isolated location-specific forecasts. The proposed framework could be applied to emergent respiratory viruses and, with appropriate modifications, other infectious diseases.
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In many infectious diseases, an unknown fraction of infections produce symptoms mild enough to go unrecorded, a fact that can seriously compromise the interpretation of epidemiological records. This is true for cholera, a pandemic bacterial disease, where estimates of the ratio of asymptomatic to symptomatic infections have ranged from 3 to 100 (refs 1-5). In the absence of direct evidence, understanding of fundamental aspects of cholera transmission, immunology and control has been based on assumptions about this ratio and about the immunological consequences of inapparent infections. Here we show that a model incorporating high asymptomatic ratio and rapidly waning immunity, with infection both from human and environmental sources, explains 50 yr of mortality data from 26 districts of Bengal, the pathogen's endemic home. We find that the asymptomatic ratio in cholera is far higher than had been previously supposed and that the immunity derived from mild infections wanes much more rapidly than earlier analyses have indicated. We find, too, that the environmental reservoir (free-living pathogen) is directly responsible for relatively few infections but that it may be critical to the disease's endemicity. Our results demonstrate that inapparent infections can hold the key to interpreting the patterns of disease outbreaks. New statistical methods, which allow rigorous maximum likelihood inference based on dynamical models incorporating multiple sources and outcomes of infection, seasonality, process noise, hidden variables and measurement error, make it possible to test more precise hypotheses and obtain unexpected results. Our experience suggests that the confrontation of time-series data with mechanistic models is likely to revise our understanding of the ecology of many infectious diseases.
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Background: Since Dec 31, 2019, the Chinese city of Wuhan has reported an outbreak of atypical pneumonia caused by the 2019 novel coronavirus (2019-nCoV). Cases have been exported to other Chinese cities, as well as internationally, threatening to trigger a global outbreak. Here, we provide an estimate of the size of the epidemic in Wuhan on the basis of the number of cases exported from Wuhan to cities outside mainland China and forecast the extent of the domestic and global public health risks of epidemics, accounting for social and non-pharmaceutical prevention interventions. Methods: We used data from Dec 31, 2019, to Jan 28, 2020, on the number of cases exported from Wuhan internationally (known days of symptom onset from Dec 25, 2019, to Jan 19, 2020) to infer the number of infections in Wuhan from Dec 1, 2019, to Jan 25, 2020. Cases exported domestically were then estimated. We forecasted the national and global spread of 2019-nCoV, accounting for the effect of the metropolitan-wide quarantine of Wuhan and surrounding cities, which began Jan 23-24, 2020. We used data on monthly flight bookings from the Official Aviation Guide and data on human mobility across more than 300 prefecture-level cities in mainland China from the Tencent database. Data on confirmed cases were obtained from the reports published by the Chinese Center for Disease Control and Prevention. Serial interval estimates were based on previous studies of severe acute respiratory syndrome coronavirus (SARS-CoV). A susceptible-exposed-infectious-recovered metapopulation model was used to simulate the epidemics across all major cities in China. The basic reproductive number was estimated using Markov Chain Monte Carlo methods and presented using the resulting posterior mean and 95% credibile interval (CrI). Findings: In our baseline scenario, we estimated that the basic reproductive number for 2019-nCoV was 2·68 (95% CrI 2·47-2·86) and that 75 815 individuals (95% CrI 37 304-130 330) have been infected in Wuhan as of Jan 25, 2020. The epidemic doubling time was 6·4 days (95% CrI 5·8-7·1). We estimated that in the baseline scenario, Chongqing, Beijing, Shanghai, Guangzhou, and Shenzhen had imported 461 (95% CrI 227-805), 113 (57-193), 98 (49-168), 111 (56-191), and 80 (40-139) infections from Wuhan, respectively. If the transmissibility of 2019-nCoV were similar everywhere domestically and over time, we inferred that epidemics are already growing exponentially in multiple major cities of China with a lag time behind the Wuhan outbreak of about 1-2 weeks. Interpretation: Given that 2019-nCoV is no longer contained within Wuhan, other major Chinese cities are probably sustaining localised outbreaks. Large cities overseas with close transport links to China could also become outbreak epicentres, unless substantial public health interventions at both the population and personal levels are implemented immediately. Independent self-sustaining outbreaks in major cities globally could become inevitable because of substantial exportation of presymptomatic cases and in the absence of large-scale public health interventions. Preparedness plans and mitigation interventions should be readied for quick deployment globally. Funding: Health and Medical Research Fund (Hong Kong, China).
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Nonlinear stochastic dynamical systems are widely used to model systems across the sciences and engineering. Such models are natural to formulate and can be analyzed mathematically and numerically. However, difficulties associated with inference from time-series data about unknown parameters in these models have been a constraint on their application. We present a new method that makes maximum likelihood estimation feasible for partially-observed nonlinear stochastic dynamical systems (also known as state-space models) where this was not previously the case. The method is based on a sequence of filtering operations which are shown to converge to a maximum likelihood parameter estimate. We make use of recent advances in nonlinear filtering in the implementation of the algorithm. We apply the method to the study of cholera in Bangladesh. We construct confidence intervals, perform residual analysis, and apply other diagnostics. Our analysis, based upon a model capturing the intrinsic nonlinear dynamics of the system, reveals some effects overlooked by previous studies.
Real-time tentative assessment of the epidemiological characteristics of novel coronavirus infections in Wuhan, China, as at 22
  • P Wu
  • X Hao
  • Ehy Lau
Wu P, Hao X, Lau EHY, et al. Real-time tentative assessment of the epidemiological characteristics of novel coronavirus infections in Wuhan, China, as at 22 January 2020. Euro Surveill. 2020;25(3):pii=2000044.