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Correcting under-reported COVID-19 case numbers

March 2020

DOI:10.1101/2020.03.14.20036178

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The COVID-19 virus has spread worldwide in a matter of a few months, while healthcare systems struggle to monitor and report current cases. Testing results have struggled with the relative capabilities, testing policies and preparedness of each affected country, making their comparison a non-trivial task. Since severe cases, which more likely lead to fatal outcomes, are detected at a higher rate than mild cases, the reported virus mortality is likely inflated in most countries. Lockdowns and changes in human behavior modulate the underlying growth rate of the virus. Under-sampling of infection cases may lead to the under-estimation of total cases, resulting in systematic mortality estimation biases. For healthcare systems worldwide it is important to know the expected number of cases that will need treatment. In this manuscript, we identify a generalizable growth rate decay reflecting behavioral change. We propose a method to correct the reported COVID-19 cases and death numbers by using a benchmark country (South Korea) with near-optimal testing coverage, with considerations on population demographics. We extrapolate expected deaths and hospitalizations with respect to observations in countries that passed the exponential growth curve. By applying our correction, we predict that the number of cases is highly under-reported in most countries and a significant burden on worldwide hospital capacity. The full analysis workflow and data is available at: https://github.com/lachmann12/covid19

Case progression for eight countries with highest number of COVID-19 cases with corresponding recoveries and deaths.

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Death rates for US, Italy, and China in comparison with Korea over time.

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Correcting under-reported COVID-19 case

numbers

Alexander Lachmann1

1Department of Pharmacological Sciences, Mount Sinai Center for Bioinformatics, Icahn School of Medicine at Mount Sinai, One Gustave L. Levy Place, Box 1603, New

York, NY 10029, USA

The COVID-19 virus has spread worldwide in a matter of a

few month. Healthcare systems struggle to monitor and report

current cases. Limited capabilities in testing result in difﬁcult

to guide policies and mitigate lack of preparation. Since severe

cases, which more likely lead to fatal outcomes, are detected at

a higher percentage than mild cases, the reported death rates

are likely inﬂated in most countries. Such under-estimation can

be attributed to under-sampling of infection cases and results in

systematic death rate estimation biases.

The method proposed here utilizes a benchmark country

(South Korea) and its reported death rates in combination with

population demographics to correct the reported COVID-19

case numbers. By applying a correction, we predict that the

number of cases is highly under-reported in most countries. In

the case of China, it is estimated that more than 700.000 cases

of COVID-19 actually occurred instead of the conﬁrmed 80,932

cases as of 3/13/2020.

The full analysis workﬂow and data is available at:

https://www.kaggle.com/lachmann12/

population-demographics-correction-covid-19

COVID-19 | COVID-19 | demographics | public health

Correspondence: alexander.lachmann@mssm.edu

Introduction

Severe acute respiratory syndrome-related COVID-19

(COVID-19) is a novel virus with the initial outbreak most

likely in China (1). It has reached pandemic status by the

World Health Organization within less than four months of

initial reports of the disease. The origin of the virus can be

traced back to related strains predominantly found in bats (2).

Individuals infected by the disease can experience a series

of symptoms, including cough, chills, fever, and shortness

of breath (3). From data currently available, fatal disease

progression is higher than that of the common inﬂuenza

strains and as such it resulted in more deaths than recent

virus of Severe Acute Respiratory Syndrome (SARS) and

Search Results Middle East Respiratory Syndrome (MERS)

combined. (?). The infection rate of COVID-19 has been

estimated between a R0of 2 and up to 6.49 (4) compared

to inﬂuenza with about 1.3 (5). The severity of infection

is highly correlated to the age of the infected individual.

Younger parts of a population present a much lower risk than

older populations. A current data release from the Center for

Disease Control in South Korea shows that while there are

no reported fatalities for individuals under 30 years of age,

the death rate for individuals older than 80 is over 8% (6).

Figure 1shows eight countries with a signiﬁcant number of

reported COVID-19 cases. China, which has been the origin

of the outbreak, registered the most cases with over 80,000.

Through severe measures such as curfews, new infections

have slowed signiﬁcantly. Other countries that have been

only recently affected are still in the exponential growth

curve. Countries like Italy have only recently taken action

to slow the spread of the virus. With a reported incubation

time of about ﬁve days, it will take several days until the

effects of a slowdown will be visible (7). Another country

that is currently experiencing high numbers of reported

COVID-19 cases is Iran, with more than 12,000 conﬁrmed

cases. Due to the limited information available, most pa-

rameters describing the dynamics of the disease spread have

signiﬁcant uncertainties around them. Healthcare systems in

most countries are not capable of monitoring the exponential

growth of a virus in this manner. South Korea, as of writing,

has the most extensive capabilities of testing individuals

with a capacity of around 20,000 tests a day. Hence, South

Korea represents the best benchmark country in order to

correct reported COVID-19 cases in other countries. The

proposed method uses demographic information to identify

the fraction of the vulnerable population. Countries such

as China have a generally younger population reducing the

overall risk of fatal outcomes and thereby should result in a

lower death rate compared to South Korea. Countries, such

as Italy with an older population compared to South Korea,

should have a higher death rates. Estimating the true case

count is relevant in identifying the correct measures to stop

the disease from spreading.

Methods

A. Data. The case correction relies on two datasets. The

ﬁrst is the data published by the WHO, which is updated

every day and contains case, recovery, and death numbers for

countries reporting all known COVID-19 cases (8). The sec-

ond dataset is a global demographic database maintained by

the United Nations (9). This database contains the number of

individuals per year of age for more than 200 countries. For

the analysis, we extracted the data between 2007 and 2019.

We always choose the most recent data entry for the coun-

tries if multiple exist. This ﬁle is hosted as a Kaggle dataset

at: https://www.kaggle.com/lachmann12/

world-population-demographics-by-age-2019.

B. Assumptions. This method makes a series of assump-

tions in order to adjust reported COVID-19 cases compared

to the benchmark country (South Korea).

A. Lachmann | bioRχiv | March 14, 2020 | 1–5

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author/funder, who has granted medRxiv a license to display the preprint in perpetuity. is the(which was not peer-reviewed) The copyright holder for this preprint .https://doi.org/10.1101/2020.03.14.20036178doi: medRxiv preprint

Fig. 1. Case progression for eight countries with highest number of COVID-19 cases with corresponding recoveries and deaths.

•Deaths are conﬁrmed equally It is assumed that if a

death occurs, caused by COVID-19, the case is con-

ﬁrmed. When there is under-reporting, the death rate

would be lower than the true death rate.

•The population is infected uniformly We assume that

the probability of infection is uniformly distributed

across. The probability of an 80-year-old person to be-

come infected is equal to the probability of a 30-year-

old to become infected.

•Treatment has minor inﬂuence on outcome The pro-

vided healthcare in countries is comparable. For de-

veloped countries such as Italy and South Korea, it is

assumed that the population has similar access to treat-

ment. The death rates reported by age group are thus

applicable in all countries.

C. Case Adjustment. Figure 2shows the progression of

death rate estimates for the US, Italy, China, and South Ko-

rea. It can be noted that South Korea shows the most consis-

tent death rate estimates. Additionally, it also shows a signif-

icantly lower death rate compared to other countries, with the

exception of Germany (not shown). The change of death rate

over time within the same country is potentially caused by

changes in the number of false-negative cases, meaning that

many infections go unnoticed until they become fatal. In the

case of Italy, there might not have been sufﬁcient capacity to

conﬁrm infections. With a smaller fraction of potential cases

tested, the estimated death rate will increase. In the case of

Italy, the estimated rate increased from 2% to more than 6%.

Fig. 2. Death rates for US, Italy, and China in comparison with Korea over time.

2 | bioRχiv A. Lachmann |

. CC-BY 4.0 International licenseIt is made available under a

C Case Adjustment

This method requires the comparison of two countries with

sufﬁcient conﬁrmed cases and reported deaths. One country

(target country) will be adjusted, given the information from

the second country (benchmark country). In order to adjust

for the difference in the population demographics of the tar-

get country, T, and the benchmark country, B, we compute a

Vulnerability Factor (VTB ).

VTB =PN

i=0 fTiri

i=0 fBiri

, where fTiis the fraction of the population with age ifor

target country T,fBiis the fraction of the population with

age ifor benchmark country B, and rithe death rate for age

i.riis listed in Table 1.

If VTB >1, then the population of Thas a higher risk of fatal

outcomes due to a larger percentage of the older population.

It results in a higher death rate compared to B. If VTB <1,

then Thas a younger population and it should result in a

lower death rate compared to B.

Another correction factor is the ﬁxed average death rate of

the benchmark country, DB.

DB=PK

i=0 dBi

, where dBiis the death rate of day i.

With both normalization factors we can now adjust the ex-

pected cases relative to B. The methods applies the normal-

ization to each time point. The original case number oTiis

adjusted for Tand Bat time point iwith:

aTB(oTi) = oTi

VTBDB

Results

By applying the proposed correction, the number of adjusted

cases is signiﬁcantly higher for most countries. Figure 3a il-

lustrates population age distributions. Figure 3b shows the

expected number of fatal outcomes for a 100% infection rate.

The vulnerability factor for the US compared to South Ko-

rea is 1.07. This means that the population is equally vul-

nerable to fatal outcomes of COVID-19 infections. Italy, in

contrast, has a vulnerability factor of 1.57. This is due to

a higher fraction of the population being at a higher risk of

death. This would indicate the expected death rate would be

57% higher in Italy compared to South Korea. China, with

a younger population relative to South Korea, has a vulnera-

bility factor of 0.63. The expected death rate in China should

be lower than in South Korea based on the population risk.

After applying the case adjustment, we observe a signiﬁcant

increase in the number of COVID-19 infections. The dis-

crepancy in reported death rates in combination with favor-

able population scores in the case of China suggests a large

number of unreported COVID-19 infections. The adjustment

suggests around 702,518 cases compared to 80,932 reported

cases. This equates to an 868% higher case count than pre-

viously reported. The corrections for Italy and the US are

similar, but not as extreme. Italy has an adjusted number of

cases of 112,182 cases and the US potentially 6,085 cases.

Table 2shows the adjusted number of cases for a selected

number of countries. Iran is the country with the most sub-

stantial adjustment of 1,363%, reaching 154,853 cases.

Summary

This study suggests that the current reporting of COVID-19

cases is signiﬁcantly underestimating the true scale of the

pandemic. The lack of testing makes the estimation of the

true death rate difﬁcult and causes a signiﬁcant misinforma-

tion. This study tries to leverage the information derived from

a well-tested sub-population (South Korea). With testing ca-

pacities of 20,000 tests daily, it has the largest and most ac-

curate coverage compared to all other countries as of writ-

ing. The low false-negative rate in detecting COVID-19 in-

fections leads to the lowest death rate compared to all other

countries (0.84) with major case count. By applying the pa-

rameters, estimated from this benchmark country, the pro-

posed method can adjust global COVID-19 case numbers.

This method is limited in its ability to predict the exact num-

ber of cases accurately. The method relies on the assumption

that deaths by COVID-19 are detected and reported reliably.

False-negative rates can have a distorting effect on the case

adjustment. This is especially true if the benchmark coun-

try does not adequately report deaths from COVID-19. Ger-

many, as an example, only reports eight deaths from with

3,675 reported cases. This could be due to the very recent

increase in actual cases leaving not enough time for fatal

disease progression. Over time, when more data is avail-

able, death rates will most likely increase in Germany. Ad-

ditionally, the assumption of a globally similar death rate is

untested. Improvements in this method could look at the case

number of other viral diseases to see if there are signiﬁcant

differences between countries. This method explains the ob-

served ﬂuctuations in death rate over time by country. It is

unlikely that the death rate in the same country can ﬂuctu-

ate by multiple percent points over a period of a few days.

This method suggests that due to the fast exponential growth

of true case counts, most modern healthcare systems are not

able to track the changes adequately. In addition, the method

suggests that computational tools can be used to impute miss-

ing information based on regions where testing and tracking

is more advanced. It also highlights the importance of pub-

licly accessible real time data and the relevance of combining

global healthcare efforts.

ACKNOWLEDGEMENTS

I want to thank Dr Avi Ma’ayan and Federico Giorgi for feedback on the original

manuscript and Alon Bar Tal for insightful discussion as well as the Kaggle com-

munity. Special thanks to the seamless accessibility of up-to-date COVID-19 case

statistics published on GitHub by Johns Hopkins and the World Health Organization.

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Conﬁrmed Cases n (%) Deaths n (%) Fatality Rate %

Total 7,979 (100.0) 67 (100.0) 0.84

Age Groups 80 and above 253 (3.2) 21 (31.3) 8.30

70-79 506 (6.3) 24 (35.8) 4.74

60-69 985 (12.3) 14 (20.9) 1.42

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Fig. 3. a) Population demographic comparison between US, Italy, and China compared to South Korea. b) Population demographic with fatal outcome of COVID-19 at 100%

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Mar 2020
ANN INTERN MED

Background: A novel human coronavirus, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), was identified in China in December 2019. There is limited support for many of its key epidemiologic features, including the incubation period for clinical disease (coronavirus disease 2019 [COVID-19]), which has important implications for surveillance and control activities. Objective: To estimate the length of the incubation period of COVID-19 and describe its public health implications. Design: Pooled analysis of confirmed COVID-19 cases reported between 4 January 2020 and 24 February 2020. Setting: News reports and press releases from 50 provinces, regions, and countries outside Wuhan, Hubei province, China. Participants: Persons with confirmed SARS-CoV-2 infection outside Hubei province, China. Measurements: Patient demographic characteristics and dates and times of possible exposure, symptom onset, fever onset, and hospitalization. Results: There were 181 confirmed cases with identifiable exposure and symptom onset windows to estimate the incubation period of COVID-19. The median incubation period was estimated to be 5.1 days (95% CI, 4.5 to 5.8 days), and 97.5% of those who develop symptoms will do so within 11.5 days (CI, 8.2 to 15.6 days) of infection. These estimates imply that, under conservative assumptions, 101 out of every 10 000 cases (99th percentile, 482) will develop symptoms after 14 days of active monitoring or quarantine. Limitation: Publicly reported cases may overrepresent severe cases, the incubation period for which may differ from that of mild cases. Conclusion: This work provides additional evidence for a median incubation period for COVID-19 of approximately 5 days, similar to SARS. Our results support current proposals for the length of quarantine or active monitoring of persons potentially exposed to SARS-CoV-2, although longer monitoring periods might be justified in extreme cases. Primary funding source: U.S. Centers for Disease Control and Prevention, National Institute of Allergy and Infectious Diseases, National Institute of General Medical Sciences, and Alexander von Humboldt Foundation.

Pathological findings of COVID-19 associated with acute respiratory distress syndrome

Article

Feb 2020

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and coronavirus disease-2019 (COVID-19): The epidemic and the challenges

Article

Feb 2020
INT J ANTIMICROB AG

Emergence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2, previously provisionally named 2019 novel coronavirus or 2019-nCoV) disease (COVID-19) in China at the end of 2019, has caused a large global outbreak and a major public health issue. As of February 11, 2020, data from the WHO has shown that more than 43,000 confirmed cases have been identified in 28 countries/regions, with more than 99% of the cases being detected in China. On January 30, 2020, WHO has declared COVID-19 as the sixth public health emergency of international concern. The SARS-CoV-2 is closely related to two bat-derived severe acute respiratory syndrome-like coronaviruses, bat-SL-CoVZC45 and bat-SL-CoVZXC21. It is spread by human-to-human transmission via droplets or direct contact, and infection has been estimated to have mean incubation period of 6.4 days and a basic reproduction number of 2.24-3.58. Among the patients with pneumonia caused by the SARS-CoV-2 (novel coronavirus pneumonia or Wuhan pneumonia), fever was the most common symptom, followed by cough. Bilateral lung involvement with ground glass opacity was the most common finding from computerized tomography images of the chest. Although the one case of SARS-CoV-2 pneumonia in the United States responding well to remdesivir, which is now undergoing a clinical trial in China. Currently, controlling infection to prevent the spread of the SARS-CoV-2 is the primary intervention being used. However, public health authorities should keep monitoring the situation closely, as the more we can learn about this novel virus and its associated outbreak, the better we can respond.

Brief Review of World Demographic Trends - Trends in Age Distributions

Article

Nov 2012

This report focuses on one demographic trend: Age Distributions. The basic findings of this report are: 1) in all regions, the largest group is the adults (15-59 years old), 2) in Asia, Africa, and Latin America and the Caribbean, there are more children than there are seniors, while, recently, in Europe there are more seniors than children, and in Northern America there will soon be more seniors than children, 3) in almost all regions, the proportion of the population who are children is declining while the proportion who are seniors is increasing. Sub-Saharan Africa is an exception. There are almost as many children as there are seniors, and the proportions of the population who are seniors and children have not yet changed.Changes in age distributions have many implications for society. For example, a larger proportion of younger people means more people who have yet to attain adulthood and who can be expected to have more children, which means continued population growth. So, Sub-Saharan Africa, which has the highest proportion of children, also has the highest population growth rates (as seen in previous reports), and can be expected to continue to have the highest population growth rates. Similarly, Europe and North America, which have the lowest proportion of children, also have the lowest population growth rates, which can be expected to continue to be low. Also, since most regions have declining proportions of children, most regions have declining population growth rates and will likely continue to have declining population growth rates.

World Health Organization et al. Laboratory testing for coronavirus disease 2019 (covid-19) in suspected human cases: interim guidance

Mar 2020

World Health Organization et al. Laboratory testing for coronavirus disease 2019 (covid-19) in suspected human cases: interim guidance, 2 march 2020. Technical report, World Health Organization, 2020.