Available via license: CC BY-ND 4.0
Content may be subject to copyright.
Forecasting Novel Corona Positive Cases in India
using Truncated Information: A Mathematical Approach
Brijesh P. Singh
Department of Statistics, Institute of Science
Banaras Hindu University, Varanasi-221005 INDIA
Email: brijesh@bhu.ac.in
Abstract
Novel corona virus is declared as pandemic and India is struggling to control this from a massive
attack of death and destruction, similar to the other countries like China, Europe, and the United
States of America. India reported 2545 cases novel corona confirmed cases as of April 2, 2020
and out of which 191 cases were reported recovered and 72 deaths occurred. The first case of
novel corona is reported in India on January 30, 2020. The growth in the initial phase is
following exponential. In this study an attempt has been made to model the spread of novel
corona infection. For this purpose logistic growth model with minor modification is used and the
model is applied on truncated information on novel corona confirmed cases in India. The result is
very exiting that till date predicted number of confirmed corona positive cases is very close to
observed on. The time of point of inflexion is found in the end of the April, 2020 means after
that the increasing growth will start decline and there will be no new case in India by the end of
July, 2020.
Introduction
A novel corona virus is responsible for epidemic popularly known as COVID-19 is a new strain
that has not been identified previously in humans. WHO declared COVID-19 a pandemic on
March 11, 2020.[1] The virus that caused the incidence of Severe Acute Respiratory Syndrome
(SARS) in 2002 in China, Middle East respiratory syndrome (MERS) in 2012 in Saudi Arabia
and the virus that causes COVID-19 are genetically related to each other, but the diseases they
caused are quite different.[2] These viruses, in general, are a family of viruses that target and
affect mammal’s respiratory systems. The SARS corona virus spread to humans via civet cats,
while the MERS virus spread via dromedaries. In case of the novel corona virus, typically
happens via contact with an infected animal, perhaps the common carriers are bats initial reports
from seafood market in central Wuhan, China.
Novel corona virus is spreading throughout the world at alarming speed. Worldwide it has
exploded to 1118684 cases and caused 58909 deaths by April 3, 2020.[3] Developed countries
like Italy, Spain, France and United State of America etc. are struggling to overcome from the
. CC-BY-ND 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 certified by peer review) The copyright holder for this preprint this version posted May 5, 2020. .https://doi.org/10.1101/2020.04.29.20085175doi: medRxiv preprint
pressure created by novel corona virus. India with a huge population about 1.3 billion, amongst
majority of the people are living in poor hygienic condition and the medical facilities like
number of doctors and hospitals are less in India as compared to developed countries indicates
that the situation of India will become very critical but comparatively better public health system
and political control in India than the above developed countries. India reported 2545 cases novel
corona confirmed cases as of April 2, 2020 and out of which 191 cases were reported recovered
and 72 deaths occurred. The first case of novel corona is reported in India on January 30, 2020
when a student returned from Wuhan, China.[4] The Government of India was quick to launch
various levels of travel advisories beginning from February 26, 2020, with restrictions on travel
to China and nonessential travel restrictions to Singapore, South Korea, Iran and Italy.[5] The
efforts to control by the Hon’ble Prime Minister Narendra Modi Ji through Janata Curfew (public
curfew) on March 22, 2020, can be seen as the beginning of wide-scale public preventive
measures. India has launched several social distancing measures and personal hygiene measures
during the second week of March.[6]
Since huge population of about 1.3 billion, thus India has chosen a flexible strategy of large-
scale quarantine and limited testing because of less number of testing kits and also the cost of
testing is too much. The country is relying on the people power; thousands of health-care
workers are working out across the country to trace and quarantine people who might have had
contact with those with novel corona. People are typically only tested if they develop symptoms.
Countries such as South Korea isolated infected people based on widespread testing, but some
scientists say that India’s mass surveillance approach could achieve a similar goal, and be
relevant for other low and low-middle income countries facing kit shortages. Under the
lockdown, people are allowed out for essentials, such as food and medical care, but in most
states people under quarantine are closely monitored by social workers and cannot leave their
homes in some places. If public health workers do not trace all infected individuals during the
lockdown, India will need to continue its period of stringent physical distancing.
For the spread of novel corona virus, when disease dynamics are still unclear, mathematical
modeling helps us to estimate the cumulative number of positive cases in the present scenarios.
Now India is interring in the mid stages of the epidemic. It is important to predict how the virus
is likely to grow amongst the population. A mathematical modeling approach is a suitable tool to
understand the dynamics of epidemic. In the study some mathematical approach to understand
the dynamics of novel corona virus in India has been discuss.
Methodology
We obtained the truncated information on cumulative number of corona positive confirmed cases
in India from March 13 to April 2, 2020 from covid19india.org.[4] All cases are laboratory
confirmed following the case definition by the Govt. of India. Some studies modeled the
. CC-BY-ND 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 certified by peer review) The copyright holder for this preprint this version posted May 5, 2020. .https://doi.org/10.1101/2020.04.29.20085175doi: medRxiv preprint
epidemic curve obeying the exponential growth.[7, 8] The nonlinear least square framework is
adopted for data fitting and parameter estimation for 2019-nCoV at this early stage. In this study
first exponential and then logistic growth curve has been used to model the novel corona
epidemic, since epidemics grow exponentially not linearly. But it is surprising that exponential
growth curve always provide increasing number of daily new cases. There is no saturation point.
Another deterministic model used for understanding the dynamics of epidemic is the SIR model,
which has been used to accurately predict incidence like SARS. In the SIR model, we need to
know the input parameters first the stats we feed into the model.[9, 10, 11] The first one is R0 called
the basic reproduction Number. It is essentially the number of new cases a single infected person
will cause during their infectious period. It is one of the most important parameters for assessing
any epidemic. Corona virus has an R0~2.4. In contrast, the H1N1 virus had an R0~1.5 in the 2009
swine flu epidemic.[12] The R0 will inform us about how many people will get infected with one
infected person. Other one is the case fatality rate (CFR), which is the percentage of infected
people that will die due to the infection. The CFR for corona virus has been reported between
0.5–4%. The lower values are more appropriate in resource better settings of medical facility.
But SIR model assumes that every person is moving and has equal chance of contact with each
and every other person among the population irrespective of the space or distance between
different people. It is assumed that the transmission rate remains constant throughout the period
of pandemic. Also this model considered to have the same transmission rate for who have been
diagnosed and are in quarantine or those who have not been quarantined. The harmonic analysis
methods and dynamic model estimates show that the number of COVID-19 infected would be
9225 (if there were 10 infected individuals as of March 1, 2020, who was not taking any
precautions to spread), 17,986 (if there were 20) and 44,265 (if there were 50).[13]
Growth Models
A growth curve is an empirical model of the evolution of a quantity over time. Growth curves are
widely used in biology for quantities such as population size in population ecology and
demography for population growth analysis, individual body height in physiology for growth
analysis of individuals. Growth is also a key property of many systems such as an economic
expansion, spread of an epidemic, the formation of a crystal, an adolescent’s growth and the
condensation of a stellar mass.
Linear growth
This is the simplest growth model, in which population grows at a constant rate over time.
Linear growth is described by the equation
APP tt
1
(1)
. CC-BY-ND 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 certified by peer review) The copyright holder for this preprint this version posted May 5, 2020. .https://doi.org/10.1101/2020.04.29.20085175doi: medRxiv preprint
where
t
P
represents the numbers or size of the system at time t,
1t
P
represents the system’s
numbers or size of the system one time unit later, and A is the system’s (linear) growth rate.
Many times this model fails to explain natural phenomenon.
Exponential growth (Unlimited population growth)
Another simple model describes exponential growth, in which population grows at a constant
proportional rate over time. The relation may be expressed in either of two forms, depending on
whether reproduction is assumed to be continuous or periodic.[14] Exponential growth results in a
continuous curve of increase or decrease, whose slope varies in direct relation to the size of the
population.
0rt
t
P y Pe
(2)
where r is the constant rate of growth, Po is the initial population size, and the variables t and Pt
respectively represent time and the population at time t (Method 1). Another form of exponential
curve is as follows
0t
t
P y Pk
(3)
Where
1
0
n
n
P
kP
and that therefore the growth rate in (3) does not a constant growth rate. David
A. Swanson, University of California, USA used this type equation for prediction (Method 2).
We have used truncated information i.e. only 30 days information (from March 4 to April 2,
2020) on number of corona confirmed cases for the prediction purpose. We have used two
equations of exponential curve given below
I.
0.14
28 t
e
up to March 31, 2020
II.
0.15
28 t
e
from March 31, 2020 onward (adjusting faster rate of occurrence of corona cases
due to Tablighi spread)
With the current incidence of the novel corona virus going on, we hear about exponential
growth. In this study, an attempt has been made to understand and analyze the data through
exponential growth curve. The reason for using exponential growth curve for studying the
pattern of novel corona virus incidence is that epidemiologists have studied these types of
happenings and it is well known that the first period of an epidemic follows exponential growth.
The exponential growth function is not necessarily the perfect representation of the epidemic. I
have tried to fit exponential curve first, and at the next point to study the logistic growth curve
because exponential curve is only fit the epidemic at the beginning. At some point, recovered
people will not spread the virus anymore and when someone is or has been infected, the growth
. CC-BY-ND 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 certified by peer review) The copyright holder for this preprint this version posted May 5, 2020. .https://doi.org/10.1101/2020.04.29.20085175doi: medRxiv preprint
will stop. Logistic Growth is characterized by increasing growth in the beginning period, but a
decreasing growth after point of inflexion. For example in the corona virus case, the maximum
limit would be the total number of exposed people in India because when everybody is infected,
the growth will be stopped. After that the increasing rate of curve starts to decline and reach to
the minimum.
In the figure 1, predicted values of the cumulative number of novel corona positive cases
obtained by method 1 and 2 is drawn along with observed cumulative number of novel corona
positive cases. Bothe the methods provide moderately good estimates but the tendency of both
the curves are unlimited increasing. The rate of growth of Method 2 is slightly lesser than the
rate of growth of Method 1. The number of total infected cases by April 30, 2020 would be about
144700 (Method 1) and 127700 (Method 2). If we do not adjust the Method 1 for Tablighi spread
then the total infected cases by April 30, 2020 would be about 81810. Thus we can obtain the
effect of Tablighi spread is about 75 percent.
Logistic growth (Sigmoidal)
The logistic model reveals that the growth rate of the population is determined by its biotic
potential and the size of the population as modified by the natural resistance, or, in other words,
by all the various effects of inherent characteristics, that are density dependence.[15] Natural
resistance increases as population size gets closer to the carrying capacity. Logistic growth is
similar to exponential growth except that it assumes an essential sustainable maximum point. In
exponential growth curve, the rate of growth of y per unit of time is directly proportional to y but
in practice the rate of growth cannot be in the same proportion always. The logistic curve will
continue up to certain level, called the level of saturation, sometimes called the carrying
capacity, after reaching carrying capacity it starts declining. The factor y is called the momentum
factor which increases with time t and the factor
)( yk
is known as the retarding factor which
decreases with time. A system far below its carrying capacity will at first grow almost
exponentially however, this growth gradually slows as the system expands, finally bringing it to
a halt specifically at the carrying capacity.[14, 15] The logistic relationship can be expressed as
;0
1
ta bt
k
P y b
e
(4)
Logistic curve has a point of inflexion at half of the carrying capacity k. This point is the critical
point from where the increasing rate of curve starts to decline. The time of point of inflexion can
be estimate as
a
b
. For the estimation of parameter of logistic curve, method of three selected
point has been used. The estimate of the parameters can be obtained with equation given as:
. CC-BY-ND 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 certified by peer review) The copyright holder for this preprint this version posted May 5, 2020. .https://doi.org/10.1101/2020.04.29.20085175doi: medRxiv preprint
2
2 1 3 1 2 3
2
2 1 3
( ) 2y y y y y y
ky y y
(5)
21
2 1 1 2
()
1ln ()
k y y
bt t k y y
(6)
11
1
ln ky
a bt
y
(7)
Where
1, 2 3 1, 2 3 2 1 3 2
and are thenumber atgiven time and respectivelyprovided thaty y y t t t t t t t
.
You may also estimate the parameter a and b by method of least square after fixing k.
To predict confirmed corona cases on different day, logistic growth curve has been also used and
found very exciting results. The truncated information on confirmed cases in India has been
taken from March 13 to April 2, 2020. The estimated value of the parameters are as follows
k=18708.28, a=5.495 and b=-0.174, with these estimates predicted values has been obtained and
found considerably lower values than what we observed. On April 1 and 2, 2020 the number of
confirmed corona cases are drastically increasing in some part of India due to some unavoidable
circumstances thus there is an earnest need to increase carrying capacity of the model, thus it is
increased and considered as 22000 and the other parameters a and b are estimated again which
are a=5.657 and b=-0.173. The predicted cumulative number of cases is very close to the
observed cumulative number of cases till date. The time of point of inflexion is obtained as 32.65
i.e. 35 days after beginning. We have taken data from March 13, 2020 so that the time of point of
inflexion should be April 14, 2020 and by May 30, 2020 there will be no new cases found in the
country. The distribution of the new cases is in the red color in the figure 2, which is quite
normal and obvious. As mentioned in the above paragraph Method 1 provided natural estimate
of the total infected cases by May 30, 2020 is 192400. This estimate is obtained when no
preventive measure would be taken by the Government of India. The testing rate is lower in
India than many western countries, so our absolute numbers is low, when government initiate
faster testing process then we have observed more number of cases and fount this logistic model
fail to provide cumulative number of corona confirm cases after April 17, 2020 thus there is a
need to modify this model. In order to the modification I have taken natural log of cumulative
number of corona confirm cases instead of cumulative number of corona confirm cases as taken
in the previous model. This model provides the carrying capacity is about 77000 cases and time
of point of inflexion April 30, 2020. The present model provides reasonable estimate of the
cumulative number of confirmed cases till date (see Appendix and figure 3) and by the end of
July, 2020 there will be no new cases found in the country.
. CC-BY-ND 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 certified by peer review) The copyright holder for this preprint this version posted May 5, 2020. .https://doi.org/10.1101/2020.04.29.20085175doi: medRxiv preprint
Conclusions
India is in the comfortable zone with a lower growth rate than other countries studied. Our
mathematical model shows that, the epidemic is likely to stabilize with 77000 cases by the end of
July, 2020. A study advocated of 49 days single lockdown i.e. lockdown up to May 13, 2020
reduce infected cases below 10 but our study contradict it.[11] The government has adopted a
strategy of large scale quarantine and limited testing to flatten the epidemic curve and reduce the
death rate. The projections produced by the model and after their validation can be used to
determine the scope and scale of measures that government need to initiate. In conclusion, if the
current mathematical model results can be validated within the range provided here, then the
social distancing and other prevention, treatment policies that the central and various state
governments and people are currently implementing should continue until new cases are not
seen. The spread from urban to rural and rich to poor populations should be monitor and control
is an important point of consideration. Mathematical models have certain limitations that there
are many assumptions about homogeneity of population in terms of urban/rural or rich/poor that
does not capture variations in population density.
References
[1] Coronavirus Disease (COVID-19) - events as they happen. Available at:
https://www.who.int/emergencies/diseases/novel-coronavirus-2019/events-as-theyhappen
[2] Organization WH. WHO Statement Regarding Cluster of Pneumonia Cases in Wuhan,
China; Available from: https://www.who.int/china/news/detail/09-01-2020-who- statement-
regarding-cluster-of-pneumonia-cases-in-wuhan-china
[3] Coronavirus Update (Live): COVID-19 Virus Outbreak - Worldometer. Available at:
https://www.worldometers.info/coronavirus.
[4] India Covid-19 Tracker: A Crowdsourced Initiative, Available at:
https://www.covid19india.org.
[5] Consolidated Travel advisory in view of COVID-19 (26 February 2020), Government of
India, Ministry of Health & FW.
[6] Indian Council of Medical Research, Department of Health Research, Revised Strategy of
COVID19 testing in India (version 3, dated 20 March 2020).
[7] De Silva U, Warachit J, Waicharoen S, Chittaganpitch M. A preliminary analysis of the
epidemiology of influenza A (H1N1) v virus infection in Thailand from early outbreak data,
June-July 2009. Euro surveillance 2009; 14(31):19292.
[8] Zhao S, Musa SS, Fu H, He D, Qin J. Simple framework for real-time forecast in a data
limited situation: the Zika virus (ZIKV) outbreaks in Brazil from 2015 to 2016 as an
example. Parasites Vectors 2019; 12(1):344.
[9] Chatterjee K, Chatterjee K, Kumar A, Shankar S. Healthcare impact of
COVID-19 epidemic in India: A stochastic mathematical model. Medical Journal Armed
Forces India 2020; https://doi.org/10.1016/j.mjafi.
[10] Mandal Sandip, Bhatnagar Tarun, Arinaminpathy Nimalan, Agarwal Anup et al. Prudent
public health intervention strategies to control the corona virus disease 2019 transmission in
. CC-BY-ND 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 certified by peer review) The copyright holder for this preprint this version posted May 5, 2020. .https://doi.org/10.1101/2020.04.29.20085175doi: medRxiv preprint
India: A mathematical model-based approach. Indian J Med Res 2020; Epub ahead of print
DOI: 10.4103/ijmr.IJMR_504_20
[11] Singh Rajesh & Adhikari R. Age-structured impact of social distancing on the COVID-
19 epidemic in India 2020. arXiv:2003.12055v1 [q-bio.PE]
[12] Gupta Mohak Corona virus in India: Make or Break. Available at:
https://medium.com/@mohakgupta_55841/coronavirus-in-india-make-or-break-
5a13dfb9646d
[13] Srinivasa Rao Arni S. R., Krantz Steven G., Kurien Thomas, Bhat Ramesh et al. Model-
based retrospective estimates for COVID-19 or coronavirus in India: continued efforts
required to contain the virus spread. Current Science 2020; 118(7):1023-25.
[14] Shryock. Henry S. and Jacob S. Siegel. Methods and Materials of Demography.
Washington: U.S. Dept. of Commerce, Bureau of the Census. 1973
[15] Pearl, R., & Reed, L. J. On the rate of growth of the population of the United States since
1790 and its mathematical representation. Proceedings of the National Academy of Sciences
of the United States of America, 1920; 6(6), 275.
. CC-BY-ND 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 certified by peer review) The copyright holder for this preprint this version posted May 5, 2020. .https://doi.org/10.1101/2020.04.29.20085175doi: medRxiv preprint
0
20
40
60
80
100
120
140
160
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60
Corona positive cases in Thousands
Observed
Predicted by Method 1
Predicted by Method 2
Days from starting
Figure 1
Figure 2
0
100
200
300
400
500
600
700
800
900
1000
0
4
8
12
16
20
24
04812 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80
Cumulative corona positive cases in Thousands
Observed
Predicted
New cases
Days from starting
New corona positive cases
. CC-BY-ND 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 certified by peer review) The copyright holder for this preprint this version posted May 5, 2020. .https://doi.org/10.1101/2020.04.29.20085175doi: medRxiv preprint
Figure 3
Appendix
Month
Date
Observed
Predicted
95% LCI
95% UCI
New Cases
Residual
March
13
91
91
86
96
9
14
107
108
101
114
17
-1
15
113
127
121
134
20
-14
16
127
151
144
158
24
-24
17
146
179
171
187
28
-33
18
171
213
204
222
34
-42
19
199
253
243
263
40
-54
20
258
301
290
312
48
-43
21
334
358
346
370
57
-24
22
403
425
411
439
67
-22
23
505
505
489
521
80
0
24
571
599
579
619
94
-28
25
657
709
685
733
110
-52
26
735
839
809
868
129
-104
27
886
989
952
1027
151
-103
28
1029
1165
1118
1212
175
-136
29
1139
1368
1308
1427
203
-229
30
1347
1602
1527
1676
234
-255
31
1635
1870
1777
1963
268
-235
April
1
2059
2176
2061
2291
306
-117
2
2545
2524
2383
2665
348
21
3
3105
2917
2746
3089
393
188
4
3684
3360
3153
3567
442
324
5
4289
3854
3607
4102
495
435
6
4778
4404
4111
4698
550
374
7
5351
5013
4668
5359
609
338
8
5916
5684
5280
6087
670
232
9
6729
6417
5950
6884
734
312
0
200
400
600
800
1000
1200
1400
1600
0
10
20
30
40
50
60
70
80
020 40 60 80 100 120 140
Observed
Predicted
New Cases
Days from starting
New corona positive cases
Cumulative corona positive cases in Thousands
. CC-BY-ND 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 certified by peer review) The copyright holder for this preprint this version posted May 5, 2020. .https://doi.org/10.1101/2020.04.29.20085175doi: medRxiv preprint
10
7600
7216
6680
7752
799
384
11
8454
8081
7470
8693
865
373
12
9212
9013
8321
9705
932
199
13
10455
10012
9234
10789
999
443
14
11490
11076
10209
11943
1064
414
15
12372
12205
11244
13166
1129
167
16
13434
13396
12339
14454
1191
38
17
14353
14648
13490
15805
1251
-295
18
15724
15955
14697
17213
1307
-231
19
17304
17315
15955
18675
1360
-11
20
18543
18723
17262
20184
1408
-180
21
20080
20175
18614
21736
1452
-95
22
21372
21665
20006
23325
1490
-293
23
23039
23189
21435
24943
1524
-150
24
24447
24740
22894
26586
1551
-293
25
26282
26314
24381
28247
1574
-32
26
27889
27904
25890
29918
1590
-15
27
29458
29505
27415
31596
1601
-47
28
31360
31112
28952
33272
1607
248
29
32719
30496
34942
1607
30
34321
32042
36600
1602
May
1
35914
33586
38241
1593
2
37492
35123
39861
1579
3
39053
36650
41456
1560
4
40591
38162
43020
1538
5
42103
39655
44552
1513
6
43587
41127
46048
1484
7
45039
42574
47505
1452
8
46458
43993
48922
1418
9
47840
45384
50297
1382
10
49185
46742
51627
1345
11
50490
48066
52914
1305
12
51755
49356
54154
1265
13
52979
50609
55349
1224
14
54162
51825
56498
1182
15
55302
53003
57602
1141
16
56401
54142
58659
1099
17
57457
55242
59672
1057
18
58472
56304
60640
1015
19
59446
57327
61565
974
20
60379
58311
62448
933
21
61273
59257
63289
893
22
62127
60165
64090
854
23
62944
61036
64851
816
24
63723
61871
65575
779
25
64466
62670
66263
743
26
65175
63434
66915
708
27
65849
64165
67533
674
28
66491
64862
68119
642
29
67101
65528
68674
610
30
67681
66163
69199
580
31
68231
66767
69695
551
June
1
68754
67343
70164
523
2
69250
67892
70608
496
3
69720
68413
71026
470
4
70165
68909
71421
445
5
70587
69380
71794
422
6
70987
69828
72146
400
7
71365
70253
72477
378
8
71723
70656
72789
358
9
72061
71038
73084
338
10
72381
71401
73361
320
11
72683
71745
73621
302
12
72969
72071
73867
286
13
73239
72379
74098
270
14
73493
72672
74315
255
. CC-BY-ND 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 certified by peer review) The copyright holder for this preprint this version posted May 5, 2020. .https://doi.org/10.1101/2020.04.29.20085175doi: medRxiv preprint
15
73734
72949
74520
241
16
73961
73210
74712
227
17
74175
73458
74893
214
18
74378
73693
75062
202
19
74568
73915
75222
191
20
74748
74124
75372
180
21
74918
74323
75513
170
22
75078
74510
75645
160
23
75228
74687
75770
151
24
75370
74854
75886
142
25
75504
75013
75996
134
26
75630
75162
76099
126
27
75749
75303
76195
119
28
75861
75436
76286
112
29
75967
75562
76371
105
30
76066
75681
76451
99
July
1
76160
75793
76526
94
2
76248
75899
76596
88
3
76331
75999
76662
83
4
76409
76093
76724
78
5
76482
76182
76782
74
6
76551
76266
76837
69
7
76617
76345
76888
65
8
76678
76420
76936
61
9
76736
76490
76981
58
10
76790
76557
77023
54
11
76841
76620
77062
51
12
76889
76679
77100
48
13
76934
76735
77134
45
14
76977
76787
77167
43
15
77017
76837
77197
40
16
77055
76884
77226
38
17
77090
76928
77253
35
18
77124
76970
77278
33
19
77155
77009
77302
31
20
77185
77046
77324
30
21
77213
77081
77345
28
22
77239
77114
77364
26
23
77263
77145
77382
25
24
77286
77174
77399
23
25
77308
77201
77415
22
26
77329
77227
77430
20
27
77348
77252
77444
19
28
77366
77275
77457
18
29
77383
77297
77470
17
30
77399
77317
77481
16
31
77414
77336
77492
15
. CC-BY-ND 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 certified by peer review) The copyright holder for this preprint this version posted May 5, 2020. .https://doi.org/10.1101/2020.04.29.20085175doi: medRxiv preprint