Corona virus (COVID-19) epidemic A stock-flow perspective

Abstract

The current epidemic of Corona virus can be captured using the stock and flow metrics. Differences between mortality ratio and confirmed fatality ratio appear important and suggest metrics used during the epidemic and after the epidemic should be different.

Full text

Corona virus (COVID-19) epidemic
A stock-flow perspective
S.M.R. Dente. As of February 25
th
1 Defining the metrics of the epidemic
The Corona virus epidemic started on 31 December 2019 in Wuhan City, Hubei Province of China [1]. So far,
80415 people have been infected worldwide. Of these, 2708 died (3.4%), 27905 recovered (35%) and 49802
are still infected (62%). 81 % of the infected people are in Hubei, 21% in other provinces of China and 3.4 %
outside of China. The top 5 places of infection outside China are South Korea (1.2%), Italy (0.4%), Japan (0.2%),
Iran (0.12%) and Singapore (0.11%).
The current report describes the metrics of the epidemic and shows how the stock-flow perspective taken in
environmental studies is useful to understand the epidemic evolution. Data come from the world health
organization (WHO) reports [2], the John Hopkins institution [3] and the interactive web-dashboard as
published in the Lancet infectious disease journal [4 and starts from January 22
nd
. Table 1 describes the symbols
used in the report. Figure 1 shows the relationships between these symbols in a stock-flow perspective.
Table 1: Symbol used
Symbol
Description
C.I
.
Number of
confirmed infected
people (c
umulated input
)
C.O.
Nu
mber of
people not infected an
ymore (cumulate
d output)
(
𝐶
.
𝐷
+
𝐶
.
𝑅
)
C
.D.
Number of people not infected a
nymore beca
us
e dead
(cumulated dea
th
s
)
C.R.
Number of people not infected a
nymore beca
us
e
recove
red
(cumulated
recovery
)
Cu.I
Number of
people
stil
l infected
(
𝐶
.
𝐼
−
𝐶
.
𝑂
)
D.I
.
Number of newly infected people (daily input)
D.O.
Number of
people not infected
an
ymore (daily outp
ut)
(
𝐷
.
𝐷
+
𝐷
.
𝑅
)
D.D.
Nu
mber of
people
d
ead on th
at da
y
(
da
ily death
)
D
.R
Number of people
that recovered on that d
ay (daily recovery
)
M.R.
Mortali
ty
rat
io
(
𝐶
.
𝐷
𝐶
.
𝑂
⁄
)
C.F.R
Confirmed
Fat
ality
ratio
(
𝐶
.
𝐷
𝐶
.
𝐼
⁄
)
E.R
% of people that
are not infected anymore
(
𝐶
.
𝑂
𝐶
.
𝐼
⁄
)
Figure1: Stock-flow description of the epidemic’s metrics.
𝐶𝑢 = 𝐶. 𝐼 −𝐶.𝑂
N: number of days since January 22
nd
𝐶. 𝐼.= 𝐷.𝐼




𝐶. 𝐷.= 𝐷.𝐷




𝐶.𝑅.= 𝐷.𝑅





2 Confirmed Fatality ratio Vs Mortality ratio
The confirmed case fatality ratio (C.F.R.) is the total number of deaths divided by the total number of
confirmed cases at one point in time [5]. This indicator is the one used by WHO to estimate the proportion of
cases who die and was reused by media to describe the dangerousness of the virus. On the opposite, I
advocate the mortality ratio (M.R.) corresponding to the total number of deaths divided by the total number
of people not infected anymore describe better the dangerousness of the virus as it describes the disease
outcome. The Figure 2 below shows the difference between the mortality ratio (M.R) and the confirmed case
fatality ratio (C.F.R). C.F.R. appears quite constant oscillating between 2 -3 % whereas M.R. is important at the
beginning of the epidemic before decreasing to reach 9% On February 25th.
The difference between M.R. and C.F.R. comes from the exit ratio, i.e. the number of infected people for which
we know the outcome: either death or recovery. At the end of epidemic, as 100% of the infected people would
have one of these two outcomes, E.R will be equal to 1 and C.F.R will be equal to M.R. as shown in eq.1.
𝐶. 𝐹. 𝑅 = 𝑀. 𝑅 ×𝐸. 𝑅 (1)
The high mortality ratio at the beginning of the epidemic indicates the time needed to recover to
the disease is important, probably about 2- 4 weeks.
Figure 2: Evolution of mortality ratio (M.R.), exit ratio (E.R.) and confirmed fatality ratio
(C.F.R.)
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%
22/1
23/1
24/1
25/1
26/1
27/1
28/1
29/1
30/1
31/1
1/2
2/2
3/2
4/2
5/2
6/2
7/2
8/2
9/2
10/2
11/2
12/2
13/2
14/2
15/2
16/2
17/2
18/2
19/2
20/2
21/2
22/2
23/2
24/2
25/2
TOTAL
M.R E.R C.F.R

Figure 3: Evolution of indicators (All countries)
The high increase in cases on February 13th is due to the combination of laboratory and clinically
diagnosed case in the Hubei Province after this date. After February 16th, the number of infected people
start to diminish. Still, the exit ratio is low, 38 % as shown in Figure 2.
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
55%
60%
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
50000
55000
60000
65000
70000
75000
80000
85000
22/1
23/1
24/1
25/1
26/1
27/1
28/1
29/1
30/1
31/1
1/2
2/2
3/2
4/2
5/2
6/2
7/2
8/2
9/2
10/2
11/2
12/2
13/2
14/2
15/2
16/2
17/2
18/2
19/2
20/2
21/2
22/2
23/2
24/2
25/2
TOTAL
C.I. C.O. C.D. C.R. Cu M.R
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
13000
14000
15000
16000
22/1
23/1
24/1
25/1
26/1
27/1
28/1
29/1
30/1
31/1
1/2
2/2
3/2
4/2
5/2
6/2
7/2
8/2
9/2
10/2
11/2
12/2
13/2
14/2
15/2
16/2
17/2
18/2
19/2
20/2
21/2
22/2
23/2
24/2
25/2
TOTAL
D.I D.O D.D D.R.

3 Hubei province, China
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
13000
14000
15000
22/1
23/1
24/1
25/1
26/1
27/1
28/1
29/1
30/1
31/1
1/2
2/2
3/2
4/2
5/2
6/2
7/2
8/2
9/2
10/2
11/2
12/2
13/2
14/2
15/2
16/2
17/2
18/2
19/2
20/2
21/2
22/2
23/2
24/2
25/2
D.I D.O D.D D.R.
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
50000
55000
60000
65000
70000
22/1
23/1
24/1
25/1
26/1
27/1
28/1
29/1
30/1
31/1
1/2
2/2
3/2
4/2
5/2
6/2
7/2
8/2
9/2
10/2
11/2
12/2
13/2
14/2
15/2
16/2
17/2
18/2
19/2
20/2
21/2
22/2
23/2
24/2
25/2
C.I. C.O. C.D. C.R. Cu
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
55%
60%
65%
22/1
23/1
24/1
25/1
26/1
27/1
28/1
29/1
30/1
31/1
1/2
2/2
3/2
4/2
5/2
6/2
7/2
8/2
9/2
10/2
11/2
12/2
13/2
14/2
15/2
16/2
17/2
18/2
19/2
20/2
21/2
22/2
23/2
24/2
25/2
Hubei
M.R E.R C.F.R

4 Other provinces, China
0
100
200
300
400
500
600
700
800
900
22/1
23/1
24/1
25/1
26/1
27/1
28/1
29/1
30/1
31/1
1/2
2/2
3/2
4/2
5/2
6/2
7/2
8/2
9/2
10/2
11/2
12/2
13/2
14/2
15/2
16/2
17/2
18/2
19/2
20/2
21/2
22/2
23/2
24/2
25/2
D.I D.O D.D D.R.
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
13000
14000
22/1
23/1
24/1
25/1
26/1
27/1
28/1
29/1
30/1
31/1
1/2
2/2
3/2
4/2
5/2
6/2
7/2
8/2
9/2
10/2
11/2
12/2
13/2
14/2
15/2
16/2
17/2
18/2
19/2
20/2
21/2
22/2
23/2
24/2
25/2
C.I. C.O. C.D. C.R. Cu
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
55%
60%
65%
70%
75%
22/1
23/1
24/1
25/1
26/1
27/1
28/1
29/1
30/1
31/1
1/2
2/2
3/2
4/2
5/2
6/2
7/2
8/2
9/2
10/2
11/2
12/2
13/2
14/2
15/2
16/2
17/2
18/2
19/2
20/2
21/2
22/2
23/2
24/2
25/2
China without Hubei
M.R E.R C.F.R

5 South Korea
0
20
40
60
80
100
120
140
160
180
200
220
240
22/1
23/1
24/1
25/1
26/1
27/1
28/1
29/1
30/1
31/1
1/2
2/2
3/2
4/2
5/2
6/2
7/2
8/2
9/2
10/2
11/2
12/2
13/2
14/2
15/2
16/2
17/2
18/2
19/2
20/2
21/2
22/2
23/2
24/2
25/2
D.I D.O D.D D.R.
0
100
200
300
400
500
600
700
800
900
1000
22/1
23/1
24/1
25/1
26/1
27/1
28/1
29/1
30/1
31/1
1/2
2/2
3/2
4/2
5/2
6/2
7/2
8/2
9/2
10/2
11/2
12/2
13/2
14/2
15/2
16/2
17/2
18/2
19/2
20/2
21/2
22/2
23/2
24/2
25/2
C.I. C.O. C.D. C.R. Cu
0%
5%
10%
15%
20%
25%
30%
35%
40%
22/1
23/1
24/1
25/1
26/1
27/1
28/1
29/1
30/1
31/1
1/2
2/2
3/2
4/2
5/2
6/2
7/2
8/2
9/2
10/2
11/2
12/2
13/2
14/2
15/2
16/2
17/2
18/2
19/2
20/2
21/2
22/2
23/2
24/2
25/2
South Korea
M.R E.R C.F.R

6 Italy
0
10
20
30
40
50
60
70
80
90
100
22/1
23/1
24/1
25/1
26/1
27/1
28/1
29/1
30/1
31/1
1/2
2/2
3/2
4/2
5/2
6/2
7/2
8/2
9/2
10/2
11/2
12/2
13/2
14/2
15/2
16/2
17/2
18/2
19/2
20/2
21/2
22/2
23/2
24/2
25/2
D.I D.O D.D D.R.
0
20
40
60
80
100
120
140
160
180
200
220
240
260
280
300
320
340
22/1
23/1
24/1
25/1
26/1
27/1
28/1
29/1
30/1
31/1
1/2
2/2
3/2
4/2
5/2
6/2
7/2
8/2
9/2
10/2
11/2
12/2
13/2
14/2
15/2
16/2
17/2
18/2
19/2
20/2
21/2
22/2
23/2
24/2
25/2
C.I. C.O. C.D. C.R. Cu
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
100%
22/1
23/1
24/1
25/1
26/1
27/1
28/1
29/1
30/1
31/1
1/2
2/2
3/2
4/2
5/2
6/2
7/2
8/2
9/2
10/2
11/2
12/2
13/2
14/2
15/2
16/2
17/2
18/2
19/2
20/2
21/2
22/2
23/2
24/2
25/2
Italy
M.R E.R C.F.R

7 Japan
0
2
4
6
8
10
12
14
16
18
20
22
24
26
22/1
23/1
24/1
25/1
26/1
27/1
28/1
29/1
30/1
31/1
1/2
2/2
3/2
4/2
5/2
6/2
7/2
8/2
9/2
10/2
11/2
12/2
13/2
14/2
15/2
16/2
17/2
18/2
19/2
20/2
21/2
22/2
23/2
24/2
25/2
D.I D.O D.D D.R.
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
22/1
23/1
24/1
25/1
26/1
27/1
28/1
29/1
30/1
31/1
1/2
2/2
3/2
4/2
5/2
6/2
7/2
8/2
9/2
10/2
11/2
12/2
13/2
14/2
15/2
16/2
17/2
18/2
19/2
20/2
21/2
22/2
23/2
24/2
25/2
C.I. C.O. C.D. C.R. Cu
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
22%
24%
26%
28%
30%
32%
34%
36%
22/1
23/1
24/1
25/1
26/1
27/1
28/1
29/1
30/1
31/1
1/2
2/2
3/2
4/2
5/2
6/2
7/2
8/2
9/2
10/2
11/2
12/2
13/2
14/2
15/2
16/2
17/2
18/2
19/2
20/2
21/2
22/2
23/2
24/2
25/2
Japan
M.R E.R C.F.R

8 Iran
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
22/1
23/1
24/1
25/1
26/1
27/1
28/1
29/1
30/1
31/1
1/2
2/2
3/2
4/2
5/2
6/2
7/2
8/2
9/2
10/2
11/2
12/2
13/2
14/2
15/2
16/2
17/2
18/2
19/2
20/2
21/2
22/2
23/2
24/2
25/2
D.I D.O D.D D.R.
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
22/1
23/1
24/1
25/1
26/1
27/1
28/1
29/1
30/1
31/1
1/2
2/2
3/2
4/2
5/2
6/2
7/2
8/2
9/2
10/2
11/2
12/2
13/2
14/2
15/2
16/2
17/2
18/2
19/2
20/2
21/2
22/2
23/2
24/2
25/2
C.I. C.O. C.D. C.R. Cu
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
100%
22/1
23/1
24/1
25/1
26/1
27/1
28/1
29/1
30/1
31/1
1/2
2/2
3/2
4/2
5/2
6/2
7/2
8/2
9/2
10/2
11/2
12/2
13/2
14/2
15/2
16/2
17/2
18/2
19/2
20/2
21/2
22/2
23/2
24/2
25/2
Iran
M.R E.R C.F.R

9 Singapore
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
22/1
23/1
24/1
25/1
26/1
27/1
28/1
29/1
30/1
31/1
1/2
2/2
3/2
4/2
5/2
6/2
7/2
8/2
9/2
10/2
11/2
12/2
13/2
14/2
15/2
16/2
17/2
18/2
19/2
20/2
21/2
22/2
23/2
24/2
25/2
D.I D.O D.D D.R.
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
22/1
23/1
24/1
25/1
26/1
27/1
28/1
29/1
30/1
31/1
1/2
2/2
3/2
4/2
5/2
6/2
7/2
8/2
9/2
10/2
11/2
12/2
13/2
14/2
15/2
16/2
17/2
18/2
19/2
20/2
21/2
22/2
23/2
24/2
25/2
C.I. C.O. C.D. C.R. Cu
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
55%
60%
22/1
23/1
24/1
25/1
26/1
27/1
28/1
29/1
30/1
31/1
1/2
2/2
3/2
4/2
5/2
6/2
7/2
8/2
9/2
10/2
11/2
12/2
13/2
14/2
15/2
16/2
17/2
18/2
19/2
20/2
21/2
22/2
23/2
24/2
25/2
Singapore
M.R E.R C.F.R

10 Reference
[1] World health organization (WHO). Situation report-1, 21 January 2020
[2] World health organization (WHO). Situation report website. Available at
https://www.who.int/emergencies/diseases/novel-coronavirus-2019/situation-reports
[3] Coronavirus COVID-19 Global cases by Johns Hopkins CSSE. Available at
https://gisanddata.maps.arcgis.com/apps/opsdashboard/index.html#/bda7594740fd4029942346
7b48e9ecf6
[4] E. Dong, H.Du, L. Gardner (2020). An interactive web-based dashboard to track COVID-19 in
real time. The Lancet infectious diseases. Available at
https://www.sciencedirect.com/science/article/pii/S1473309920301201?via%3Dihub (article)
https://github.com/CSSEGISandData/COVID-
19/tree/master/csse_covid_19_data/csse_covid_19_time_series (data)
[5] World health organization (WHO). Situation report-30, 19 February 2020