Research Article
Austin J Infect Dis. 2021; 8(4): 1058.
Research on the Fluctuation Trend of the Spread of New Coronary Pneumonia Epidemic under Non-Strict Prevention and Control Conditions: Analysis Based on the Data of India’s Epidemic
Liu HL¹*, Liang Q² and Wang W³
1Associate Researcher, Health and Family Planning Statistics Information Center and Northwest Population Information Center Gansu, China
2Associate Researcher, Health Care Security Administration Gansu, China
3Health Care Security Administration Gansu, China
*Corresponding author: Hong Liang Liu, Associate Researcher, Health and Family Planning Statistics Information Center and Northwest Population Information Center Gansu, China
Received: September 06, 2021; Accepted: October 08, 2021; Published: October 15, 2021
Abstract
After a long time of joint efforts, the Covid-19 pandemic in some countries and regions has been effectively controlled, but since April 2021, the outbreak of the epidemic in India has posed new challenges for the prevention and control of the global epidemic. How to understand and interpret the rebound trend of the epidemic in India is an important reference for other regions to prevent and control the epidemic. Based on time-series analysis, this paper uses the system dynamics epidemic model to treat the population in the region as a whole and decomposes the spread of the Covid-19 in India into 4 fluctuating transmission processes. These processes show that the spread of the Covid-19 may have annual periodic characteristics and long-term trends. There is a critical period of about 45 days before the outbreak of the epidemic. The global prevention and control requires the joint efforts of all countries to end as soon as possible.
Keywords: Covid-19; Fluctuating trend; India; Non-strict Prevention and Control Conditions
Introduction
With the implementation of stricter isolation prevention and control measures and the wider application of vaccine, the prevention and control of the Covid-19 has achieved decisive progress in some countries, and the spread of the epidemic has been effectively controlled [1]. However, with the relaxing regional vigilance against the virus and the emergence of new mutations, the epidemic in some regions has a trend of secondary outbreaks, the most typical of which is India.
Since 2020, the epidemic situation in India has undergone several major stages: rapid spread, initial control, and easing. However, since late April 2021, with the holding of several large festivals such as the Big Pot Festival in India and the emergence of new mutant viruses, the Covid-19 in India is showing a trend of second outbreak. In the face of complex situations, quickly judging the trend of the epidemic and identifying key links in epidemic prevention and control are important for government to make effective decisions in the postepidemic era [2,3].
Based on limited bulletins and demographic data. This paper uses the system dynamics method to establish an estimation model of the spread of the epidemic and make a theoretical estimate of the long-term fluctuating trend of the spread of the Covid-19 under nonstrictly controlled conditions in India which has important reference value for in-depth understanding of the severity and extent of the spread of the epidemic.
Data Source
This study uses the daily updated Indian epidemic progress data published in the real-time big data report of the new coronavirus pneumonia epidemic on the Baidu platform. The population and other data come from the Indian census data (Table 1) [4].
Date
Number of newly infected
peopleDate
Number of newly infected
peopleDate
Number of newly infected
peopleDate
Number of newly infected people
Date
Number of newly infected
peopleDate
Number of newly infected
peopleDate
Number of newly infected people
4.8
565
6.4
9551
7.31
57704
9.26
72404
11.2
63702
1.18
5952
3.16
6490
4.9
809
6.5
9361
8.1
59225
9.27
125885
11.2
41822
1.19
9975
3.17
62246
4.1
875
6.6
10157
8.2
52783
9.28
45816
11.2
23157
1.2
23568
3.18
36330
4.11
846
6.7
10607
8.3
50681
9.29
69268
11.3
51126
1.21
13388
3.19
42635
4.12
759
6.8
9803
8.4
70385
9.3
88682
11.3
45960
1.22
14811
3.2
38393
4.13
1248
6.9
9300
8.5
57258
10.1
77843
11.3
17683
1.23
11166
3.21
17175
4.14
1034
6.1
11311
8.6
62815
10.2
115721
11.3
84288
1.24
15558
3.22
74892
4.15
835
6.11
12247
8.7
61455
10.3
70948
11.3
39036
1.25
10897
3.23
43924
4.16
1060
6.12
8950
8.8
71338
10.4
63762
11.3
42098
1.26
17167
3.24
53793
4.17
922
6.13
11417
8.9
69947
10.5
76778
12.1
21252
1.27
1077
3.25
14250
4.18
1370
6.14
7114
8.1
45334
10.6
73924
12.2
39172
1.28
12451
3.26
66265
4.19
1250
6.15
11703
8.11
78320
10.7
40330
12.3
33203
1.29
18241
3.27
105259
4.2
924
6.16
11636
8.12
49563
10.8
77103
12.4
36807
1.3
19338
3.28
24422
4.21
1541
6.17
11685
8.13
59240
10.9
104785
12.5
31601
1.31
9915
3.29
99523
4.22
1290
6.18
12228
8.14
74689
10.1
51254
12.6
41795
2.1
13953
3.3
20817
4.23
1669
6.19
13542
8.15
24696
10.1
66103
12.7
22218
2.2
4814
3.31
93260
4.24
1408
6.2
15448
8.16
103313
10.1
96850
12.8
25006
2.3
19145
4.01
25837
4.25
1836
6.21
21041
8.17
50058
10.1
45118
12.9
42302
2.4
10888
4.02
90046
4.26
1607
6.22
8943
8.18
47904
10.1
69665
12.1
23876
2.5
6766
4.03
156632
4.27
1561
6.23
18905
8.19
81939
10.2
73702
12.1
33578
2.6
10357
4.04
32141
4.28
1873
6.24
15940
8.2
59016
10.2
67248
12.1
30258
2.7
15132
4.05
116537
4.29
1738
6.25
15626
8.21
52164
10.2
59034
12.1
37035
2.8
14749
4.06
107822
4.3
1800
6.26
20685
8.22
112676
10.2
61197
12.1
20905
2.9
2017
4.7
114706
5.1
2394
6.27
25874
8.23
41912
10.2
37398
12.2
22800
2.1
11012
4.8
130458
5.2
2442
6.28
20416
8.24
69834
10.2
70812
12.2
8935
2.11
19701
4.9
186103
5.3
2806
6.29
14303
8.25
62089
10.2
56386
12.2
32969
2.12
2036
4.1
97141
5.4
3932
6.3
12469
8.26
74664
10.2
25924
12.2
20983
2.13
13844
4.11
183468
5.5
2963
7.1
18777
8.27
91396
10.2
54457
12.2
28024
2.14
15951
4.12
119717
5.6
3587
7.2
18783
8.28
76605
10.2
47480
12.2
31158
2.15
9027
4.13
149858
5.7
3364
7.3
20895
8.29
22737
10.3
44438
12.2
20065
2.16
11876
4.14
246155
5.8
3342
7.4
31107
8.3
106557
10.3
44438
12.2
27605
2.17
11456
4.15
307867
5.9
3113
7.5
23272
8.31
65832
10.3
56861
12.2
16455
2.18
13234
4.16
197356
5.1
4353
7.6
25160
9.1
66292
10.3
31377
12.2
29959
2.19
13048
4.17
266277
5.11
3607
7.7
26726
9.2
94694
10.3
64249
12.3
16688
2.2
20438
4.18
308056
Table 1: Statistics on the number of newly infected people in India from April 8, 2020 to May 5, 2021.
5.12
3475
7.8
21115
9.3
93883
10.3
24047
12.3
20689
2.21
8153
4.19
199100
5.13
3763
7.9
29888
9.4
88904
10.3
84009
12.3
30133
2.22
10844
4.2
288956
5.14
3942
7.1
27998
9.5
99138
11.1
30129
12.3
16072
2.23
19449
4.21
315802
5.15
3787
7.11
28928
9.6
67943
11.2
42177
12.3
12320
2.24
15811
4.22
332503
5.16
4864
7.12
23924
9.7
76468
11.3
54316
12.3
23501
2.25
13008
4.23
326769
5.17
5050
7.13
27181
9.8
76168
11.4
47251
12.3
22006
2.26
21024
4.24
350013
5.18
4463
7.14
34770
9.9
104421
11.5
28216
1.1
10404
2.27
16292
4.25
246812
5.19
3131
7.15
26543
9.1
76839
11.6
58655
1.2
17750
2.28
8697
4.26
402732
5.2
4527
7.16
41870
9.11
111760
11.7
39300
1.3
26291
3.1
18240
4.27
348279
5.21
6659
7.17
34634
9.12
82321
11.8
52731
1.4
8049
3.2
15266
4.28
307219
5.22
9595
7.18
37407
9.13
100123
11.9
45269
1.5
24396
3.3
15675
4.29
386888
5.23
6433
7.19
50203
9.14
89449
11.1
25248
1.6
18504
3.4
19039
4.3
402110
5.24
7102
7.2
36810
9.15
85055
11.1
57576
1.7
17079
3.5
19485
5.01
392562
5.25
3620
7.21
44165
9.16
97721
11.1
31108
1.8
21310
3.6
13528
5.02
370059
5.26
9085
7.22
48987
9.17
81087
11.1
60633
1.9
21727
3.7
24109
5.03
355828
5.27
4507
7.23
42903
9.18
86573
11.1
39506
1.1
12045
3.8
13702
5.04
382691
5.28
8300
7.24
60135
9.19
95429
11.2
46277
1.11
13517
3.9
18760
5.05
412618
5.29
9239
7.25
59701
9.2
93367
11.2
30820
1.12
11724
3.1
5466
5.3
8262
7.26
41030
9.21
100327
11.2
19130
1.13
12050
3.11
21327
5.31
9144
7.27
41857
9.22
62685
11.2
38480
1.14
27982
3.12
39586
6.1
5072
7.28
63594
9.23
89324
11.2
49443
1.15
14913
3.13
26583
6.2
8023
7.29
49587
9.24
96134
11.2
46110
1.16
15819
3.14
28898
6.3
11804
7.3
54966
9.25
77605
11.2
44281
1.17
10536
3.15
21669
Table 1 of 1:
Model Construction
Analysis of epidemic spread in India
The growth of the cumulative number of confirmed cases in India can be roughly divided into three main stages. The first stage is the period from India’s reporting of the number of infections to July 12, 2020. At this stage, the cumulative number of confirmed infections remains below 1 million, and the cumulative scale of infections is exponentially distributed. The exponential function is used to estimate the scale growth. Goodness of fitR2 = 0.9798, the function form is:
Pi1 = 94289e0.023i (i = 1, 2,…,96) (1)
The second stage is from July 13, 2020 to April 2, 2021. In this stage, the cumulative number of confirmed diagnoses gradually declines after experiencing a rapid increase in a slightly normal distribution. The epidemic control form is basically stable. The cumulative infection scale increases as a function of a long quadratic curve which is used to estimate the scale growth, the goodness of fitR2 = 0.9994, and the function form is:
Pi2 = 0.0115i4 - 5.9487i3 + 801.21i2 + 35756i + 895069 (i = 1, 2, …, 264) (2)
The third stage is from April 3, 2021 to May 5, 2021 (Number of changes in the scale of May 5 notified on May 6). At this stage, the cumulative number of confirmed infections returns to an exponential growth pattern. Using the double-exponential function to estimate the scale growth, the goodness of fitR2 = 0.9997, the function form is:
Pi3 = 1.954E6e-0.1129i + 1.075E7e0.0204i (i = 1, 2, …, 33) (3)
From the analysis of the changes in the scale of the cumulative number of confirmed infections, since April 2021 Covid-19 in India has entered a new round of explosive growth (Figure 1).
Figure 1: Statistics of the cumulative number of confirmed cases in India from April 8, 2020 to May 5, 2021.
Figure 2: Statistics of daily changes in the proportion of the cumulative number of confirmed diagnoses in India to the uninfected population.
Establishing a trend-fitting function based on the daily change of the proportion of the cumulative number of confirmed diagnose to the uninfected population
In order to more intuitively observe and analyze the trend of changes in the scale of the cumulative number of confirmed cases in India, this paper uses the bulletin data and the total population of India (1.354 billion people) in the census bulletin to calculate the next day’s growth rate of the cumulative number of confirmed cases to the uninfected population since April 8, 2020, and analyze its distribution [5]. A clear trend of fluctuations can be observed. Using Matlab to establish a general model of sum of Sin4 for fitting, Goodness of fit R² = 0.8818, the function form is:
Pit = a1 sin (b1i + c1) + a2 sin (b2i + c2) + a3 sin (b3i + c3) + a4 sin (b4i + c4) (i = 1, 2, …, 392) (4)
a1=0.02354, b1=0.009094, c1=-0.466; a2=0.02698, b2=0.01779, c2=0.2827; a3=0.008255, b3=0.03032, c3=0.9764; a4=0.004568, b4=0.03796, c4=3.267.
Based on the analysis of the distribution of daily changes in the proportion of the cumulative number of diagnosed people in the uninfected population, the development of the new case in India has experienced three main processes of rise, fall, and slowdown. Now it has a clear trend of entering the rising stage again.
Predictions of the future 60-day change
Assuming that from May 6, 2021, the Indian government continues to adopt stricter epidemic prevention and control measures after July 13, 2020, and can continue to provide medical assistance services, then it can be assumed that the spread of Covid-19 is likely to follow the pattern of spread since July 13, 2020 in India within the next 60 days. The fitting function (4) can be used to estimate the daily change of the cumulative number of confirmed diagnoses to the number of uninfected population in the next 60 days, and then to get the daily newly diagnosed number and cumulative number of confirmed diagnoses. The steps are as follows:
Ki = K(i-1)(1 + Pt i) (i = 393, 394,…, 454)
(i = 393, 394, …, 454) (6)
(i = 393,394,…,454) (7)
In formulas (5)-(7), Ki, Pti, PAi, P2i are the proportion of the daily cumulative number of confirmed diagnoses to the number of uninfected people, the change the proportion of the daily cumulative number of confirmed diagnoses to the number of uninfected people calculated by the fitting function (4), the daily number of newly diagnosed and daily uninfected people.
Results
The spread of the Covid-19 in India has entered a new round of rapid growth
If there is no effective epidemic prevention and control to prompt or immediately stop the interpersonal transmission of the virus and treatment methods, India will face an extremely complicated process of explosive transmission in the next 60 days. The total number of confirmed cases after 60 days is likely to exceed 40 million (Table 2).
Date
Number of diagnoses per day
Cumulative confirmed number
Date
Number of diagnoses per day
Cumulative confirmed number
Date
Number of diagnoses per day
Cumulative confirmed number
5.6
350719
21421571
5.26
404774
29413790
6.15
323210
35801920
5.7
510110
21931681
5.27
355302
29769092
6.16
257365
36059285
5.8
375741
22307422
5.28
528189
30297281
6.17
118326
36177610
5.9
456995
22764417
5.29
323830
30621112
6.18
248560
36426170
5.1
408275
23172692
5.3
291031
30912143
6.19
216715
36642885
5.11
388220
23560911
5.31
350441
31262584
6.2
202830
36845715
5.12
446031
24006943
6.1
337414
31599997
6.21
202830
37048545
5.13
370108
24377051
6.2
184080
31784077
6.22
259533
37308078
5.14
395148
24772199
6.3
351924
32136001
6.23
143215
37451293
5.15
435570
25207769
6.4
478274
32614275
6.24
293254
37744547
5.16
426158
25633927
6.5
233940
32848215
6.25
109759
37854305
5.17
457926
26091854
6.6
301716
33149932
6.26
383445
38237750
5.18
286115
26377969
6.7
442056
33591987
6.27
137519
38375269
5.19
407705
26785674
6.8
205934
33797921
6.28
192510
38567779
5.2
438788
27224461
6.9
317974
34115896
6.29
247916
38815696
5.21
354215
27578677
6.1
336401
34452296
6.3
215669
39031365
5.22
330476
27909153
6.11
306942
34759239
7.1
128787
39160152
5.23
574581
28483734
6.12
269451
35028690
7.2
267721
39427873
5.24
209120
28692854
6.13
279324
35308013
7.3
179378
39607252
5.25
316162
29009016
6.14
170697
35478710
7.4
240682
39847934
Unit: Person.
Table 2: Prediction of the number of new and cumulative diagnoses in India within 60 days after May 6, 2021.
The number of deaths will continue to increase in India
Calculated based on the estimated death rate of India’s Covid-19 reported on May 5, 2021, which is about 1%, if the cumulative number of confirmed diagnoses in India exceeds 40 million, as the pressure of treatment continues to increase, the death toll may exceed 400000 in the next 60 days people.
Adopting strict isolation and control measures is the first choice for India’s current response strategy
Based on the experience of epidemic prevention and control in various countries around the world, to maintain moderate social distance and implement strict epidemic prevention and control measures before effective protection measures for vaccination are effective measures for India.
Discussion
From the perspective of time series, the spread of the Covid-19 may have annual periodic characteristics and long-term transmission trends. If we put aside the concern about the transmission pattern of how specific cases were infected, and treat the population in the region as a whole, the transmission process of Covid-19 in India can be approximately decomposed into four different cases in a time series (Figure 3). The main reason for the large-scale spread of the epidemic in India since April 2021 can be seen as the superimposed effect caused by the fluctuation trends 2, 3, and 4 in the figure, which have entered the upward space. Among them, the trend 2 that may represent inter-annual fluctuations is the main aspect. From a practical perspective, it can be considered that the increase in the spread of the epidemic has become a reality due to the loosening of prevention and control measures.
Figure 3: Decomposition of fluctuation trends in the spread of the epidemic in India.
The outbreak trend has a critical window period of approximately 45 days for prevention and control. Observing the daily changes in the proportion of the number of infected people in the uninfected population in India, we can find that the critical turning point is the 315th day, and the exact date is February 17, 2021.It took 45 days from this day to April 2nd. During these 45 days, if strict prevention and control measures continue to be implemented, it is entirely possible that the Indian epidemic will continue to maintain a steady decline. Unfortunately, India has relaxed its epidemic prevention and control efforts during this critical period. The rebound trend of the epidemic in India has also provided warnings to other countries and regions where the epidemic is basically under control. After the epidemic is stable and controllable, strict prevention and control measures should be maintained for at least 45 days, especially in areas with strong population mobility. Normalization and strict control will be the most efficient prevention and control strategy.
The predicted value of the model may reflect the serious consequences that India will have if it does not adhere to strict prevention and control measures, but the severity of the consequences is not limited to the upper limit predicted by the model. The prevention and control of the epidemic should not only focus on densely populated urban communities, but rural areas with inconvenient transportation and insufficient medical service provision should be the key areas for strict prevention.
Faced with the risk that the new crown virus may continue to mutate, rapidly expanding the scope of effective vaccines is a permanent solution to the global pandemic of the new crown pneumonia epidemic. As long as the epidemic is still spreading in some areas and the movement of people between regions cannot be stopped, the danger of another outbreak still exists at all times. From this perspective, no matter how different the region, ethnic group, culture, system is, human beings as a group should unite and deal with it together.
The shortcomings of this study are also obvious. It did not systematically summarize the evidence of the previous research, did not do too much authenticity inference about the data source, did not list the cluster analysis process and results due to space limitations, and did not explicitly give the estimated results and process of the scale of the cured population and the dead population. These problems will be solved in detail in other follow-up studies.
Funding
Monitoring and Evaluation of the Implementation of the Gansu Population Development Plan (2016-2030) (WTHT2020-XXZX001); Gansu Health Industry Research Plan Project: Epidemic Monitoring, Prevention and Control and Emergency Management Decision Support Based on Health and Medical Big Data (GSWSKY2020-34).
References
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- Hong Liang Liu, Hong Wen Jia, et al. System Dynamics Model Estimation Method and Evaluation of the Early Spreading Scale of New Coronary Pneumonia-A Case Study of Gansu Province. Journal of Electronic Science University. 2020.
- Yan Wang, Jiyu Wu, et al. Model construction and analysis of the growth law of the mid-term scale of the spread of new coronary pneumonia--a study based on the Italian epidemic data. Northwest Population Journal. 2020: 114- 126.
- Baidu Epidemic.
- India population.