A significant increase in the number of coronavirus cases can easily be noticed in most of the countries around the world. Inspite of the consistent preventive initiatives being taken to contain the spread of this virus, the unabated increase in the cases is both alarming and intriguing. The role of mathematical models in predicting and estimating the spread of the virus, and identifying various preventive factors dependencies has been found important and effective in most of the previous pandemics like Severe Acute Respiratory Syndrome (SARS) 2003. In this research work, authors have proposed the Susceptible-Infectected-Removed (SIR) model variation in order to forecast the pattern of coronavirus disease (COVID-19) spread for the upcoming eight weeks in perspective of Saudi Arabia. The study has been performed by using SIR model with a proposed simplification using average progression for further estimation of β and γ values for better curve fittings ratios. The predictive results of this study clearly show that under the current public health interventions, there will be an increase in the COVID-19 cases in Saudi Arabia in the next four weeks. Hence, a set of strong health primitives and precautionary measures are recommended in order to avoid and prevent the further spread of COVID-19 in Saudi Arabia.
Coronavirus disease, commonly named as (COVID-19), is caused by Severe Acute Respiratory Syndrome 2 (SARS-CoV-2) and the first case of the virus was detected in Wuhan city of south China. After few days, the World Health Organization (WHO) declared it to be a pandemic [1,2]. COVID-19 pandemic has brought the whole world at a standstill. The last few months have witnessed an exponential growth and spread around the globe. So far, the tally of COVID-19 cases around the world is 29487100. Since the COVID-19 cases continue to rise at a relentless pace, more inventive mechanisms need to be worked at to not only detect but also predict the possible spread of the contagion. Prompt prediction mechanisms of the disease will aid in the implementation of more effective countermeasures [3–5]. In this paper, the authors have discussed the prediction of the spread of COVID-19 cases in the coming months in Saudi Arabia. So far total number of cases on Johns Hopkins University (JHU) is 29487100, out of which 326930 are from Saudi Arabia. The rapid increase in cases can only be stemmed by efficacious vaccination. However as per several laboratories working on developing vaccines, even the earliest launch of any safe and inclusive vaccination campaign is not likely to happen in 2020. Continuous battle with the virus has already rendered the healthcare systems across the world fragile and the situation is likely to worsen in the coming months due to change in the climate and increase in human to human contact as the cities across the world open to the unlock mode. One possible solution in this league would be early prediction of the spread of the virus so that remedial interventions can be introduced to contain the infection. More specifically in the context of Saudi Arabia, it is one of the first twenty countries in the world. Hence, preemptive measures to predict the reach of virus and identify the more vulnerable zones will add to the steps being undertaken in Saudi Arabia for combating the spread of COVID-19.
The economy of Saudi Arabia is based on petroleum sector and 87% of the total revenue is generated from this sector alone [6]. 90% of this revenue is drawn from the earnings due to export, which is 42% of the country’s Gross Domestic Product (GDP). Saudi oil reserves are ranked second in the world and the country is the world’s leading oil exporter. The oil reserves are largely managed by stated owned corporation Saudi Amarco. The private sector of Saudi Arabia also plays a vital role in the economy and accounts for 40% of GDP. With a booming economy and a thriving petroleum industry, Saudi Arabia is known to be the prized destination for professionals from across the world. As per the last available data of 2013, 7.5 million foreigners work legally in petroleum industry in Saudi Arabia, forming an important part of the country’s workforce and economy. Unfortunately, COVID-19 has reversed the economic growth curve and the economists believe that more rude shocks are expected in the aftermath of the pandemic. Recession has already arrived in Saudi Arabia, and the oil prices are at all-time low in two decades. Lockdowns in almost all parts of the world deteriorated the condition of tourism and other industries, ultimately affecting the balance of demand and supply. Most of the countries are reeling under the pressure of economic crisis, and the global economy will take sufficient amount of time to revive. Many economists have stated that stable, complex and diverse economies will be able to cope and handle future shocks in an effective manner as they are more adaptable. Now almost all parts of the earth are exposed to this virus and so far large community of population has got infected. SARS-CoV-2 is the biggest challenge for humanity at present. Further, we propose forecasting the outbreak of COVID-19 in following next two months for public health practitioners in managing the COVID-19 crisis in Saudi Arabia. The study focuses on the analysis of data of COVID-19 confirmed cases, death cases and recovered cases and figure out the infection rate and removal rate in order to estimate the outbreak. The structure of this paper is as follows: Section 1 introduces COVID-19 situation around the globe, especially in Saudi Arabia. Section 2 describes the related works of different computational models that have been used for the prediction of COVID-19. Section 3 explains data collections and modelling. Section 4 defines the methodologies for performance measures estimation. Data analysis and validation is explained in Section 5. In Section 6 prediction and control measures are analyzed.
Related Work
Huang, collected and analyzed data on patients with laboratory confirmed COVID-19 infection by real time Polymerase Chain Reaction (PCR) and next generation sequencing [1]. Lauer, estimated the incubation period of COVID-19 [2]. Alzahrani, implemented the epidemic situation and forecasting of COVID-19 in Saudi Arabia using Autoregressive Integrated Moving Average (ARIMA) model [3]. Cooper, purposed the assumption of COVID-19 spread in different communities using SIR model [4]. Yang, optimized the modified Susceptible-Exposed-Infectious-Removed (SEIR) model and Artificial Intelligence (AI) has been used to forecast the epidemic trends of in COVID-19. Here four parameters like susceptible, exposed, infectious and removed has taken into account to determine the probability of transmission and authors also used AI approach, trained on SARS data, to predict the epidemic [5]. Waqas [6], presented the prediction of COVID-19 for Pakistan and Zhong [7] predicted for mainland China using time dependent SIR model. Waqas and Zhong have determined input variables like infection rate β(t) by using Eq. (6) however Zhong added some modification in equation of β(t) and recovery rate γ(t) by using Eq. (7). Moreover analysis is then performed to predict the pandemic situation based on different value of recovery rate Y(t) respectively. Roda, estimated the impact of the Wuhan lockdown and traffic restriction in the Wuhan city after January 23 and February 6, 2020 and suggested if more restriction control and prevention measures were not implemented in the city, the epidemic will monotonically increase [8]. Malavika carried out the short term projection of new cases to predict the maximum number of active cases in India and high incidence states. Here authors used Logistic Growth Curve (LGC) model, SIR model and regression model to estimate the impact of lock down and other interventions [9]. Tuli, has explored several new directions of research for the current and future pandemics [10]. Ghosh, defined the data driven understanding of COVID-19 dynamics using optimized cellular data [11]. Similarly Hartono, explored the dynamics of COVID-19 using neural networks predictor namely Long Short Term Memory (LSTM) [12]. Finalli, forecasted the COVID-19 spreading in Italy, China and France in the time window of 22 January to 15 March 2020. Here authors has defined the predictive trends based on the fits of the Susceptible-Infected-Recovered-Deaths (SIRD) model [13]. D’Arienzo, studied the early spread of SARS-CoV-2 in Italy, and found the range of basic reproduction number associated with Italian outbreak [14]. Ceylan, defined the significance of different time series method for estimation of COVID-19 prevalence in Italy and found that ARIMA (0, 2, 1), ARIMA (1, 2, 0) are best model for Spain, France and Italy [15]. Mahajan, considered purely asymptomatic infected persons along with the symptomatic cases and also determined the impact of number of test case per and lock down on contamination of COVID-19 [16]. Mahajan, applied the SIR model for outbreak prediction of COVID-19 in India and USA [17]. Rafiq, studied the contamination spread of COVID-19 worst hit in 10 most affected states of India, authors has developed an epidemic model to simulate and predict the rapid increases in new infected cases in India for 30 days ahead prediction window [18]. Sarkar, explained the transmission dynamics of COVID-19 by conducting the sensitive analysis to identify the most effective parameters using the real data up to 30 April [19]. Bagal, studied the classical SIR model approach to identify the different parameters for India [20]. Authors defined the various assumptions for fitting of the model in the Python simulation for each lockdown scenario. Eikenberry, defined the pandemic peak scenario in New York and Washington and also discussed the impact of mask use by general and asymptomatic public [21]. Zhao, studied the MH optimization algorithm is used to predict the epidemic spreading spreads in six African countries [22]. Finally, analyzed and forecast the COVID-19 spreading in China, Italy and France [23]. He discussed the impact of returning back to work on the transmission of the disease and different strength of control measures [24]. Weissman, projected the different COVID-19 related demands like hospital beds, ICU, ventilators and when it would be sutured in 3 hospitals located in Philadelphia [25]. Ndairou, explained the case study of Wuhan by considering the sensitive of basic reproduction number with respect to the parameters of the model [26]. Albert, analyzed the epidemic evolution in China and Italy and predicted those extrapolations is not only depend on quality of data but also on stage of epidemics [27]. Wieczorek, presented the research result based on neural network model for COVID-19 spread prediction [28]. Vaishnav, analyzed the effect of lockdown relaxation on COVID-19 in India [29]. Huang, defined the impact of implement schedule and intensity of containment policies of the spread of COVID-19 [30]. Alrashed, described the impact of lock down on infection rate of COVID-19 in Saudi Arabia [31]. Now, the Fig. 2 demonstrate the situation of COVID-19 in Saudi Arabia till 15 September based the real data of confirmed, death and recovered data collected from JHU dashboard.
Total confirmed, death and recovered cases scenario in Saudi Arabia
Data Collection and Modeling
The first case in Saudi Arabia was detected in the month of March in 2020. From then on, the COVID-19 cases tally has reached to 326930 confirmed cases. There are 17570 active cases and 4338 deaths due to COVID-19. The data used in this paper has been taken from COVID-19 dashboard by the Center for System Science and Engineering (CSSE) at JHU. This university provides a daily update on the global map of the pandemic at- https://coronaviru s.jhu.edu/map.html. The dataset provided by the JHU is most widely used by researchers and journal media. This dashboard provides the latest epidemiological data from January 2020 onwards and the data includes the count of confirmed cases, deaths and the number of recovered patients. In this research work, the authors have collected daily number of confirmed cases, deaths and recovered COVID-19 cases data with specific reference to Saudi Arabia. The period which has been taken in account is from 1 March 2020 to 15 September 2020. Fig. 1 represents the situation of COVID-19 till present.
Model Description
This research work focuses on forecasting the spread of COVID-19 by using the computation mathematical model. The simplest and most widely applied model structure is SIR model. SIR model is used for forecasting the spread of infectious disease, this mathematical model is helpful in defining the important concept of probability of disease to be an epidemic or not. SIR is the epidemiological model used to define the theoretical number of individuals contained within an infectious ailment in a closed period of time.
Forecasting by SIR Model
The model was given by Kermack and Mckendrick in 1927. In this research work, the standard SIR model is used to find out the spread of COVID-19 in the next 60 days. The growth index has been calculated from March 2020 to September 2020. The SIR model is one of the simplest models; it has three main components of: Susceptible (S), Infectious (I) and Removed (R).
Susceptible: are people who are most likely to be infected. In this case, it can be assumed from the very beginning itself that everybody is going to be in the susceptible category. Thus, around 34,937,072 are susceptible as this disease is contagious.
Infected: represents the fraction of population that is infected
Removed: represents number of removed individual who have good immune system and hence are not likely to be infected. or decrease individual
So, the assumption as an Eq. (1) by saying that sum of the susceptible, the infected and recovered people adds on to represent entire population N.
S(t)+I(t)+R(t)=N
where, S(t), I(t) and R(t) represent the number of susceptible, infected, recovered individuals over time, respectively. The population of three classes is governed by the following system of differential equation means the rate of change with respect of T, dS/dt means how the number of susceptible is changing in time, dI/dt how the number of infected people is changing expect a time and likewise dR/dt the number of recovered people how that is changing with respect of time hence the equation for each of these in this model are
dS/dt=−βSI
where [β] = contacts per infected person per day
dI/dt=βSI−γI
dR/dT=γI
where [γ] = recoveries per person per day
Notation of Eq. (2) means the change in S over the change in time which is going to decrease because the susceptible are getting smaller as the time goes on and as per the transition to being infected, it is a negative with constant β it is sort of proportionally constant and then multiply by S and I together because the larger that multiplication is the larger the number of interactions between susceptible and infected people are, that’s why dS/dt shows change in susceptible people that depend on the more there are connections between the S and the I. So, in this model, the unit β(t) constant represents infectious rate. The depletion in susceptible population depends upon both S and I.
The impact on infected population is as shown in Eq. (3), it defines the rate of change which is not negative in case of dI/dt but positive because the infected people is that susceptible people transition to infect it so if we lost -βSI out of the susceptible then there is gain in the infected as well get plus βSI but it is not the only factor that affects infecting people, but there are also losses of infected people when they get recovered from the disease when their immune system sort of kicks in, and they fight it off, and then they are no longer capable of infecting anybody so that happens there is loss of infected people therefore negative γI turn the more infected, there are the bigger the rate of change of infect. So, rate in change infected population is depended on both time variant constant β and γ. The rate of change of recovered population is represented in Eq. (4) this notation explains that it is just opposite of the rate at which transit to infected population so the dR/dt, the rate of change of recovered people with respect of change of time is just the rate at which the infected people get transit to recovered people that’s depends on how good the medical treatment or immunity of people, this model relates these two constants beta is contacts per infected person per day and γ is recoveries per person per day. Another most important parameter R0, which represents basic reproduction rate can be defined as β(t) over γ(t). Here R0 is actually used to define the peak position of distribution of infected population with reference to time. The parameter R0 is directly influenced by β(t) and γ(t), as R0 is directly proportional to β(t) and inversely proportional to γ(t). When R0 reaches equal to one, then the infection is going to spread in population, and if it is less than one, it will not spread exponentially in the population. The increase in the contact rate can exponentially increase the spread of disease, however it can be reduced by social distancing by reducing the contacts per day.
Model Performance Measures: β and γ
In order to implement the SIR model, the primary step is to estimate the parameters β and γ, where β is defined as the contacts per infected person per day and γ is rate of recovery and death in infected population. Using epidemic data of Saudi Arabia from JHU, we modeled the SIR model to determine the probability of COVID-19 transmission, for that β and γ are derived. The above set of equations can be further simplified for prediction of COVID-19 pandemic. Eq. (5) in the finite difference form by using discrete function is as follows:
I(t+Δt)=I(t)+(β−γ)I(t)Δt
where ∆t is interval of numerical integration and the change in susceptible in unit time is combined into infection rate β with the definition of:
βt=[I(t+Δt)−I(t)]/[I(t)Δt]
The second parameter of the model γ represents the difference of recoveries can be described as:
γt=[R(t+Δt)−R(t)]/[I(t)Δt]
For performing the prediction of cumulative infected cases, firstly both of the time variant β and γ are need to be set, then it can be determined by using Eq. (5). To estimate the situation of real epidemic transition, β can be estimated via fitting the epidemiological data. Another parameter, recovery rate (γ) can also be obtained using the similar method. Here, Eqs. (6) and (7) have been used for estimation of β and γ respectively. With the estimation of infection rate β(t) and removed infective γ(t), we can estimate the further cumulative number of infected cases I(t).
Method for Performance for Measures Estimation
We collected the daily number of confirmed cases, deaths and recovered cases by JHU dashboard from 1 March to 15 September and create a real time database. In Saudi Arabia, the total infected population has increased from zero to 326930 in last seven months as shown in Tab. 1. By using the Eqs. (6) and (7), two important time variant constant infection rate β(t) and removal rate γ(t) have also been approximated.
Cumulative infected cases and recovered cases estimated by SIR model
Date
I(t)
R(t)
β(t)
γ(t)
Predicted I(t)
01-03-2020
0
0
0
0
0
02-03-2020
1
0
0
0
0
03-03-2020
1
0
0
0
1
04-03-2020
1
0
0
0
1
05-03-2020
5
0
4
0
1
06-03-2020
5
0
0
0
6
07-03-2020
5
0
0
0
6
08-03-2020
11
0
1.2
0
6
09-03-2020
15
0
0.363636
0
14
10-03-2020
20
1
0.333333
0.066667
19
11-03-2020
21
1
0.05
0
24
12-03-2020
45
1
1.142857
0
30
13-03-2020
86
1
0.911111
0
38
14-03-2020
103
1
0.197674
0
47
15-03-2020
103
1
0
0
60
16-03-2020
118
2
0.145631
0.009709
75
17-03-2020
171
6
0.449153
0.033898
95
18-03-2020
171
6
0
0
119
19-03-2020
274
6
0.602339
0
150
20-03-2020
344
8
0.255474
0.007299
189
21-03-2020
392
16
0.139535
0.023256
238
22-03-2020
511
16
0.303571
0
300
23-03-2020
562
16
0.099804
0
378
24-03-2020
767
29
0.364769
0.023132
477
25-03-2020
900
31
0.173403
0.002608
601
26-03-2020
1012
36
0.124444
0.005556
757
27-03-2020
1104
38
0.090909
0.001976
953
28-03-2020
1203
41
0.089674
0.002717
1201
29-03-2020
1299
74
0.0798
0.027431
1514
30-03-2020
1453
123
0.118553
0.037721
1907
31-03-2020
1563
175
0.075705
0.035788
2403
01-04-2020
1720
280
0.100448
0.067179
2616
02-04-2020
1885
349
0.09593
0.040116
2852
03-04-2020
2039
376
0.081698
0.014324
3108
04-04-2020
2179
449
0.068661
0.035802
3388
05-04-2020
2402
522
0.102341
0.033502
3693
06-04-2020
2605
589
0.084513
0.027893
4025
07-04-2020
2795
656
0.072937
0.02572
4388
08-04-2020
2932
672
0.049016
0.005725
4782
09-04-2020
3287
710
0.121078
0.01296
5213
10-04-2020
3651
732
0.110739
0.006693
5682
11-04-2020
4033
772
0.104629
0.010956
6193
12-04-2020
4462
820
0.106372
0.011902
6751
13-04-2020
4934
870
0.105782
0.011206
7358
14-04-2020
5369
962
0.088164
0.018646
8021
15-04-2020
5862
1010
0.091823
0.00894
8743
16-04-2020
6380
1073
0.088366
0.010747
9529
17-04-2020
7142
1136
0.119436
0.009875
10387
18-04-2020
8274
1421
0.158499
0.039905
11322
19-04-2020
9362
1495
0.131496
0.008944
12341
20-04-2020
10484
1593
0.119846
0.010468
13451
21-04-2020
11631
1749
0.109405
0.01488
14662
22-04-2020
12772
1926
0.0981
0.015218
15982
23-04-2020
13930
2046
0.090667
0.009396
17420
24-04-2020
15102
2176
0.084135
0.009332
18988
25-04-2020
16299
2351
0.079261
0.011588
20697
26-04-2020
17522
2496
0.075035
0.008896
22559
27-04-2020
18811
2675
0.073565
0.010216
24590
28-04-2020
20077
2936
0.067301
0.013875
26803
29-04-2020
21402
3110
0.065996
0.008667
29215
30-04-2020
22753
3325
0.063125
0.010046
31845
01-05-2020
24097
3724
0.059069
0.017536
32461
02-05-2020
25459
3941
0.056522
0.009005
33759
03-05-2020
27011
4318
0.060961
0.014808
35110
04-05-2020
28656
4667
0.060901
0.012921
36514
05-05-2020
30251
5631
0.05566
0.03364
37975
06-05-2020
31938
6992
0.055767
0.04499
39494
07-05-2020
33731
8017
0.05614
0.032093
41073
08-05-2020
35432
9349
0.050428
0.039489
42716
09-05-2020
37136
10383
0.048092
0.029183
44425
10-05-2020
39048
11703
0.051486
0.035545
46202
11-05-2020
41014
12992
0.050348
0.033011
48050
12-05-2020
42925
15521
0.046594
0.061662
49972
13-05-2020
44830
17895
0.04438
0.055306
51971
14-05-2020
46869
19334
0.045483
0.032099
54050
15-05-2020
49176
22161
0.049222
0.060317
56212
16-05-2020
52016
23968
0.057752
0.036746
58460
17-05-2020
54752
26034
0.052599
0.039719
60799
18-05-2020
57345
29068
0.047359
0.055414
63230
19-05-2020
59854
31963
0.043753
0.050484
65760
20-05-2020
62545
33817
0.044959
0.030975
68390
21-05-2020
65077
36391
0.040483
0.041154
71126
22-05-2020
67719
39367
0.040598
0.04573
73971
23-05-2020
70161
41615
0.036061
0.033196
76930
24-05-2020
72560
43910
0.034193
0.03271
80007
25-05-2020
74795
46067
0.030802
0.029727
83207
26-05-2020
76726
48861
0.025817
0.037355
86535
27-05-2020
78541
51447
0.023656
0.033704
89997
28-05-2020
80185
54994
0.020932
0.045161
93597
29-05-2020
81766
57471
0.019717
0.030891
97340
30-05-2020
83384
59363
0.019788
0.023139
101234
31-05-2020
85261
62945
0.02251
0.042958
105283
01-06-2020
87142
64831
0.022062
0.02212
109495
02-06-2020
89011
66339
0.021448
0.017305
111685
03-06-2020
91182
68738
0.02439
0.026952
113918
04-06-2020
93157
69576
0.02166
0.00919
116197
05-06-2020
95748
71258
0.027813
0.018056
118521
06-06-2020
98869
72467
0.032596
0.012627
120891
07-06-2020
101914
73529
0.030798
0.010741
123309
08-06-2020
105283
75270
0.033057
0.017083
125775
09-06-2020
108571
77122
0.03123
0.017591
128290
10-06-2020
112288
78773
0.034236
0.015207
130856
11-06-2020
116021
80876
0.033245
0.018729
133473
12-06-2020
119942
81922
0.033796
0.009016
136143
13-06-2020
123308
83480
0.028064
0.01299
138866
14-06-2020
127541
85692
0.034329
0.017939
141643
15-06-2020
132048
88901
0.035338
0.025161
144476
16-06-2020
136315
90592
0.032314
0.012806
147365
17-06-2020
141234
92753
0.036086
0.015853
150313
18-06-2020
145991
95054
0.033682
0.016292
153319
19-06-2020
150292
96948
0.029461
0.012973
156385
20-06-2020
154233
100147
0.026222
0.021285
159513
21-06-2020
157612
102397
0.021908
0.014588
162703
22-06-2020
161005
106482
0.021528
0.025918
165957
23-06-2020
164144
111231
0.019496
0.029496
169277
24-06-2020
167267
114184
0.019026
0.01799
172662
25-06-2020
170639
119310
0.020159
0.030646
176115
26-06-2020
174577
121945
0.023078
0.015442
179638
27-06-2020
178504
123639
0.022494
0.009703
183230
28-06-2020
182493
126306
0.022347
0.014941
186895
29-06-2020
186436
128717
0.021606
0.013211
190633
30-06-2020
190823
132415
0.023531
0.019835
194446
01-07-2020
194225
134458
0.017828
0.010706
190676
02-07-2020
197608
139421
0.017418
0.025553
192583
03-07-2020
201801
142416
0.021219
0.015156
194509
04-07-2020
205929
145114
0.020456
0.01337
196454
05-07-2020
209509
147152
0.017385
0.009897
198418
06-07-2020
213716
151602
0.02008
0.02124
200402
07-07-2020
217108
156856
0.015872
0.024584
202406
08-07-2020
220144
160109
0.013984
0.014983
204431
09-07-2020
223327
163196
0.014459
0.014023
206475
10-07-2020
226486
165177
0.014145
0.00887
208540
11-07-2020
229480
167577
0.013219
0.010597
210625
12-07-2020
232259
169361
0.01211
0.007774
212731
13-07-2020
235111
172085
0.012279
0.011728
214859
14-07-2020
237803
179843
0.01145
0.032997
217007
15-07-2020
240474
185373
0.011232
0.023255
219177
16-07-2020
243238
189992
0.011494
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221369
17-07-2020
245851
193568
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223583
18-07-2020
248416
196665
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225818
19-07-2020
250920
200221
0.01008
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228077
20-07-2020
253349
205782
0.00968
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230357
21-07-2020
255825
209816
0.009773
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232661
22-07-2020
258156
212999
0.009112
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234988
23-07-2020
260394
216125
0.008669
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237337
24-07-2020
262772
218403
0.009132
0.008748
239711
25-07-2020
264973
220485
0.008376
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242108
26-07-2020
266941
223056
0.007427
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27-07-2020
268934
225696
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246974
28-07-2020
270831
228413
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29-07-2020
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31-07-2020
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277478
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02-08-2020
278835
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03-08-2020
280093
245004
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237132
04-08-2020
281456
246697
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282824
248334
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06-08-2020
284226
250144
0.004957
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239989
07-08-2020
285793
252041
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08-08-2020
287262
253570
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09-08-2020
288690
255206
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10-08-2020
289947
256677
0.004354
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243852
11-08-2020
291468
258351
0.005246
0.005773
244827
12-08-2020
293037
260538
0.005383
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13-08-2020
294519
263696
0.005057
0.010777
246789
14-08-2020
295902
266297
0.004696
0.008831
247777
15-08-2020
297315
267856
0.004775
0.005269
248768
16-08-2020
298542
270361
0.004127
0.008425
249763
17-08-2020
299914
271821
0.004596
0.00489
250762
18-08-2020
301323
276381
0.004698
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251765
19-08-2020
302686
277597
0.004523
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252772
20-08-2020
303973
279024
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21-08-2020
305186
280647
0.00399
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254798
22-08-2020
306370
282060
0.00388
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255817
23-08-2020
307479
283792
0.00362
0.005653
256841
24-08-2020
308654
286579
0.003821
0.009064
257868
25-08-2020
309768
287654
0.003609
0.003483
258900
26-08-2020
310836
288700
0.003448
0.003377
259935
27-08-2020
311855
290040
0.003278
0.004311
260975
28-08-2020
312924
291216
0.003428
0.003771
262019
29-08-2020
313911
292281
0.003154
0.003403
263067
30-08-2020
314821
293537
0.002899
0.004001
264119
31-08-2020
315772
294693
0.003021
0.003672
265176
01-09-2020
316670
295443
0.002844
0.002375
302239
02-09-2020
317486
296466
0.002577
0.00323
302843
03-09-2020
318319
297946
0.002624
0.004662
303449
04-09-2020
319141
299078
0.002582
0.003556
304056
05-09-2020
319932
299891
0.002479
0.002547
304664
06-09-2020
320688
300818
0.002363
0.002897
305273
07-09-2020
321456
301730
0.002395
0.002844
305884
08-09-2020
322237
302383
0.00243
0.002031
306495
09-09-2020
323012
303131
0.002405
0.002321
307108
10-09-2020
323720
304187
0.002192
0.003269
307723
11-09-2020
324407
305146
0.002122
0.002962
308338
12-09-2020
325050
306076
0.001982
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308955
13-09-2020
325651
307138
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14-09-2020
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310812
Data Analysis and Validation
The objective of data analysis is to figure out outbreak of the pandemic in Saudi Arabia in the next two months. Based on the information about the epidemic transition in Switzerland, Italy and Spain, the same model has been proposed to predict the outbreak of COVID-19 in October and November of 2020. In the above mentioned courtiers, the values of time variant constant β and γ have been optimized, The optimized values of β(t) and γ(t) align with the data of these countries apart from the peak date prediction which is based on active infected cases rate. The first model that was suggested for the validation purpose was implemented on the countries where the pandemic had either finished or was in the last stage, like Switzerland, Italy and Spain. The β(t) and γ(t) estimation procedure concur sensibly well with the information of these countries, apart from the peak date of pandemic which depends on the circulation of dynamic trained cases as appeared. The fixed value estimation of β(t) and γ(t) could cause the inconsistency in forecasting the pandemic. These parameters have been estimated from 1 March to 15 September for Spain, Switzerland and Italy. Accordingly the distribution of cumulative invectives with respect of time for Switzerland, Italy and Spain are shown in Figs. 2–4, respectively.
Cumulative infectives as function of time for Switzerland
Cumulative infectives as function of time for Italy
Cumulative infectives as function of time for Spain
First cases of COVID-19 were found on 25 February in Switzerland, 31 January in Italy and 1 February in Spain and the total cumulative tally was 50106, 307597, 736583, respectively, up to 15 September, which can be compared with the actual cumulative cases data available on JH are as 47751 in Switzerland, 289990 in Italy, 603167 in Spain. Prediction is very much closer, as demonstrated in Figs. 2–4. The outcome validates our procedure of analysis and also provides the confidence to precisely forecast the pandemic situation for Saudi Arabia. The first confirmed case of COVID-19 was identified on 3rd March in Saudi Arabia, so initially, the infection rate β(t) was zero, but on 5th March, the infective cases increased to 5. Subsequently, in 5 days on 10 March, it reached to 20, which led to the infection rate β(t) to be at 0.33. In the early phase, the recovery rate γ(t) was also zero, but on 10 March for the first time, it jumped to 0.66 when one person recovered. But in following two days, on 12th March, the infection rate β(t) increased sharply and reached to 1.12. From 10th March onwards, the infection cases became more than double. The spike in the number of infective cases reported on March 17 resulted in β(t) rising pointedly. In view of the sudden rise in the β(t), the number of infective led to more testing, especially at community level to determine the Corona cases. To figure out the scenario of COVID-19 in Saudi Arabia, the value of β(t) and γ(t) constants have been calculated with the help of Eqs. (6) and (7) for seven months as shown Tab. 1. These generated values are further passed as an input in SIR model. To build a model on training data, we first calculated the β(t) from March to September by using real data available on JHU, then average of time dependent variant infection rate β(t) was obtained for March 2020. Similarly, the average β(t) was calculated for April, May, June, July, August September. Similarly, by using the Eq. (6), the infected cases I(t) was calculated for March to September which was slightly on the higher side of actual infected cases because here the recovery cases are not considered. Fig. 5 explains the scenario of COVID-19 spread in case, if only β(t) is considered to estimate the infective cases. For pandemic prediction and evaluation in the coming months, the parameterization of β(t) and γ(t) both are required so that it can be passed in SIR model for precise prediction of actual infected cases. For this, we also need to find out the exponential fit of γ(t)parameter. γ(t) is slow varying variable so the average value of γ(t) from March to September has been estimated to find out the suitable fit of removal rate γ(t) parameter.
Cumulative infective cases based on parametrize β(t) and Y(t) as function of time
In this analysis, different optimize window of β(t) and γ(t) have been used instead of fix values for accurate prediction of cumulative I(t), optimized window of time varying variable β(t) and γ(t) is considered. The infected cases obtained by SIR model from March to September, is quite close to the actual data available on the dashboard of JHU, as shown in Fig. 5. This also provides the confidence to precisely forecast the pandemic situation for the following two months of Saudi Arabia. The modeling has been done for forecasting the outbreak of COVID-19 in next two months, based on the previous learning of β(t) and γ(t). The prediction has to be made by using several subset window of different value of β(t) and γ(t). Infection rate considered here is 0.003 in October, and 0.002 in November Similarly the Recovery Rate γ(t) is 0.004 in October, and 0.003 in November. Predictions show that there are likely to be 351082 COVID-19 cases in October, and 373142 cases in November in Saudi Arabia. Any changes in Safe Measures, Social Distancing could rapidly affect the prediction outcome. The cumulative infective cases with time varying variable β(t) and γ(t) are represented in Fig. 5. The recovery rate γ(t) with the value of 0.004 shows a significant change in cumulative infective cases. In October, the total number of infective cases may reach to a recovery rate of 0.003 in November. This suggests that better health care, and following the safety and precautionary measures can shorten the period of pandemic.
Results and Conclusion
The input epidemiological data of COVID-19 spread has been discussed in Tab. 1 of this paper. Two inputs- infection rate β(t) and removal rate γ(t) have been estimated by Eqs. (6) and (7). For this, the parameterization of both variables β(t) and γ(t) exponential fits for model has been defined. The validation of analysis procedure is based on the data obtained through the use of similar model in Switzerland, Italy and Spain where COVID-19 cases are on decline. The agreeability of the prediction results obtained from the SIR in these countries further corroborates the use of SIR for the prediction of COVID-19 cases in Saudi Arabia. Following are the prediction and control measures:
Prediction
In this study, the predictions have been made for infective cases of COVID-19 in Saudi Arabia in October and November by using mathematical modeling SIR and respective curve fittings. The estimate shows that at the beginning of the spread, the infection rate was around 0.26. After that, preventive measures have been taken and the infection rate further declined to 0.002. This implies that the transmission rate should also subside to some extent. In Fig. 5, the simulation shows the dynamics of the spread of COVID-19 after 197 days. With the help of this assumption and different important estimation, we can predict the trend of the spread of contagious diseases in Saudi Arabia
Control Measures
Various important measures have already been taken into consideration to prevent the transmission of COVID-19 disease. People are quarantined at home, most of the companies have stopped their working and schools have been closed as one of the preventive measures. These preventive steps have certainly reduced the transmission rate of COVID-19. But still there are questions for which there are yet no definitive answers like, how long will such situations linger on and when will the normalcy be restored. If people go back to their work and schools will reopen, will it increase the contact rate? Based on these assumptions and fixing other parameters according to data fitting, authors have numerically investigated the current dynamics of Corona spread in Saudi Arabia. In Fig. 4, the authors have demonstrated the total confirmed cases. As per the statistical analysis, continuous growth can be seen in the next two months as depicted in Fig. 4. Thus, for controlling the transmission rate further, we need to control the contact rate. So, a set of strong precautionary measures are recommended in order to prevent the further spread of COVID-19 in Saudi Arabia.
Funding Statement: The authors received no specific funding for this study.
Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.
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