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. 2020 Jul 28;14(5):1419–1427. doi: 10.1016/j.dsx.2020.07.042

ARIMA modelling & forecasting of COVID-19 in top five affected countries

Alok Kumar Sahai a,∗, Namita Rath a, Vishal Sood a, Manvendra Pratap Singh b
PMCID: PMC7386367  PMID: 32755845

Abstract

Background and aims

In a little over six months, the Corona virus epidemic has affected over ten million and killed over half a million people worldwide as on June 30, 2020. With no vaccine in sight, the spread of the virus is likely to continue unabated. This article aims to analyze the time series data for top five countries affected by the COVID-19 for forecasting the spread of the epidemic.

Material and methods

Daily time series data from 15th February to June 30, 2020 of total infected cases from the top five countries namely US, Brazil, India, Russia and Spain were collected from the online database. ARIMA model specifications were estimated using Hannan and Rissanen algorithm. Out of sample forecast for the next 77 days was computed using the ARIMA models.

Results

Forecast for the first 18 days of July was compared with the actual data and the forecast accuracy was using MAD and MAPE were found within acceptable agreement. The graphic plots of forecast data suggest that While Russia and Spain have reached the inflexion point in the spread of epidemic, the US, Brazil and India are still experiencing an exponential curve.

Conclusion

Our analysis shows that India and Brazil will hit 1.38 million and 2.47 million mark while the US will reach the 4.29 million mark by 31st July. With no effective cure available at the moment, this forecast will help the governments to be better prepared to combat the epidemic by ramping up their healthcare facilities.

Keywords: COVID-19, SARV-2 Cov, Pandemic, ARIMA, Forecasting

Highlights

  • •

    Time series trend analysis for COVID-19 forecasting for top 5 countries.

  • •

    Considerable accuracy indicated in daily case forecasts upto September 15th.

  • •

    SARS Cov-2 explosion in India with cases doubling at fastest rate in the world.

  • •

    Useful forecast for governments to ramp up their healthcare preparations.

The Corona pandemic which originated in Wuhan, China in December 2019 has spread out to the whole world and in six months has caused unprecedented havoc. This extremely virulent strain of corona virus is highly contagious and has already affected over 10,101,998 cases worldwide and has claimed 501,644 lives within seven months [1]. The earlier instances of corona virus namely SARS and MERS were not as contagious and persistent as the 2019-nCov or COVID-19 as it has come to be known. The confusion and lack of transparency in the initial stages of the outbreak only worsened the situation and today 185 countries are suffering from the virus with no cure in sight. The virus in the current form is highly contagious and causes death due to respiratory failure. Due to the differences in epidemiological conditions and testing facilities the spread of the virus has been varied in countries. The worst affected are developed countries like Spain, Italy, France, Germany and the US. Today, US tops the list followed by Brazil, Russia, India and Spain respectively [1].

In India, the first case of COVID19 was reported on January 30, 2020 and the spread in India was extremely slow. As the severity of the viral infection became known the Government of India resorted to a complete lockdown to contain the spread of the virus. The first lockdown was announced on 25th March which was extended gradually till the end of May. Owing to the all-round collapse of the industry and the miseries of the daily wage earners and migrant labours, the government decided to lift the lockdown in a phased manner from June 2, 2020. Migrant labours from the two hotspots of New Delhi and Mumbai migrated to their home states and this large scale export of corona virus resulted in the explosion of the number of cases. Slowly India has entered the top ten countries affected by COVID-109 and today is the third most badly affected country in the world [1].

Despite the claims of the government of increased medical and testing facilities, the number of affected cases is not flattening or abating. The number of new patients every day is reaching 20,000 per day and many concerns are looming over the spread of COVID-19. How many people will be infected tomorrow? How many deaths will happen tomorrow? When will the infection curve reach inflexion or get flattened? How many people will be affected during the peak period of the outbreak? Are there mathematical models available to answer these questions? Under the circumstances, it is very important to estimate the spread of COVID-19 so that the policymakers, medical personnel and the general public could be better prepared to deal with the emergency.

In this paper, we have employed Auto Regressive Integrated Moving Average (ARIMA) model to predict the incidence and spread of the COVID-19 in India, Russia, Brazil, Spain and the US as the five most badly hit countries [1]. As compared to other econometric models ARIMA models have been used with success in the prediction of several diseases [[2], [3], [4], [5], [6], [7]].

1. Literature review

The past two decades have seen research focused on statistical issues pertaining to a prospective detection of outbreaks of infectious diseases. The challenges arise in early detection and possible evolution of the epidemic for taking the appropriate preventive measures. The rapid growth in this area is called biosurveillance [8,9].

An early model of regression method of outbreak detection was presented by Shewhart [10]. Assuming a normally distributed incidence of infected cases the regression tested for exceeding the mean by a certain multiple of the standard deviation. However, with epidemics, the normal distribution is no longer a valid distribution and most epidemics show an exponential distribution or a highly skewed bell curve [11]. used a simple regression model which computer the expected number of cases at month t calculated as the mean count over t-1, t and t+1 months over a specified number of years. Regression models are used to detect the onset of influenza epidemics [12,13]. When data frequency is not much the normal errors regression model are inadequate and Poisson regression models have been used [14,15]. Unlike the parametric regression models described so far semi parametric models can be used to create a baseline model as used in monitoring the mortality and other related effects. A smoothing method to obtain baseline and standard deviations while working with Salmonella outbreaks was used by Ref. [16,17]. Most regression-based models define a mean at time t and issue an alarm at t if the observed value lies above a certain threshold predetermined by the sample statistics and the quantiles of a suitable normal or Poisson distribution [18]. described non-thresholding regression methods which test the hypothesis that a given value yt at time t belongs to the same distribution as the baseline distribution.

The regression techniques do not capture the correlation structure of the data. Time series methods offer this advantage over the regression methods. Syndromic and laboratory data collected with daily or weekly frequency are generally autocorrelated with some lags. They may further exhibit correlations associated with the seasonal patterns in the data arising out of weekly or yearly seasonality. Failure to account properly for the autocorrelation in the time series data leads to misspecified models and incorrect forecasts. The Box Jenkins model is designed to take care of the autocorrelation of times series into account.

With outbreak surveillance, the trend is best estimated through a relatively simple procedure. A Serfling model [19] based on trigonometric functions may be used to estimate the trend and seasonal components for time series data with regular seasonality. Simple exponential smoothing [20,21] and Holt- Winters procedure are employed in surveillance studies. Simple exponential smoothing makes predictions by taking a weighted average of past observations, the weights decreasing the farther we go in past with the higher weightage on the more recent data. The Hold-Winters procedure is a variant of simple exponential soothing which allows for local trend and seasonality. This method has been used with success in many surveillance studies and has done better than other forecasting methods [22].

Auto Regressive Integrated Moving Average (ARIMA) models [23] have been widely used for detecting outbreaks of infectious diseases [[24], [25], [26], [27]]. Stationarity of the time series is a prerequisite for fitting an ARIMA model. An investigation of ARIMA modelling showed that it was unable to model eight out of 17 syndromic time series resulting from sparse data [28]. However, for the series which were successfully modelled, one step ahead forecasts were highly acceptable and forecasts up to 3 years in future were obtained by continuously updated models. The traditional ARIMA models require a fairly large number of parameters for the auto correlation to be detected. Further, a model for one syndrome or outbreak cannot be automatically applied to another and the model has to be identified each time. For shorter lengths of time series data, it is prudent to use a hierarchical time series model. It is claimed that the hierarchical times series model can detect outbreaks faster than the lab based exceedance system [29].

The ARIMA model has seen widespread usage in the study of infectious diseases for several time series events. These include leptospirosis and its relationship with rainfall and temperature [5] and the relationship of suicide cases with changes in national alcohol policies [30] among others. Time series modelling of infectious disease specially COVID-19 has been reported by several researchers [4,7,[31], [32], [33], [34], [35], [36], [37], [38]].

2. Methodology

COVID-19 daily data of all reported cases were taken from the Worldometers website (worldometers.info/coronavirus/#countries). Data for India was of primary interest but data for the other two countries above and below India in the severity of epidemic were also studied to have a comparison of the epidemic and also investigate the onset of flattening of the curve. Daily data from 15 February to June 30, 2020 was collected and analysed separately for each country. We used data 30th June for modelling and then 77 days out of sample forecast was done based on the ARIMA models fitted to the data. Actual data from 1st to 7th was used to compute the accuracy and forecast error.

2.1. Box Jenkins procedure

Box and Jenkins (1971) popularised a method which combines both autoregressive (AR) and moving average (MA) models. An ARMA (p,q) model is a combination of AR(p) and MA(q) models and is best used for univariate time series modelling. In AR(p) model the future value of a variable is assumed to be dependent upon a linear combination of p past observations and a random error term. Mathematically and AR(p) model can be expressed as follows-

Yt = c+ ϕ1yt-1+ ϕ2yt-2+ ϕ3yt-3+ ϕ4yt-4+ …. .+ ϕpyt-p +εt

Yt and εt are the actual value and the error terms at time period t, ϕi (i = 1,2,3,4 …. ) are model parameters and c is a constant. Integer p is known as the order of the model. Unlike AR(p) model an MA(q) model uses past errors as explanatory variables. The MA(q) model is given below-

Yt = μ+ θ1εt-1+ θ2εt-2+ θ3εt-3+ θ4εt-4+ …. .+ θpεt-q +εt

Here μ is the mean of the series, θj(j = 1,2,3 … q) are model parameters and is the order of the model. Mathematically an ARMA (p,q) model is represented as follows-

Yt = c+ μ+ ϕ1yt-1+ ϕ2yt-2+ ϕ3yt-3+ ϕ4yt-4+ …. .+ ϕpyt-p + θ1εt-1+ θ2εt-2+ θ3εt-3+ θ4εt-4+ …. .+ θpεt-q +εt

The AR and MA can only be applied to a univariate stationary times series. To test the stationarity of a times series we need to test for the presence of unit root. If the series is not stationary in level, we need to differentiate it d (d = 1,2,3 …) times to make it stationary. Such a time series model is called an ARIMA (p,d,q) model.

2.2. ARIMA modelling steps

  • 1.

    The first step is to check for the stationarity of the times series. This can be done by graphically plotting the series or conducting Augmented Dicky Fuller Test (ADF).

  • 2.

    Identification of the model. Graphically the AR and MA terms can be deduced from the Autocorrelation function (ACF) and partial autocorrelation function (PACF) plots.

  • 3.

    ARIMA parameters are estimated by least square method. EVIEWS 8 and JMulti software were used. While EVIEWS required naming of the model(p,d,q) based on ACF and PACF plots, JMulti does the model specification automatically using the Hannan Rissanen model selection algorithm(1982). The best model is selected on the basis of AIC values.

  • 4.

    The residual analysis is done.

  • 5.

    Out of sample forecast is carried out based on data from February 15, 2020 to June 30, 2020. A 77 days forward forecast upto September 15, 2020 is done based on the model.

  • 6.

    The procedure is repeated for the US, Brazil, Russia and Spain to check the model specification and forecasting accuracy for the five most severely affected countries.

3. Results

The first step was to test for unit root in all the five time series. A visual examination of the data plot suggested that the series were exponentially rising and were non stationary. Other than Russian time series of COVID incidence, all other series had to be differentiated. Augmented Dickey Fuller test was conducted to establish that Russian series was stationary in level while Brazil was integrated in the first order and the remaining three series namely India, Spain and US were integrated in second order. The model specification determined by Hannan Rissanen algorithm [29] was India (4,2,4), Brazil (3,1,2), Russia (3,0,0), Spain (4,2,4) and US (1,2,1) respectively. The residuals of the ARIMA series were plotted and found to be stationary.

The ARIMA models were then used to forecast the out of sample COVID outbreak for 77 days up to September 15, 2020. The forecast values for each country are presented in Table 1, Table 2, Table 3, Table 4, Table 5 . The graphical plots with 95% confidence intervals are presented in Fig. 1, Fig. 2, Fig. 3, Fig. 4, Fig. 5 . We compared the actual data from 1st July to 18th July and checked the forecast efficiency using mean absolute deviation (MAD) and the mean absolute percentage error (MAPE). The MAD was lowest for Spain followed by Russia whereas India, Brazil and US exhibited increasing absolute deviations indicating that actual forecasts lean towards the upper bound of the forecast. In other words, the forecast indicated worsening situation and steepening of the case graph for India, Brazil and US in the days to come. A better measure of the forecast efficiency is the mean absolute percentage error (MAPE) which converts the absolute deviations as percentage of actual numbers. Percentage numbers are easily compared to have a relative estimate of the severity of the spread across the countries under consideration. MAPE for India, Brazil and US were 3.701%,1.844% and 2.885% respectively. It was lowest for Russia and Spain at 1.090% and 0.832% indicating a very tight forecast accuracy. The smaller numbers for Russia and Spain further indicate that the forecast is following the linear trend established by the past data. Spain has even dropped out of the top five countries in the world. Even though the MAPE numbers for US, India and Brazil are all less than 4.0%, the relatively larger numbers indicate a trend which is steepening and leaning towards the upper bound of the forecast. The MAPE numbers validate the accuracy of the forecast. The results are presented in Table 6 .

Table 1.

ARIMA model specifications.

INDIA BRAZIL RUSSIA SPAIN US
MODEL (4,2,4) (3,1,2) (3,0,0) (4,2,4) (1,2,1)
AR1 1.375893 1.38224 1.821833 −0.1032 0.224382
Std Err 0.13892 0.232872 0.080456 0.24914 0.199694
T 9.90423 5.93562 22.64392 −0.41423 1.12363
P 0.00000 0.00000 0.00000 0.67941 0.26321
AR2 −1.02318 −0.83395 −0.647 0.265827
Std Err 0.112545 0.328354 0.161136 0.201803
T −9.09125 −2.53978 −4.01521 1.31726
P 0.00000 0.01227 0.00010 0.19014
AR3 1.369517 0.448294 −0.17526 −0.43591
Std Err 0.105984 0.12919 0.080759 0.125818
T 12.92191 3.47003 −2.17015 −3.46459
P 0.00000 0.00071 0.03177 0.00073
AR4 −0.72424 −0.63051
Std Err 0.132004 0.160281
T −5.48652 −3.93377
P 0.00000 0.00014
MA1 1.794408 0.824621 0.380611 0.594318
Std Err 0.24318 0.165616
T 3.39099 3.58854
P 0.00092 0.00047
MA2 −1.50841 −0.11077 0.150048
Std Err 0.23289
T −0.47564
P 0.63513
MA3 1.591911 −0.37507
Std Err
T
P
MA4 −0.89826 −0.4913
Std Err
T
P
AIC 2128.399 2689.998 2077.294 2179.333 2624.271
SBC 2154.546 2707.474 2088.974 2205.481 2632.987
Log Likelihood −1055.2 −1339 −1034.65 −1080.67 −1309.14
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Source: Authors’ own calculation.

Table 2.

Forecast data for COVID-19 outbreak in India.

DATE LOWER CI FORECAST UPPER CI STD_ERR
January 07, 2020 603,907 605,084 606,262 600.9606
February 07, 2020 621,640 623,844 626,048 1124.4701
March 07, 2020 639,485 642,773 646,062 1677.9432
April 07, 2020 658,599 663,129 667,658 2311.0731
May 07, 2020 678,031 683,792 689,552 2939.1669
June 07, 2020 697,137 704,039 710,940 3521.313
July 07, 2020 717,145 725,228 733,311 4123.9509
August 07, 2020 738,198 747,529 756,861 4760.9582
September 07, 2020 759,060 769,604 780,147 5379.2975
October 07, 2020 780,073 791,821 803,570 5994.242
November 07, 2020 802,265 815,308 828,351 6654.942
December 07, 2020 824,890 839,280 853,670 7341.9044
07/13/2020 847,242 862,980 878,719 8029.8984
07/14/2020 870,285 887,448 904,610 8756.6787
07/15/2020 894,290 912,992 931,694 9542.059
07/16/2020 918,216 938,511 958,807 10355.0318
07/17/2020 942,191 964,142 986,093 11199.8207
07/18/2020 967,129 990,871 1,014,612 12113.2121
07/19/2020 992,534 1,018,184 1,043,834 13087.0884
07/20/2020 1,017,713 1,045,348 1,072,982 14099.6111
07/21/2020 1,043,389 1,073,132 1,102,875 15175.4833
07/22/2020 1,069,915 1,101,928 1,133,942 16333.7611
07/23/2020 1,096,454 1,130,855 1,165,256 17551.9068
07/24/2020 1,122,982 1,159,885 1,196,787 18828.2916
07/25/2020 1,150,284 1,189,858 1,229,433 20191.4058
07/26/2020 1,178,063 1,220,473 1,262,884 21638.3565
07/27/2020 1,205,677 1,251,050 1,296,423 23149.8286
07/28/2020 1,233,645 1,282,138 1,330,631 24741.8074
07/29/2020 1,262,358 1,314,163 1,365,968 26431.5544
07/30/2020 1,291,161 1,346,437 1,401,714 28202.6936
07/31/2020 1,319,928 1,378,826 1,437,724 30050.3959
January 08, 2020 1,349,317 1,412,029 1,474,740 31996.3832
February 08, 2020 1,379,180 1,445,899 1,512,619 34041.2004
March 08, 2020 1,408,942 1,479,831 1,550,720 36168.6273
April 08, 2020 1,438,956 1,514,196 1,589,436 38388.456
May 08, 2020 1,469,620 1,549,422 1,629,224 40715.8197
June 08, 2020 1,500,436 1,584,987 1,669,539 43139.4772
July 08, 2020 1,531,212 1,620,691 1,710,170 45653.2561
DATE LOWER CI FORECAST UPPER CI STD_ERR
August 08, 2020 1,562,487 1,657,101 1,751,715 48273.3948
September 08, 2020 1,594,221 1,694,184 1,794,147 51002.6718
October 08, 2020 1,625,914 1,731,415 1,836,916 53828.1115
November 08, 2020 1,657,789 1,769,027 1,880,266 56755.2362
December 08, 2020 1,690,226 1,807,426 1,924,625 59796.9572
08/13/2020 1,722,857 1,846,229 1,969,601 62946.0768
08/14/2020 1,755,460 1,885,202 2,014,944 66196.2032
08/15/2020 1,788,461 1,924,794 2,061,128 69559.2399
08/16/2020 1,821,897 1,965,051 2,108,205 73039.2166
08/17/2020 1,855,344 2,005,528 2,155,713 76626.1288
08/18/2020 1,888,925 2,046,354 2,203,784 80322.6473
08/19/2020 1,922,987 2,087,897 2,252,808 84139.5271
08/20/2020 1,957,271 2,129,890 2,302,509 88072.5738
08/21/2020 1,991,544 2,172,088 2,352,631 92115.7886
08/22/2020 2,026,135 2,214,836 2,403,537 96277.7173
08/23/2020 2,061,130 2,258,229 2,455,329 100562.9208
08/24/2020 2,096,178 2,301,903 2,507,629 104963.9251
08/25/2020 2,131,328 2,345,908 2,560,488 109481.5652
08/26/2020 2,166,887 2,390,567 2,614,248 114124.6156
08/27/2020 2,202,684 2,435,706 2,668,728 118891.0175
08/28/2020 2,238,488 2,481,084 2,723,679 123775.4657
08/29/2020 2,274,547 2,526,959 2,779,371 128783.9514
08/30/2020 2,310,975 2,573,455 2,835,936 133921.0867
08/31/2020 2,347,488 2,620,279 2,893,070 139181.4645
January 09, 2020 2,384,084 2,667,426 2,950,768 144564.7979
February 09, 2020 2,421,026 2,715,174 3,009,322 150078.1141
March 09, 2020 2,458,210 2,763,417 3,068,624 155720.8153
April 09, 2020 2,495,420 2,811,932 3,128,443 161488.4038
May 09, 2020 2,532,836 2,860,904 3,188,973 167384.9613
June 09, 2020 2,570,583 2,910,470 3,250,357 173414.8553
July 09, 2020 2,608,441 2,960,401 3,312,360 179574.3196
August 09, 2020 2,646,370 3,010,654 3,374,938 185862.4365
September 09, 2020 2,684,590 3,061,462 3,438,333 192284.7388
October 09, 2020 2,723,048 3,112,770 3,502,493 198841.583
November 09, 2020 2,761,551 3,164,381 3,567,211 205529.2858
December 09, 2020 2,800,221 3,216,420 3,632,619 212350.5262
09/13/2020 2,839,186 3,269,024 3,698,863 219309.2637
09/14/2020 2,878,278 3,322,020 3,765,762 226403.0034
09/15/2020 2,917,435 3,375,343 3,833,250 233630.5279
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Source: Authors’ own computation.

Table 3.

Forecast and 95% confidence interval for COVID outbreak in Brazil.

DATE LOWER CI FORECAST UPPER CI STD_ERR
January 07, 2020 1,439,607 1,448,644 1,457,681 4610.585
February 07, 2020 1,467,503 1,484,229 1,500,956 8534.161
March 07, 2020 1,494,870 1,517,010 1,539,150 11296.27
April 07, 2020 1,523,982 1,550,697 1,577,411 13630.03
May 07, 2020 1,554,011 1,585,926 1,617,841 16283.47
June 07, 2020 1,583,200 1,621,272 1,659,344 19424.84
July 07, 2020 1,611,204 1,655,902 1,700,600 22805.37
August 07, 2020 1,638,688 1,690,134 1,741,580 26248.49
September 07, 2020 1,666,099 1,724,467 1,782,836 29780.16
October 07, 2020 1,693,346 1,758,950 1,824,554 33,472
November 07, 2020 1,720,204 1,793,378 1,866,551 37334.16
December 07, 2020 1,746,635 1,827,649 1,908,663 41334.32
07/13/2020 1,772,737 1,861,818 1,950,898 45,450
07/14/2020 1,798,577 1,895,950 1,993,322 49680.85
07/15/2020 1,824,148 1,930,047 2,035,947 54031.33
07/16/2020 1,849,425 1,964,081 2,078,736 58498.89
07/17/2020 1,874,411 1,998,039 2,121,667 63076.58
07/18/2020 1,899,125 2,031,931 2,164,736 67759.09
07/19/2020 1,923,581 2,065,764 2,207,948 72543.85
07/20/2020 1,947,782 2,099,540 2,251,298 77428.9
07/21/2020 1,971,730 2,133,254 2,294,777 82411.53
07/22/2020 1,995,430 2,166,904 2,338,379 87488.69
07/23/2020 2,018,887 2,200,493 2,382,099 92657.68
07/24/2020 2,042,109 2,234,022 2,425,934 97916.23
07/25/2020 2,065,099 2,267,490 2,469,880 103262.2
07/26/2020 2,087,862 2,300,897 2,513,933 108693.6
07/27/2020 2,110,400 2,334,244 2,558,088 114208.2
07/28/2020 2,132,719 2,367,531 2,602,343 119804.1
07/29/2020 2,154,822 2,400,757 2,646,693 125479.6
07/30/2020 2,176,713 2,433,924 2,691,136 131232.8
07/31/2020 2,198,395 2,467,032 2,735,669 137062.1
January 08, 2020 2,219,872 2,500,080 2,780,288 142965.9
February 08, 2020 2,241,146 2,533,068 2,824,990 148942.6
March 08, 2020 2,262,222 2,565,998 2,869,774 154990.8
April 08, 2020 2,283,101 2,598,869 2,914,636 161108.9
May 08, 2020 2,303,787 2,631,681 2,959,574 167295.8
June 08, 2020 2,324,283 2,664,434 3,004,586 173549.9
July 08, 2020 2,344,591 2,697,130 3,049,669 179870.1
DATE LOWER CI FORECAST UPPER CI STD_ERR
August 08, 2020 2,364,714 2,729,767 3,094,820 186255.1
September 08, 2020 2,384,654 2,762,346 3,140,039 192703.7
October 08, 2020 2,404,414 2,794,868 3,185,322 199214.7
November 08, 2020 2,423,997 2,827,332 3,230,667 205787.1
December 08, 2020 2,443,404 2,859,739 3,276,074 212419.8
08/13/2020 2,462,637 2,892,088 3,321,539 219111.7
08/14/2020 2,481,700 2,924,381 3,367,062 225861.7
08/15/2020 2,500,594 2,956,617 3,412,639 232668.9
08/16/2020 2,519,321 2,988,796 3,458,270 239532.4
08/17/2020 2,537,883 3,020,918 3,503,954 246451.1
08/18/2020 2,556,282 3,052,985 3,549,687 253424.2
08/19/2020 2,574,521 3,084,995 3,595,469 260450.9
08/20/2020 2,592,600 3,116,950 3,641,299 267530.1
08/21/2020 2,610,522 3,148,848 3,687,174 274661.2
08/22/2020 2,628,289 3,180,691 3,733,094 281843.2
08/23/2020 2,645,902 3,212,479 3,779,057 289075.4
08/24/2020 2,663,363 3,244,212 3,825,061 296,357
08/25/2020 2,680,673 3,275,889 3,871,106 303687.3
08/26/2020 2,697,835 3,307,512 3,917,189 311065.4
08/27/2020 2,714,850 3,339,080 3,963,311 318490.7
08/28/2020 2,731,719 3,370,594 4,009,469 325962.5
08/29/2020 2,748,444 3,402,053 4,055,662 333,480
08/30/2020 2,765,027 3,433,458 4,101,890 341042.7
08/31/2020 2,781,469 3,464,810 4,148,151 348649.7
January 09, 2020 2,797,771 3,496,107 4,194,443 356300.6
February 09, 2020 2,813,935 3,527,351 4,240,767 363994.6
March 09, 2020 2,829,962 3,558,541 4,287,121 371731.1
April 09, 2020 2,845,853 3,589,678 4,333,503 379509.5
May 09, 2020 2,861,611 3,620,762 4,379,914 387329.3
June 09, 2020 2,877,236 3,651,793 4,426,351 395189.8
July 09, 2020 2,892,729 3,682,772 4,472,814 403090.4
August 09, 2020 2,908,092 3,713,697 4,519,303 411030.7
September 09, 2020 2,923,326 3,744,571 4,565,815 419,010
October 09, 2020 2,938,433 3,775,392 4,612,351 427027.9
November 09, 2020 2,953,412 3,806,161 4,658,909 435083.7
December 09, 2020 2,968,267 3,836,878 4,705,489 443,177
09/13/2020 2,982,997 3,867,543 4,752,089 451307.2
09/14/2020 2,997,604 3,898,157 4,798,709 459473.9
09/15/2020 3,012,090 3,928,719 4,845,348 467676.6
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Source: Authors’ own computation.

Table 4.

Forecast and 95% confidence interval for COVID-19 outbreak in Russia.

DATE LOWER CI FORECAST UPPER CI STD_ERR3
January 07, 2020 653,535 654,393 655,251 437.7359
February 07, 2020 659,024 660,807 662,590 909.7199
March 07, 2020 664,181 667,085 669,990 1481.792
April 07, 2020 669,040 673,227 677,413 2135.867
May 07, 2020 673,619 679,229 684,840 2862.586
June 07, 2020 677,928 685,091 692,254 3654.641
July 07, 2020 681,978 690,810 699,642 4506.393
August 07, 2020 685,775 696,385 706,994 5413.246
September 07, 2020 689,326 701,813 714,301 6371.346
October 07, 2020 692,635 707,095 721,554 7377.383
November 07, 2020 695,707 712,226 728,746 8428.454
December 07, 2020 698,545 717,208 735,870 9521.978
07/13/2020 701,152 722,037 742,921 10655.63
07/14/2020 703,531 726,712 749,893 11827.27
07/15/2020 705,684 731,232 756,781 13034.97
07/16/2020 707,615 735,597 763,579 14276.89
07/17/2020 709,323 739,804 770,284 15551.35
07/18/2020 710,813 743,852 776,890 16856.75
07/19/2020 712,085 747,740 783,395 18191.59
07/20/2020 713,142 751,468 789,794 19554.42
07/21/2020 713,985 755,034 796,083 20943.87
07/22/2020 714,615 758,438 802,260 22358.65
07/23/2020 715,035 761,677 808,320 23797.49
07/24/2020 715,246 764,753 814,260 25259.17
07/25/2020 715,249 767,663 820,078 26742.52
07/26/2020 715,046 770,408 825,770 28246.4
07/27/2020 714,639 772,986 831,334 29769.71
07/28/2020 714,029 775,398 836,767 31311.38
07/29/2020 713,217 777,642 842,066 32870.36
07/30/2020 712,205 779,718 847,230 34445.63
07/31/2020 710,996 781,625 852,255 36036.18
January 08, 2020 709,589 783,365 857,140 37641.05
February 08, 2020 707,988 784,935 861,882 39259.28
March 08, 2020 706,193 786,336 866,479 40889.93
April 08, 2020 704,207 787,568 870,929 42532.08
May 08, 2020 702,030 788,631 875,232 44184.84
June 08, 2020 699,665 789,524 879,384 45847.3
July 08, 2020 697,114 790,249 883,384 47518.61
DATE LOWER CI FORECAST UPPER CI STD_ERR
August 08, 2020 694,378 790,804 887,230 49197.9
September 08, 2020 691,459 791,190 890,922 50884.34
October 08, 2020 688,359 791,408 894,457 52577.09
November 08, 2020 685,079 791,457 897,835 54275.33
December 08, 2020 681,623 791,338 901,053 55978.26
08/13/2020 677,991 791,051 904,112 57685.09
08/14/2020 674,185 790,597 907,010 59395.04
08/15/2020 670,209 789,977 909,745 61107.34
08/16/2020 666,063 789,190 912,318 62821.23
08/17/2020 661,750 788,238 914,726 64535.97
08/18/2020 657,272 787,121 916,970 66250.81
08/19/2020 652,631 785,840 919,049 67965.05
08/20/2020 647,830 784,396 920,963 69677.95
08/21/2020 642,870 782,790 922,710 71388.83
08/22/2020 637,755 781,022 924,290 73096.99
08/23/2020 632,485 779,094 925,703 74801.74
08/24/2020 627,065 777,007 926,949 76502.43
08/25/2020 621,495 774,761 928,027 78198.38
08/26/2020 615,778 772,358 928,937 79888.95
08/27/2020 609,918 769,799 929,680 81573.5
08/28/2020 603,916 767,086 930,255 83251.4
08/29/2020 597,775 764,219 930,663 84922.04
08/30/2020 591,497 761,200 930,903 86584.81
08/31/2020 585,085 758,030 930,976 88239.11
January 09, 2020 578,542 754,712 930,882 89884.37
February 09, 2020 571,870 751,246 930,621 91519.99
March 09, 2020 565,072 747,633 930,195 93145.44
April 09, 2020 558,150 743,877 929,603 94760.14
May 09, 2020 551,108 739,977 928,846 96363.57
June 09, 2020 543,948 735,937 927,925 97955.19
July 09, 2020 536,673 731,757 926,841 99534.49
August 09, 2020 529,285 727,439 925,593 101,101
September 09, 2020 521,788 722,986 924,184 102654.1
October 09, 2020 514,184 718,399 922,615 104193.4
November 09, 2020 506,476 713,680 920,885 105718.5
December 09, 2020 498,667 708,832 918,996 107228.8
09/13/2020 490,760 703,855 916,950 108,724
09/14/2020 482,758 698,753 914,748 110203.5
09/15/2020 474,664 693,527 912,390 111,667
Open in a new tab

Source: Authors’ own computation.

Table 5.

Forecast and 95% confidence intervals for COVID-19 outbreak in Spain.

DATE LOWER CI FORECAST UPPER CI STD_ERR
January 07, 2020 295,067 296,504 297,942 733.5741
February 07, 2020 294,084 296,695 299,307 1332.366
March 07, 2020 292,753 296,853 300,952 2091.702
April 07, 2020 291,496 297,115 302,735 2867.293
May 07, 2020 290,095 297,437 304,779 3745.853
June 07, 2020 288,393 297,774 307,155 4786.492
July 07, 2020 286,419 298,102 309,786 5960.999
August 07, 2020 284,043 298,345 312,648 7297.349
September 07, 2020 281,496 298,554 315,611 8702.891
October 07, 2020 278,836 298,739 318,642 10154.9
November 07, 2020 276,180 298,962 321,744 11623.88
December 07, 2020 273,539 299,246 324,954 13116.37
07/13/2020 270,811 299,568 328,326 14672.39
07/14/2020 267,937 299,903 331,869 16309.53
07/15/2020 264,825 300,198 335,571 18047.73
07/16/2020 261,506 300,447 339,388 19868.05
07/17/2020 258,046 300,664 343,282 21744.3
07/18/2020 254,525 300,883 347,241 23652.35
07/19/2020 251,003 301,140 351,277 25580.76
07/20/2020 247,457 301,439 355,421 27542.25
07/21/2020 243,841 301,766 359,691 29554.04
07/22/2020 240,084 302,085 364,086 31633.81
07/23/2020 236,156 302,372 368,587 33784.09
07/24/2020 232,078 302,623 373,169 35993.12
07/25/2020 227,903 302,859 377,814 38243.43
07/26/2020 223,688 303,107 382,526 40520.45
07/27/2020 219,457 303,387 387,318 42822.67
07/28/2020 215,190 303,700 392,209 45158.72
07/29/2020 210,843 304,024 397,204 47541.89
07/30/2020 206,374 304,335 402,296 49980.92
07/31/2020 201,770 304,619 407,467 52474.53
January 08, 2020 197,055 304,879 412,703 55013.3
February 08, 2020 192,270 305,134 417,999 57585.04
March 08, 2020 187,451 305,406 423,362 60182.65
April 08, 2020 182,605 305,705 428,805 62807.22
May 08, 2020 177,713 306,024 434,336 65466.29
June 08, 2020 172,739 306,347 439,955 68168.54
July 08, 2020 167,658 306,654 445,651 70917.92
DATE LOWER CI FORECAST UPPER CI STD_ERR
August 08, 2020 162,468 306,940 451,413 73711.6
September 08, 2020 157,194 307,213 457,232 76541.85
October 08, 2020 151,865 307,488 463,111 79400.95
November 08, 2020 146,502 307,779 469,056 82285.62
December 08, 2020 141,106 308,091 475,077 85198.3
08/13/2020 135,655 308,416 481,177 88144.96
08/14/2020 130,124 308,737 487,351 91130.88
08/15/2020 124,500 309,045 493,590 94157.34
08/16/2020 118,788 309,338 499,887 97220.94
08/17/2020 113,008 309,624 506,239 100315.8
08/18/2020 107,183 309,916 512,649 103437.3
08/19/2020 101,322 310,224 519,125 106584.3
08/20/2020 95,421 310,546 525,671 109759.7
08/21/2020 89,462 310,874 532,287 112967.7
08/22/2020 83,427 311,198 538,968 116211.4
08/23/2020 77,312 311,509 545,706 119490.5
08/24/2020 71,123 311,810 552,497 122801.8
08/25/2020 64,879 312,110 559,342 126,141
08/26/2020 58,592 312,418 566,244 129505.5
08/27/2020 52,269 312,739 573,209 132895.5
08/28/2020 45,900 313,070 580,239 136313.5
08/29/2020 39,473 313,402 587,332 139762.5
08/30/2020 32,975 313,729 594,482 143244.1
08/31/2020 26,407 314,046 601,684 146,757
January 09, 2020 19,778 314,358 608,938 150298.7
February 09, 2020 13,099 314,671 616,243 153866.1
March 09, 2020 6381 314,993 623,605 157,458
April 09, 2020 −377 315,325 631,026 161075.2
May 09, 2020 −7182 315,663 638,507 164719.7
June 09, 2020 −14045 316,000 646,045 168393.4
July 09, 2020 −20972 316,331 653,635 172096.9
August 09, 2020 −27961 316,657 661,275 175828.7
September 09, 2020 −35004 316,979 668,963 179586.8
October 09, 2020 −42091 317,306 676,703 183369.2
November 09, 2020 −49217 317640 684,497 187175.5
December 09, 2020 −56385 317,981 692,347 191006.6
09/13/2020 −63601 318,326 700,252 194864.2
09/14/2020 −70873 318,668 708,210 198749.2
09/15/2020 −78203 319,006 716,216 202661.6
Open in a new tab

Source: Authors’ own computation.

Fig. 1.

Fig. 1

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Covid-19 forecast plot for India.

Fig. 2.

Fig. 2

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Covid 19 forecast plot for Brazil.

Fig. 3.

Fig. 3

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Covid-19 forecast plot for Russia.

Fig. 4.

Fig. 4

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Covid-19 forecast plot for Spain.

Fig. 5.

Fig. 5

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Covid-19 forecast plot for US.

Table 6.

Forecast and 95% confidence intervals for COVID-19 outbreak in US.

DATE LOWER CI FORECAST UPPER CI STD_ERR
January 07, 2020 2,765,075 2,772,875 2,780,674 3979.266
February 07, 2020 2,803,614 2,818,529 2,833,443 7609.775
March 07, 2020 2,841,873 2,864,474 2,887,074 11530.92
April 07, 2020 2,879,825 2,910,744 2,941,664 15775.66
May 07, 2020 2,917,466 2,957,348 2,997,230 20348.26
June 07, 2020 2,954,817 3,004,288 3,053,759 25240.75
July 07, 2020 2,991,899 3,051,562 3,111,226 30440.89
August 07, 2020 3,028,741 3,099,173 3,169,605 35935.59
September 07, 2020 3,065,365 3,147,119 3,228,874 41712.28
October 07, 2020 3,101,794 3,195,401 3,289,008 47759.35
November 07, 2020 3,138,051 3,244,019 3,349,986 54066.19
December 07, 2020 3,174,153 3,292,972 3,411,791 60623.19
07/13/2020 3,210,117 3,342,261 3,474,405 67421.61
07/14/2020 3,245,959 3,391,885 3,537,812 74453.5
07/15/2020 3,281,694 3,441,846 3,601,998 81711.6
07/16/2020 3,317,334 3,492,142 3,666,950 89189.26
07/17/2020 3,352,892 3,542,774 3,732,656 96880.35
07/18/2020 3,388,377 3,593,741 3,799,104 104779.2
07/19/2020 3,423,802 3,645,044 3,866,286 112880.6
07/20/2020 3,459,175 3,696,683 3,934,191 121179.7
07/21/2020 3,494,505 3,748,657 4,002,809 129671.8
07/22/2020 3,529,801 3,800,967 4,072,134 138352.9
07/23/2020 3,565,070 3,853,613 4,142,157 147218.8
07/24/2020 3,600,319 3,906,595 4,212,870 156265.9
07/25/2020 3,635,557 3,959,912 4,284,267 165490.5
07/26/2020 3,670,788 4,013,565 4,356,342 174889.5
07/27/2020 3,706,020 4,067,554 4,429,087 184459.5
07/28/2020 3,741,257 4,121,878 4,502,498 194197.7
07/29/2020 3,776,507 4,176,538 4,576,569 204101.1
07/30/2020 3,811,774 4,231,533 4,651,293 214167.2
07/31/2020 3,847,062 4,286,865 4,726,667 224393.2
January 08, 2020 3,882,378 4,342,532 4,802,686 234776.8
February 08, 2020 3,917,725 4,398,535 4,879,344 245315.6
March 08, 2020 3,953,108 4,454,873 4,956,638 256007.4
April 08, 2020 3,988,531 4,511,547 5,034,563 266849.9
May 08, 2020 4,023,998 4,568,557 5,113,116 277841.2
June 08, 2020 4,059,513 4,625,902 5,192,291 288979.3
July 08, 2020 4,095,081 4,683,584 5,272,087 300262.2
DATE LOWER CI FORECAST UPPER CI STD_ERR
August 08, 2020 4,130,703 4,741,600 5,352,498 311688.2
September 08, 2020 4,166,384 4,799,953 5,433,522 323255.3
October 08, 2020 4,202,128 4,858,641 5,515,155 334962.1
November 08, 2020 4,237,936 4,917,665 5,597,394 346806.8
December 08, 2020 4,273,814 4,977,025 5,680,236 358787.8
08/13/2020 4,309,763 5,036,720 5,763,678 370903.6
08/14/2020 4,345,786 5,096,751 5,847,717 383152.7
08/15/2020 4,381,886 5,157,118 5,932,350 395533.7
08/16/2020 4,418,067 5,217,820 6,017,574 408045.1
08/17/2020 4,454,329 5,278,858 6,103,387 420685.8
08/18/2020 4,490,677 5,340,232 6,189,787 433454.2
08/19/2020 4,527,113 5,401,942 6,276,770 446349.3
08/20/2020 4,563,639 5,463,987 6,364,335 459369.7
08/21/2020 4,600,257 5,526,368 6,452,478 472514.2
08/22/2020 4,636,969 5,589,084 6,541,199 485781.8
08/23/2020 4,673,779 5,652,136 6,630,494 499171.2
08/24/2020 4,710,687 5,715,524 6,720,361 512681.4
08/25/2020 4,747,697 5,779,248 6,810,799 526311.3
08/26/2020 4,784,809 5,843,307 6,901,805 540059.8
08/27/2020 4,822,027 5,907,702 6,993,377 553925.9
08/28/2020 4,859,352 5,972,433 7,085,513 567908.8
08/29/2020 4,896,786 6,037,499 7,178,212 582007.3
08/30/2020 4,934,330 6,102,901 7,271,472 596220.5
08/31/2020 4,971,988 6,168,639 7,365,290 610547.6
January 09, 2020 5,009,759 6,234,712 7,459,665 624987.6
February 09, 2020 5,047,647 6,301,121 7,554,596 639539.7
March 09, 2020 5,085,652 6,367,866 7,650,080 654202.9
April 09, 2020 5,123,777 6,434,947 7,746,116 668976.5
May 09, 2020 5,162,022 6,502,363 7,842,703 683859.7
June 09, 2020 5,200,391 6,570,115 7,939,838 698851.6
July 09, 2020 5,238,883 6,638,202 8,037,521 713951.5
August 09, 2020 5,277,501 6,706,625 8,135,750 729158.5
September 09, 2020 5,316,246 6,775,384 8,234,523 744,472
October 09, 2020 5,355,119 6,844,479 8,333,838 759891.3
November 09, 2020 5,394,123 6,913,909 8,433,696 775415.5
December 09, 2020 5,433,258 6,983,675 8,534,093 791,044
09/13/2020 5,472,525 7,053,777 8,635,029 806,776
09/14/2020 5,511,926 7,124,214 8,736,502 822,611
09/15/2020 5,551,463 7,194,987 8,838,512 838548.3
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Source: Authors’ own computation.

The graphs show that for the US, Brazil and India the situation does not seem to be coming under control. For Russia and Spain, the situation is seemingly under control and it can be said that the epidemic has reached the inflexion point. (see Table 7)

Table 7.

Forecast accuracy with mean absolute deviation (MAD) and mean absolute percentage error (MAPE).

DATE INDIA
 BRAZIL
 RUSSIA
 SPAIN
 US
ACTUAL FORECAST ACTUAL FORECAST ACTUAL FORECAST ACTUAL FORECAST ACTUAL FORECAST
1-Jul-20 605,220 605,084 1,453,369 1,448,644 654,405 654,393 296,739 296,504 2,778,452 2,772,875
2-Jul-20 627,168 623,844 1,543,341 1,484,229 661,165 660,807 297,183 296,695 2,835,684 2,818,529
3-Jul-20 649,889 642,773 1,543,341 1,517,010 667,883 667,085 297,625 296,853 2,890,588 2,864,474
4-Jul-20 673,904 663,129 1,578,376 1,550,697 674,904 673,227 297,625 297,115 2,935,770 2,910,744
5-Jul-20 697,836 683,792 1,604,585 1,585,926 681,261 679,229 297,625 297,437 2,982,928 2,957,348
6-Jul-20 720,346 704,039 1,626,071 1,621,272 687,862 685,091 298,869 297,774 3,040,833 3,004,288
7-Jul-20 743,481 725,228 1,674,655 1,655,902 694,230 690,810 299,210 298,102 3,097,084 3,051,562
8-Jul-20 769,052 747,529 1,716,196 1,690,134 700,792 696,385 299,593 298,345 3,163,318 3,099,173
9-Jul-20 794,842 769,604 1,759,103 1,724,467 707,301 701,813 300,136 298,554 3,224,892 3,147,119
10-Jul-20 822,603 791,821 1,804,338 1,758,950 713,936 707,095 300,988 298,739 3,297,170 3,195,401
11-Jul-20 850,358 815,308 1,840,812 1,793,378 720,547 712,226 301,670 298,962 3,359,174 3,244,019
12-Jul-20 879,466 839,280 1,866,176 1,827,649 727,162 717,208 302,352 299,246 3,417,795 3,292,972
13-Jul-20 907,645 862,980 1,887,959 1,861,818 733,699 722,037 303,033 299,568 3,483,584 3,342,261
14-Jul-20 937,487 887,448 1,931,204 1,895,950 739,947 726,712 303,699 299,903 3,549,632 3,391,885
15-Jul-20 970,169 912,992 1,970,909 1,930,047 746,797 731,232 304,574 300,198 3,621,637 3,441,846
16-Jul-20 1,005,637 938,511 2,014,738 1,964,081 752,797 735,597 305,935 300,447 3,695,025 3,492,142
17-Jul-20 1,040,457 964,142 2,048,697 1,998,039 759,203 739,804 307,335 300,664 3,770,012 3,542,774
18-Jul-20 1,077,864 990,871 2,075,246 2,031,931 765,437 743,852 307,335 300,883 3,833,271 3,593,741
MAD 33,614 33,277 8040.4 2530 100,761
MAPE 3.701% 1.844% 1.090% 0.832% 2.885%
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4. Discussion

India had controlled the spread of the pandemic very successfully until the May 31, 2020. Once the lockdown was lifted the migrant labourers and moving out from the hotspots of Delhi and Mumbai resulted in the explosion of the pandemic. The viral explosion that resulted from the lifting of lockdown has seen India break into the top ten affected countries. By the end of June India already touched third place after US and Brazil. The data for Spain showed a flattening of the curve while Russia showed a clear inflexion point and a downward trend. At the time of writing Spain has been pushed down by Peru and Chile.

At the current rate, we estimate India and Brazil to touch 1.38 million and 2.47 million mark respectively while the US is expected to touch 4.29 million mark by the end of July 2020. This modelling is expected to better prepare these countries for the burgeoning demand for healthcare facilities.

Though the results of the forecast were very agreeable, the ARIMA models suffer serious limitations in forecasting, characteristic of the time series models. Regression models take into account the causal variables but ARIMA models have found widespread and successful application in disease outbreak modelling. ARIMA forecast, built on the autoregressive nature of the time series coupled with corrective incremental adjustments, essentially, predicts a linear pattern and fails to predict a series with turning points. We have forecasted the COVID incidence up to September 15, 2020 assuming that no vaccine or other cure would be found by then. The exponentially rising graph of total cases indicates a possible community spread. Any successful medical intervention would, however, change the forecast significantly. Further, even without a vaccine, Russia and Spain have shown slowdown and flattening in the growth curves. If and when that will happen in case of the US, Brazil and India cannot be said based on this forecast. The ARIMA model does not help in predicting the onset of flattening of the pandemic cases.

5. Conclusion

ARIMA modelling of daily reported cases of COVID-19, in the top five countries showed a good forecast as measured by MAD and MAPE. The forecast could be used by the concerned governments to better manage and ramp up their healthcare preparedness for the pandemic.

Declaration of competing interest

On behalf of my co-authors, I, Dr. Alok Kumar Sahai, confirm that none of the authors have any conflict of interest to report.

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