key: cord-0684524-s7fzex7v authors: Bayyurt, Lutfi; Bayyurt, Burcu title: Forecasting of COVID-19 Cases and Deaths Using ARIMA Models date: 2020-04-22 journal: nan DOI: 10.1101/2020.04.17.20069237 sha: 3341ac3f736310af3c46fb7ba21c1ed07fbb05dd doc_id: 684524 cord_uid: s7fzex7v After the outbreak of severe acute respiratory syndrome (SARS-2002/2003) and middle east respiratory syndrome (MERS-2012/2014) in the world, new public health crisis, called new coronavirus disease (COVID-19), started in China in December 2019 and has spread all over countries. COVID-19 coronavirus has been global threat of the disease and infected humans rapidly. Control of the pandemi is urgently essential, and science community have continued to research treatment agents. Support therapy and intensive care units in hospitals are also efective to overcome of COVID-19. Statistic forecasting models could aid to healthcare system in preventation of COVID-19. This study aimed to compose of forecasting model that could be practical to predict the spread of COVID-19 in Italy, Spain and Turkey. For this purpose, we performed Auto Regressive Integrated Moving Average (ARIMA) model on the European Centre for Disease Prevention and Control COVID-19 data to predict the number of cases and deaths in COVID-19. According to the our results, while number of cases in Italy and Spain is expected to decrease as of July, in Turkey is expected to decline as of September. The number of deaths in Italy and Spain is expected to be the lowest in July. In Turkey, this number is expected to reach the highest in July. In addition, it is thought that if studies in which the sensitivity and validity of this method are tested with more cases, they will contribute to researchers working in this field. KEYWORDS: COVID-19, pandemi, ARIMA, time series analysis Most people from all of the world infected with the new Coronavirus (2019-nCoV) at the present time. Coronaviruses are enveloped, positive single-stranded RNA viruses that infect humans and many animals. 1 2019-nCoV affects different people in different ways. The common symptoms of the disease are fever, fatigue and dry cough. Coronaviruses have caused two major pandemics, such as SARS and MERS over the past two decades. 2, 3 Since the SARS outbreak 18 years ago, a large number of SARS-related Coronaviruses (SARSr CoV) have been discovered in bats. Zhou et al. (2020) reported that 2019-nCoV was identified in China (Wuhan) that caused an acute respiratory syndrome epidemic in humans. 4 The outbreak that started on 12 December 2019 continues to spread worldwide and results in fatality. Since there is no approved treatment for COVID-19 currently prevention and preparation in healthcare services are crucial. This study include Italy and Spain that have high number of case and death from Europe also Turkey in which number of the case and death start to increase. From February 2, 2020 to March 27, 2020; means of the fatality rates of Italy, Spain and Turkey are calculated as %10, %7 and %2, respectively. Modeling and future forecast of daily number of confirmed cases and deaths can help the treatment system. 5 Aim of present study, the statistical prediction models could be meaningfull in forecasting and controlling this global pandemic threat. For this purpose, Auto Regressive Integrated Moving Average (ARIMA) model was used to predict the confirmed cases and deaths of COVID-19. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2020. The daily case and death data of COVID-19 from February 2, 2020 to March 27, 2020 were collected from the official website of European Centre for Disease Prevention and Control (https://www.ecdc.europa.eu/en/publications-data/download-todays-data-geographic-distribution-COVID-19-cases-worldwide). 6 Excel 2019 was used to build a time-series database. SPSS 21 and Eviews 10 statistical software was used to perform statistical analysis on the case and death datasets, and the statistical significance level was set at 0.05. ARIMA model consists of autoregressive (AR) model, moving average (MA) model and seasonal autoregressive integrated moving average (SARIMA) model. 7 Various methods are used to estimate whether a time series is stationary. One of these methods is the Increased Dickey-Fuller (ADF) unit root test. 8 Log transformation and differences are the preferred approaches to stationary the time series. 9 Seasonal and nonseasonal differences were used to stationary the term trend and periodicity. 10 The non-seasonal ARIMA model is usually denoted as ARIMA ( , , ), in which is the order of the autoregression (AR) component, is the order of the differencing process to form a stationary times series, and is the order of the moving average (MA) process. 11 In an ARIMA model, the value of at time is estimated as equation (1) where is the value at time , is the AR parameter, and is the MA parameter. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2020. . https://doi.org/10.1101/2020.04.17.20069237 doi: medRxiv preprint Before analyzing, time series must become station-based on mean and variance. The Augmented Dickey-Fuller (ADF) is used in recognizing stationary in the mean and Ljung Box test in recognizing whether the time series is stationary based on variance or not. 8 The stationarity levels of the series are analyzed by Dickey and Fuller (1981) . 12 After the extended Dickey and Fuller test (ADF) expressed by equation (2) SPSS 21 and Eviews 10 statistical software were used to perform statistical analysis on the case and death datasets, and the statistical significance level was set at 0.05. Time series analysis were made for the number of cases and deaths in Italy, Spain and Turkey due to COVID-19 pandemic. When the time series graphs are examined, the trend is seen. Autocorrelation (ACF) and partial autocorrelation (PACF) graphics were used to see this more clearly and determine its stationary. In the ACF graph, it is seen that the series is not stationary . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 22, 2020. . https://doi.org/10.1101/2020.04.17.20069237 doi: medRxiv preprint since many delays exceed the confidence limits. In this case, the first order difference was applied to the series and it was ensured to become stationary ACF and PACF graphs of the first order difference of the series for Italy, Turkey and Spain are showed respectively ( Fig. 1) (Fig. 2) (Fig. 3) . After the first difference procedure, the series became stationary as seen from the autocorrelation graph. Parameters of the ARIMA model were estimated by autocorrelation function (ACF) and partial autocorrelation (PACF) graph. To determine the number of case and death of COVID-19, the best ARIMA models are showed (Table I) . Time series were created using the best ARIMA models selected. Goodness of fit criteria and coefficients for the time series models are given in (Table II) . According to the findings; It has been determined that the coefficients of the models used to predict the number of case and death in Italy is statistically significant (P<0.05). The constant coefficient for the number of cases and deaths was not included in the model since it was statistically insignificant (P˃0.05). It was determined that the explanatory power of the estimation equation for the number of case in Italy was 76.1% and the error terms were stationary as a result of Ljung-Box statistics. It has been determined that the model can be used for foresight due to the provision of necessary assumptions. The explanatory power of the model for the number of death in Italy was calculated as 92.7%, and it was determined that the error terms were stationary as a result of Ljung-Box statistics. Models with a MAPE (Mean Absolute Percentage Error) value below 10% are very good, models with a range of 10-20% are good, models with a range of 20-50% are acceptable, and models above 50% are classified as incorrect and inaccurate. It is determined that models can . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 22, 2020. . https://doi.org/10.1101/2020.04.17.20069237 doi: medRxiv preprint be used in making future predictions due to high determination coefficients (R 2 ) and MAPE value is less than 10%. The coefficients of the models used to predict the number of case and death in Turkey were determined to be statistically significant (P<0.05). The constant coefficient for the number of case and death was not included in the model since it was statistically insignificant (P˃0.05). It was determined that the explanatory power of the estimation equation for the number of case in Turkey was 81.7% and the error terms were stationary as a result of Ljung-Box statistic. It has been determined that the model can be used for foresight due to the provision of necessary assumptions. The explanatory power of the model for the number of death in Turkey was calculated as 71.4% and it was determined that the error terms were stationary as a result of Ljung-Box statistics. it is determined that models can be used in making future predictions since MAPE value is less than 10%. The coefficients of the models used to predict the number of case and death in Spain was statistically significant (P<0.05). It was determined that the explanatory power of the estimation equation for the number of case in Spain was 95.0%, and the error terms were stationary as a result of the Ljung-Box statistic. It has been determined that the model can be used for foresight due to the provision of necessary assumptions. The explanatory power of the model for the number of death in Spain was calculated as 95.8%, and it was determined that the error terms was stationary as a result of Ljung-Box statistics. It is determined that models can be used in making future predictions since MAPE value is less than 10%. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 22, 2020. The confirmed and prediction graphs of the number of case and death of the countries are given in (Fig. 4-6) . While number of cases in Italy and Spain is expected to decrease as of July, in Turkey is expected to decline as of September. The number of deaths in Italy and Spain is expected to be the lowest in July. In Turkey, this number is expected to reach the highest in July ( Fig. 4-6) . pandemic in Italy, China, South Korea, Iran and Thailand. It is similar to our study in estimating the number of cases in Italy. 5 However, since the results of our study are obtained from more recent data, we think that we have obtained a more consistent forecast for the future. In conclusion, ARIMA models have been created by considering the most appropriate AIC and BIC values for case and death numbers for each country. According to the results, while number of cases in Italy and Spain is expected to decrease as of July, in Turkey is expected to decline as of September. The number of deaths in Italy and Spain is expected to be the lowest in July. In Turkey, this number is expected to reach the highest in July. In addition, it is thought that studies in which the sensitivity and validity of these methods are tested with more cases will contribute to researchers working in this field. The authors have no conflicts of interest to declare in relation to this research article. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 22, 2020. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 22, 2020. . https://doi.org/10.1101/2020.04.17.20069237 doi: medRxiv preprint . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 22, 2020. . https://doi.org/10.1101/2020.04.17.20069237 doi: medRxiv preprint Figure 2 . Daily confirmed cases and deaths according to first order difference ACF and PACF plots in Turkey. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 22, 2020. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2020. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2020. . https://doi.org/10.1101/2020.04.17.20069237 doi: medRxiv preprint Figure 5 . ARIMA forecast case and death graph for the COVID-19 in Turkey . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2020. . https://doi.org/10.1101/2020.04.17.20069237 doi: medRxiv preprint Figure 6 . ARIMA forecast case and death graph for the COVID-19 in Spain . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2020. . https://doi.org/10.1101/2020.04.17.20069237 doi: medRxiv preprint The COVID-19 epidemic Identification of a novel coronavirus in patients with severe acute respiratory syndrome Isolation of a novel coronavirus from a man with pneumonia in Saudi Arabia A pneumonia outbreak associated with a new coronavirus of probable bat origin