key: cord-0991719-d76qio62 authors: Kırbaş, İsmail; Sözen, Adnan; Tuncer, Azim Doğuş; Kazancıoğlu, Fikret Şinasi title: Comperative analysis and forecasting of COVID-19 cases in various European countries with ARIMA, NARNN and LSTM approaches date: 2020-06-13 journal: Chaos Solitons Fractals DOI: 10.1016/j.chaos.2020.110015 sha: 6b2b2820b9ec2a0c1479d4faa3d6e9fcee6ce628 doc_id: 991719 cord_uid: d76qio62 In this study, confirmed COVID-19 cases of Denmark, Belgium, Germany, France, United Kingdom, Finland, Switzerland and Turkey were modeled with Auto-Regressive Integrated Moving Average (ARIMA), Nonlinear Autoregression Neural Network (NARNN) and Long-Short Term Memory (LSTM) approaches. Six model performance metric were used to select the most accurate model (MSE, PSNR, RMSE, NRMSE, MAPE and SMAPE). According to the results of the first step of the study, LSTM was found the most accurate model. In the second stage of the study, LSTM model was provided to make predictions in a 14-day perspective that is yet to be known. Results of the second step of the study shows that the total cumulative case increase rate is expected to decrease slightly in many countries. The last epidemic process, which started on named SARS-CoV-2 because of its similarity to SARS CoV [1] . The rate of contagion and spread of infection is quite fast compared to other viral infections encountered until today. Due to its rapid progress and covering the world in a short period of time, it is necessary to carry out intensive studies in it. Similar to many other infectious disease outbreaks, the success of controlling the new COVID-19 infection is based on revealing significant information, especially in the early period, with very limited data. For this, it is necessary to monitor the cases correctly and increase the reliability of the future predictions with each new data [2] . There are many studies in the literature on the prediction of epidemic diseases. The Auto-Regressive Integrated Moving Average (ARIMA) approach is often used to predict time series. The reason it is used so widely is that it can obtain useful statistical properties. They are also very flexible as they can represent multiple different time series using different order parameters. The ARIMA approach has been used to predict many diseases such as Hemorrhagic Fever with Renal Syndrome (HFRS) [3] , Brucellosis [4] , Influenza [5] and COVID-19 [6] . The Nonlinear Autoregression Neural Network (NARNN) model is a technique that performs nonlinear regression through the neural network. This machine learning technique has been used to predict various outbreaks [7] [8] [9] . The LSTM technique is a model that extends RNN (Recurrent Neural Network) memory. Typically, repetitive neural networks have "short-term memory" because they use persistent prior knowledge for use in the existing neural network. Essentially, previous information is used in the current task [10] . Studies involving the use of LSTM in the prediction of infectious diseases are rather scarce. In a study by Chimmula and Zhang (2020), COVID-19 infection in Canada was estimated by LSTM [11] . In the study by Tomar and Gupta (2020), COVID-19 infection in India was analyzed and predicted with LSTM [12] . In this study, unlike other studies, the total number of cases in COVID-19 infection was modeled and estimated by ARIMA, NAR and LSTM approaches. The performance of the models examined has been compared. As a result of this comparative analysis, the most successful model was determined by considering six different performance parameters. At the same time, the data used in this study includes the widest time interval ever made. The data used includes 8 different European countries (Denmark, Belgium, Germany, France, United Kingdom, Finland, the most successful model, prospective forecasting study was carried out for the cumulative confirmed number of cases in each country. In this study, cumulative confirmed case data of 8 different European countries (Denmark, Belgium, Germany, France, United Kingdom, Finland, Switzerland and Turley) were used for modeling. The data were obtained from European Center for Disease Prevention and Control [13] . Data were taken from the day the first case was seen, and the number of data for each country varies. The data covers 67, 90, 97, 100, 94, 90, 68 and 55 days respectively and ends on 3 May 2020. Dates of first recorded case of the investigated countries is given in Table 1 . Here, is a constant value and is error term. Time series as a qth degree of moving average process MA(q) can be found as: (2) ARMA(p,q) expression can be obtained by combining two AR(p) and MA(q) equations: ( If the processed time series is not stationary, it can be made stationary by taking the difference process times. Once the difference of non-stationary series is taken, series, which expresses stationary feature, can be calculated by Eq. (4): The ARIMA (p, d, q) process could be generally found by using Eq. (5): Particial auto correlation (PACF) can be utilized to find the AR parameter value and the correlogram graphs of the auto correlation (ACF) functions can be used to achieve the value of the MA. In order to obtain the most appropriate parameter in the ARIMA approach, the model performance is usually measured by the Akaike Information Criteria (AIC) expression. It can be calculated as: Here, L is the likelihood of the data, p is the order of the autoregressive part and q is the order of the moving average part and k is the intercept of the ARIMA model. According to this paremeter, the model with the lowest AIC criterion is considered more successful than the others. In this study, the parameters showing the highest performance were achieced from the ARIMA (2,2,5) model. Nonlinear Autoregression Neural Network (NARNN) is a frequently used approach especially in time series predictions. This artificial neural network utilizes a certain part of the time series as training data and multiplier weights in the artificial neural network are obtained. The NARNN approach assumes that the value of Y in time t, is a function of the past d number, as seen in Eq. (7). NARNN 2-delay model consisting of 10 neurons. This neural network estimates the future value by looking at two historical data. Long-short term memory (LSTM) is a machine learning algorithm with recurrent neural network architecture [14] . As a model, it stores the information learned in the short period and uses it for training in the long period. Therefore, long short-term memory contains units called "memory blocks" in hidden layer. These memory blocks can be defined as hidden units in traditional repeating neural networks. It contains one or more memory cells in the memory blocks. Each memory block contains input and output ports to control the flow of information. While the input gate controls the flow of input activation information in the memory cell, the output doors control the flow of output activation information. Later, a "forget gate" was added to the memory blocks. The forgetting gate scales the internal state of the cell, resets the memory of the cell, before the input activation through the cell's repetitive connection [15] . In order for the LSTM model to be better understood, the steps of the model must be examined. If the model input of the LSTM model is named x t at time t and the model output is h t , then the network to be created must first reset the output from the previous model at t. The model should then be decided what information should be stored in the model. This process consists of two parts. First, the input gate layer decides which values to update. Then the sigmoid layer creates a vector containing possible new values. At the end of these processes, these two steps are combined and the input is updated. Finally, the output of the network is decided. The result to be output here is formed from the decided part of the sigmoid gate. denotes the corresponding weight matrices, σ is the activation function which is taken as sigmoid, ft is forget function, Ct is candidate vector and ot is sigmoid function output. The output generated in the model is filtered output based on the model cell state. The internal architecture and LSTM architecture of the LSTM block used in this study are shown in Fig. 2 and Fig. 3 , respectively. Error (SMAPE) can be calculated by using Eqs. (5-10), respectively [16] . In the above equations, is root-mean-square deviation, is peak value and is error sum of squares. In this study, unlike other studies on COVID-19, data from different countries were estimated by three different methods. Fig. 4 shows 7-step estimates for Germany, United Kingdom, Finland and Switzerland. In Fig. 5 , the predictions of Turkey, Belgium, France and Denmark are illustrated. performance factors of the developed models are given in Table 2 . As can be seen from Fig. 4 model. In addition, the weight of the total RMSE value by models is shown in Fig. 6 . Nevertheless, it is clearly seen that the lowest RMSE value is found for LSTM. Accordingly, it is clearly seen that the LSTM model is the most successful model for all country data examined within the scope of the study. observed in the UK. It is observed that the model achievements will increase when the number of days in which the outbreak data is diversified and the data collected is increased. The limited data on COVID-19 is quite challenging for modeling and prediction. In this study, the data from cumulative confirmed cases in some European countries are modeled using three different approaches. According to the results, it was determined that LSTM approach has much higher success compared to ARIMA and NARNN. Later on, forward estimations were made with LSTM with high performance. Among the countries studied, the lowest number of cases was observed in Finland during the epidemic, while the highest rate of increase was observed in the UK. According to the 2-week prospective estimation study, in many countries, the total case increase rate is expected to decrease slightly. The study is carried out entirely by considering statistical data and methodologies, the effects of measures taken during the epidemic, compliance with hygiene rules or lockdown are ignored. Nevertheless, the rate of conformity of the developed prediction model with real data is very satisfactory and offers a strong projection for the near future. However, it is too early to draw a definitive conclusion due to the differences in available data, human behavior and measures taken on a country basis. It is observed that the model achievements will increase when the number of days in which the outbreak data is diversified and the data collected is increased. 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