key: cord-0718201-2wg8tc1c
authors: Ceylan, Zeynep
title: Short-term prediction of COVID-19 spread using grey rolling model optimized by particle swarm optimization
date: 2021-06-09
journal: Appl Soft Comput
DOI: 10.1016/j.asoc.2021.107592
sha: b6ac1bbd3c96452e8c4deced84a7a1ed91ba7442
doc_id: 718201
cord_uid: 2wg8tc1c

The prediction of the spread of coronavirus disease 2019 (COVID-19) is vital in taking preventive and control measures to reduce human health damage. The Grey Modeling (1,1) is a popular approach used to construct a predictive model with a small-sized data set. In this study, a hybrid model based on grey prediction and rolling mechanism optimized by particle swarm optimization algorithm (PSO) was applied to create short-term estimates of the total number of confirmed COVID-19 cases for three countries, Germany, Turkey, and the USA. A rolling mechanism that updates data in equal dimensions was applied to improve the forecasting accuracy of the models. The PSO algorithm was used to optimize the Grey Modeling parameters (1,1) to provide more robust and efficient solutions with minimum errors. To compare the accuracy of the predictive models, a nonlinear autoregressive neural network (NARNN) was also developed. According to the analysis results, Grey Rolling Modeling (1,1) optimized by PSO algorithm performs better than the classical Grey Modeling (1,1), Grey Rolling Modelling (1,1), and NARNN models for predicting the total number of confirmed COVID-19 cases. The present study can provide an important basis for countries to allocate health resources and formulate epidemic prevention policies effectively.

virus. To the best of the author's knowledge, the Rolling-PSO-GM (1,1) model is used for the method used to predict next values using historical values of one-dimensional series [31] . It is commonly used in different fields such as wind forecasting [32] , global solar radiation 150 forecasting [33] , disease prevalence prediction [29] , and power prediction [34] . In this study, 151 the NARNN model was built and used for short-term prediction of COVID-19 spread in 

Step 1. The non-negative row sequence with n samples is presented in Eq.

(3).

Monotonically increasing series (1) is generated by using a one-time accumulating generation 184 operation (1-AGO):

(1) = � (1) (1), (1) (2), (1) (3), … , (1) ( )� (4) 186 where,

(1) ( ) = ∑ 0 =1 ( ); = 1,2,3, … ,

Step 2. A first-order grey differential equation is formed to obtain GM (1,1) model: where,

(1) ( ) = (1) ( ) + (1 − ) (1) ( − 1); = 2,3, … ,

These are two parameters of the GM (1,1) model and can be estimated using the least square method [ ] :

where is the constant vector, and B is the accumulated matrix.

Step 3. After calculating the a and b coefficients, the GM (1,1) model can be established by 200 solving the differential equation in Eq. (10)

where the initial condition (1) (0) is taken as (1) (1).

Typically, in the original GM (1,1) model, all data is used for prediction. However, in the case 204 of chaotic data, it is recommended to use the latest data to improve the prediction accuracy of 205 the GM (1,1) model. To achieve this, the grey prediction with a rolling mechanism (Rolling- . The calculation of MAD, RMSE, and MAPE are given by the following Eqs. (13-15).

259 J o u r n a l P r e -p r o o f

where n is the observation, (0) ( ) and � (0) ( ) are actual and predicted data at time k, 261 respectively. It is known that the model with the lowest MAD, MAPE, and RMSE values 262 means better performance. Table 2 shows the parameters calculated by the 287 three grey prediction models.

-Insert Table 2 -

According to the PSO operations steps, the parameters of the PSO algorithm are set as follows: Table 3 .

-Insert Table 3-295   Table 4 shows the forecasting values of NARNN, GM (1,1), Rolling GM (1,1), and Rolling- 

-Insert Table 4 -300

As seen in Table 4 , the Rolling-GM (1,1) and Rolling-PSO-GM (1,1) models outperform the reason for this may be that the rolling-based prediction models have a mechanism that updates 305 the data at each rolling stage. It is seen that the PSO algorithm has significantly improved the accuracy of the grey model. Fig. 4 presents the forecasting results of the cumulative cases of 309 COVID-19 for Germany, Turkey, and the USA using Rolling-PSO-GM (1,1) model, 310 respectively. There appears to be good agreement between the reported confirmed cases and 311 the predicted cases. 

A novel algorithm to define infection Reference Disease Method(s) Country