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Forecasting the epidemiological trends of COVID-19 prevalence and mortality using the advanced α-Sutte Indicator

Published online by Cambridge University Press:  05 October 2020

Yongbin Wang*
Affiliation:
Department of Epidemiology and Health Statistics, School of Public Health, Xinxiang Medical University, Xinxiang, Henan Province, P.R. China
Chunjie Xu
Affiliation:
Department of Occupational and Environmental Health, School of Public Health, Capital Medical University, Beijing, P.R. China
Sanqiao Yao
Affiliation:
Department of Epidemiology and Health Statistics, School of Public Health, Xinxiang Medical University, Xinxiang, Henan Province, P.R. China
Yingzheng Zhao
Affiliation:
Department of Epidemiology and Health Statistics, School of Public Health, Xinxiang Medical University, Xinxiang, Henan Province, P.R. China
*
Author for correspondence: Yongbin Wang, E-mail: wybwho@163.com
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Abstract

Forecasting the epidemics of the diseases is very valuable in planning and supplying resources effectively. This study aims to estimate the epidemiological trends of the coronavirus disease 2019 (COVID-19) prevalence and mortality using the advanced α-Sutte Indicator, and its prediction accuracy level was compared with the most frequently adopted autoregressive integrated moving average (ARIMA) method. Time-series analysis was performed based on the total confirmed cases and deaths of COVID-19 in the world, Brazil, Peru, Canada and Chile between 27 February 2020 and 30 June 2020. By comparing the prediction reliability indices, including the root mean square error, mean absolute error, mean error rate, mean absolute percentage error and root mean square percentage error, the α-Sutte Indicator was found to produce lower forecasting error rates than the ARIMA model in all data apart from the prevalence testing set globally. The α-Sutte Indicator can be recommended as a useful tool to nowcast and forecast the COVID-19 prevalence and mortality of these regions except for the prevalence around the globe in the near future, which will help policymakers to plan and prepare health resources effectively. Also, the findings of our study may have managerial implications for the outbreak in other countries.

Keywords

Type
Original Paper
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

Introduction

Coronavirus disease 2019 (COVID-19) is an emerging respiratory infectious disease that spreads rapidly from human to human and has presented a pandemic on the global scale [1, Reference Lin and Yao2]. As of 30 June 2020, this disease still continues to take its toll and has led to a major tragedy with 10 185 374 confirmed cases and 503 862 deaths in more than 200 countries, areas or territories [1]. The disease evolves rapidly and has a notable dynamic structure. World Health Organization (WHO) estimated that COVID-19 may still show a rising trend with around 80 000 new notifications per day in the near future [1, Reference Wu, Leung and Leung3]. Importantly, the confirmed cases and deaths of this disease vary greatly owing to the differences in disease surveillance and detection capacities among countries, thus causing an obvious underestimation in some countries severely affected by the COVID-19 outbreak [Reference Ceylan4]. Regrettably, there is a current lack of the determined clinical treatment method and available vaccines for this serious disease [Reference Sun, Ni and Zhang5]. Therefore it is necessary to formulate effective planning for the health infrastructure and services under dynamic demand in order to curb and harness the continued spreading of the COVID-19 pandemic. Accurate forecasting of the epidemiological trends of the COVID-19 prevalence and mortality is essential to manage and instruct the demand to the health system [Reference Singh6Reference Sotgiu8].

Time-series analysis is of great value in developing hypotheses to understand the past and current epidemic patterns of infectious diseases and to predict the dynamics in the upcoming future [Reference Ceylan4, Reference Singh6]. Model-based mathematics and statistics have emerged as useful tools to analyse and estimate time series [Reference Chimmula and Zhang9, Reference Ayinde10]. For public health officials, such an estimate plays an important role in allocating limited health resources rationally and in directing when and which health interventions should be adopted to alleviate the disease outbreak [Reference Ceylan4, Reference Singh6, Reference Saba and Elsheikh11, Reference Tiwari, Kumar and Guleria12]. Recently, a great number of mathematical and statistical techniques have been deemed as policy-supportive tools to model the prevalence, morbidity and mortality of COVID-19 in different countries [Reference Ayinde10, Reference Salgotra, Gandomi and Gandomi13, Reference Yousaf14]. For example, Saba et al. used an autoregressive integrated moving average (ARIMA) model and a nonlinear autoregressive artificial neural networks (NARNN) to forecast the prevalence of the COVID-19 outbreak in Egypt [Reference Saba and Elsheikh11]. Ceylan et al. constructed several suitable ARIMA models to estimate the COVID-19 prevalence in Italy, Spain and France [Reference Ceylan4]. Chen et al. built a Bats-Hosts-Reservoir-People transmission network method to model the potential transmission processes of COVID-19 from bats to humans [Reference Chen7]. Sotgiu et al. proposed a new third-degree polynomial curve to simulate the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)-related mortality in Italy, Germany, Spain and New York State [Reference Sotgiu8]. Sarkodie et al. developed five dynamic statistical techniques to assess the COVID-19 prevalence across China [Reference Sarkodie and Owusu15]. Cássaro et al. constructed a simple approach of growth to model the evolution of the COVID-19 outbreak in various countries [Reference Cássaro and Pires16]. Wan et al. used a susceptible exposed infectious recovered (SEIR) method to analyse the epidemic dynamics and trends of COVID-19 in Wuhan [Reference Wan17]. Al-qaness et al. developed an optimisation method based on the Adaptive NeuroFuzzy Inference System (ANFIS) to predict the confirmed cases of COVID-19 in China [Reference Al-Qaness18]. Bekiros et al. built a stereographic Brownian diffusion epidemiology model (SBDiEM) to track the outbreak trends [Reference Bekiros and Kouloumpou19]. The epidemiological trends of COVID-19 are driven by many various factors (such as climate change [Reference Qi20], government interventions [Reference Pan21], virus variation [Reference Cagliani and Forni22] etc.), which intimated that the spreading mode of the COVID-19 pandemic is characterised by secular tendencies and irregular fluctuations. For this reason, the above-mentioned methods have a limited ability to consider the tendencies and randomness simultaneously due to their linear or nonlinear assumption, which affects the extrapolation of the results [Reference Ceylan4].

More recently, a new technical indicator, α-Sutte Indicator, is proposed by Ahmar [Reference Ahmar23], which was originally developed to analyse and estimate the stock movements by taking the opening price, the closing price, the highest price, the lowest price and the volume of transactions on the stock into consideration [Reference Ahmar23Reference Ansari Saleh25]. The α-Sutte Indicator may have the potential to accommodate the problems encountered in the above-mentioned models as it has been demonstrated that the α-Sutte Indicator can be employed to predict the trends in change of not only the stock movements but also all-time series data [Reference Ahmar23, Reference Ahmar, Rahman and Mulbar26]. Furthermore, the α-Sutte Indicator is relatively easy to evaluate and interpret in that it does not involve complex mathematical or statistical theories. Hence, the decision makers can have an idea of how the forecasting indicator is constructed and can depend more on this predictive tool during the decision-making process. Currently, some countries in the Americas have been hit the hardest with the COVID-19 outbreak and this disease still spreads rapidly, particularly in Brazil, Peru, Canada and Chile [1]. Given the advantage of α-Sutte Indicator and the current epidemic status of COVID-19 in the mentioned countries, this study aims to describe the epidemic situation of COVID-19 and to forecast the epidemiological trends of the COVID-19 prevalence and mortality in the above-mentioned countries and worldwide using this advanced α-Sutte Indicator. In the meantime, the predictive ability of the α-Sutte Indicator was also compared with that of the most common use of ARIMA model in the COVID-19 outbreak forecasting [Reference Ceylan4, Reference Saba and Elsheikh11, Reference Yousaf14, Reference Caputi and Ayers27Reference Chintalapudi, Battineni and Amenta30].

Materials and methods

Data collection

The prevalence and mortality time-series data of COVID-19 used in this study corresponded to the period between 27 February 2020 and 30 June 2020, all these data were collected from the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University (https://github.com/CSSEGISandData/COVID-19) and the WHO website (https://www.who.int/emergencies/diseases/novel-coronavirus-2019), and Microsoft Office Excel 2007 was utilised to collate database. Typically, to obtain a robust and effective model in practice, at least 50 observations and preferably 100 observations or more should be used [Reference Bartholomew, Box and Jenkins31]. Consequently, during the model-development process, the data samples from 27 February 2020 to 5 June 2020 (100 observations) were used for the training set, and the remaining 25 samples were taken for the testing set.

The study protocol was approved by the research institutional review board of the Xinxiang Medical University (No: XYLL-2019072), and it was exempt from the institutional review board assessment since all the data analysed in this study were obtained in an anonymous format and any non-essential identifying information were not accessed. In addition, this study meets all the guidelines in the Declaration of Helsinki.

ARIMA model construction

Time-series prediction aims to use a statistical technique to nowcast and forecast future unknown series by identifying the internal rules between the past and current series. Often, time series displays correlations between successive observations. The ARIMA model is designed to make forecasts by taking correlations existing in the time-series data into consideration [Reference Chen32]. ARIMA model types are listed using the standard notation of ARIMA (p, d, q), herein, p signifies the order of autoregression (AR), d refers to the order of integration and q represents the order of moving average (MA). The ARIMA method is defined for stationary time series. Hence, the stationary conditions of the targeted time series should first be judged by inspecting the time-series plots and by performing the Augmented Dickey–Fuller (ADF) statistic, if the time series displays a trend in change over time and the ADF statistic shows no statistical difference, indicating a non-stationary time series [Reference Wang33]. In this case, the time series requires to be differenced until a stationary series is obtained [Reference Wang34]. Afterward, the values of p and q can roughly be identified by examining the autocorrelation function (ACF) and partial ACF (PACF) graphs of the differenced time series [Reference Wang34]. The ‘Expert Modeler’ in SPSS software and ‘auto.arima()’ in R software have an ability to automatically identify the best-performing ARIMA model by considering the goodness of fit measures such as a larger value of R-squared (R 2), a lower value of normalised Bayesian information criterion (NBIC) and the appropriate ACF and PACF graphs of the errors [Reference Zeng35, Reference Wang36]. In this study, both these two tools were used to determine the best model. After that, statistical tests were conducted for the resulting best ARIMA model. The estimated key parameters of the AR and MA should be statistically significant under the t test [Reference Li37, Reference Liu38]. A Ljung-Box Q test was then applied to the residual series produced by the best-fitting ARIMA model, if this statistic provided a P-value greater than 0.05, suggesting that the residuals behaved like a white-noise series [Reference Li37, Reference Liu38]. At this time, the best ARIMA model passed all the required checking, and then it can be used to implement out-of-sample forecasting. The general forms of the AR process, the MA process and the ARIMA process are given in Eqs. (1), (2), and (3), respectively, below

(1)$$Y_t = \phi _1Y_{t-1} + \phi _2Y_{t-2} + \cdots + \phi _pY_{t-p} + \varepsilon _t$$
(2)$$Y_t = \varepsilon {}_t-\theta _1\varepsilon _{t-1}-\theta _2\varepsilon _{t-2}-\cdots -\theta _q\varepsilon _{t-q}$$
(3)$$Y_t = \phi _1Y_{t-1} + \phi _2Y_{t-2} + \cdots + \phi _pY_{t-p} + \varepsilon _t-\theta _1\varepsilon {}_{t-1}-\theta _2\varepsilon _{t-2}-\cdots -\theta _q\varepsilon _{t-q}$$

where ϕ and θ represent the key parameters of AR and MA, respectively, p and q correspond to the orders of AR and MA, respectively,Y t refers to the observation at time t andɛtis the residual series that is assumed to be uncorrelated in the final ARIMA model.

α-Sutte Indicator

α-Sutte Indicator is a novel technical analysis based on the Sutte Indicator method that was initially proposed in 2017 by Ahmar [Reference Ahmar, Rahman and Mulbar26]. As known, the stock movements failed to be always consistent, sometimes suddenly descended and sometimes suddenly ascended, which caused less accuracy in the domain of stock forecasting using the common technical indicators such as simple moving average (SMA), moving average convergence/divergence (MACD), relative strength index (RSI), stochastic and Bolinger Band [Reference Ahmar23, Reference Ahmar, Rahman and Mulbar26, Reference Kurniasih39]. Hence, the development of α-Sutte Indicator is expected to overcome the weakness of the mentioned methods in predicting the stock movements by considering five elements of the stock movements, namely price at the time of opening, closing, highest and lowest, along with the volume of transactions [Reference Ahmar24]. Paralleling the advance in methodology, the α-Sutte Indicator is found to be not only limited to forecast the stock movements but can to perform prediction for the time series of data as it can track the dynamic dependence of certain data reasonably well [Reference Ahmar, Rahman and Mulbar26, Reference Kurniasih39, Reference Ahmar40]. The formula of α-Sutte Indicator can be in the form as below

(4)$$\alpha _t = \displaystyle{{\alpha {[ {\Delta x/\lpar \lpar \alpha + \delta \rpar /2\rpar } } ] + \beta {[ {\Delta y/\lpar \lpar \beta + \alpha \rpar /2\rpar } } ] + \gamma {[ {\Delta z/\lpar \lpar \gamma + \beta \rpar /2\rpar } } ] } \over 3}$$

where

(5)$$\delta = \alpha _{t-4}$$
(6)$$\alpha = \alpha _{t-3}$$
(7)$$\beta = \alpha _{t-2}$$
(8)$$\gamma = \alpha _{t-1}$$
(9)$$\Delta x = \alpha -\delta = \alpha _{t-3}-\alpha _{t-4}$$
(10)$$\Delta y = \beta -\alpha = \alpha _{t-2}-\alpha _{t-3}$$
(11)$$\Delta z = \gamma -\beta = \alpha _{t-1}-\alpha _{t-2}$$

where α t denotes the observed value at t time and α tk signifies the observed value at (tk) time.

Measuring for the prediction reliability level

The forecasting reliability level between two models was assessed by different measurement metrics, including the scale-dependent measurement metrics (e.g. root mean square error (RMSE) and mean absolute error (MAE)) and the measurement metrics based on percentage errors (e.g. mean error rate (MER), mean absolute percentage error (MAPE) and root mean square percentage error (RMSPE)). A smaller value of these measurement metrics corresponded to the best model and this optimal model was then constructed to produce the out-of-sample forecasting. In the process of predicting data, the 95% confidence limits (CL) of the out-of-sample forecasts were generated by forecasting the in-sample counterparts.

(12)$${\rm RMSE} = \sqrt {\displaystyle{1 \over N}\sum\limits_{i = 1}^N {{\lpar Y_i-{\hat{Y}}_i\rpar }^ 2} } $$
(13)$${\rm MAE} = \displaystyle{1 \over N}\sum\limits_{i = 1}^N {\vert {Y_i-{\hat{Y}}_i} \vert } $$
(14)$${\rm MER} = \displaystyle{{\lpar 1/N\rpar \sum\nolimits_{i = 1}^N {\vert {Y_i-{\hat{Y}}_i} \vert } } \over {{\bar{Y}}_i}}$$
(15)$${\rm MAPE} = \displaystyle{1 \over N}\sum\limits_{i = 1}^N {\displaystyle{{\vert {Y_i} - {{\hat{Y}}_i} \vert } \over {Y_i}} \times 100} $$
(16)$${\rm RMSPE} = \sqrt {\displaystyle{1 \over N}\sum\limits_{i = 1}^N {{\left({\displaystyle{{Y_i-{\bar{Y}}_i} \over {Y_i}}} \right)}^2} } $$

where Y i refers to the original observations, $\hat{Y}_i$ is the prediction values, denotes the average of the original observations and N signifies the number of original observations. In this research study, we used SPSS software (version 17.0, IBM Corp, Armonk, NY) and R software (version 4.0.0, R Development Core Team, Vienna, Austria) to construct the ARIMA model and the α-Sutte Indicator. The statistical significance level was set at P < 0.05.

Results

Statistical description

Between 27 February 2020 and 30 June 2020, the overall confirmed cases were 10 185 374, 1 344 143, 279 419, 103 250 and 275 999 with an average of 81 483, 107 53, 2235, 826 and 2208 case notifications per day in the world, Brazil, Peru, Canada and Chile, respectively (Figs. 1A and 1B). Among them, the reported deaths due to the COVID-19 outbreak have reached 503 862, 57 622, 9317, 8522 and 5575 cases with an average of 4031, 461, 75, 38 and 45 cases per day in the world, Brazil, Peru, Canada and Chile, respectively (Figs. 1A and 1C).

Fig. 1. Time series plots displaying the prevalence and mortality cases of COVID-19. (a) The total confirmed cases and deaths worldwide;(b) The total confirmed cases in Brazil, Peru, Canada, and Chile; (c) The total deaths in Brazil, Peru, Canada, and Chile. Worth noting that manycountries, areas or territories recently reconciliated the reported prevalence and mortality data of the COVID-19 outbreak, and thus the prevalenceand mortality data used to build the ARIMA and α-Sutte Indicator models were retrospectively updated on the basis of the additional detailsprovided by WHO, so that we can develop a reliable model for estimating the epidemiological trends of the prevalence and mortality of the COVID-19 outbreak in the upcoming days or weeks.

Building the ARIMA model

By comparing the best models identified by running the ‘Expert Modeler’ function in SPSS software and auto.ARIMA code in R software, the ARIMA(0,2,(1,7)), ARIMA(0,2,4), ARIMA(0,2,2), ARIMA(1,2,2) and ARIMA(1,2,1) models were considered as the best specifications for forecasting the prevalence time series in the world, Brazil, Peru, Canada and Chile, respectively, as they provided a greater value of the stationary R 2 and R 2, as well as a smaller value of the NBIC in all potential models. Also, as evidenced by the augmented Dickey−Fuller (ADF) test and the ACF and PACF plots for the differenced prevalence series (Supplementary Table S1 and Figs. S1 and S2), it appeared that these selected models are suitable. Further statistical checking suggested that the key parameters of these best models were indicated to be statistically significant under the t test (Table 1), and the residuals were indicated to behave like a white-noise series because of a P-value greater than 0.05 at different lags under the Box−Ljung Q test and the sample ACF and PACF lying inside the estimated 95% uncertainty limits (Supplementary Table S2 and Fig. S3). These results demonstrated that the chosen best ARIMA models are appropriate and adequate for simulating the prevalence data in these regions. Similarly, we could determine the best-fitting ARIMA models for the mortality time series in these five regions according to the modelling steps, and the resulting results of the identified key parameters and the statistical tests for the best ARIMA models are summarised in Table 2, Supplementary Tables S1 and S3, Figs. S4 and S5. Subsequently, these derived best ARIMA models can be employed to the testing sets to produce out-of-sample projections (Fig. 2).

Fig. 2. Time series plots displaying the resulting forecasts for the testing sets of COVID-19 prevalence and mortality in the five regions using the α-Sutte Indicator and ARIMA models. (a) The resulting forecasts for the testing sets of the COVID-19 prevalence and mortality globally; (b) The resulting forecasts for the testing sets of the COVID-19 prevalence and mortality in Brazil; (c) The resulting forecasts for the testing sets of the COVID-19 prevalence and mortality in Peru; (d) The resulting forecasts for the testing sets of the COVID-19 prevalence and mortality in Canada; (e) The resulting forecasts for the testing sets of the COVID-19 prevalence and mortality in Chile. Here the forecasts for testing data are plotted as gray shaded area. As seen above, it seemed that the forecasts for the testing sets of both the prevalence and mortality from the α-Sutte Indicator yielded more sufficient prediction accuracy compared with that from the ARIMA model in the five regions except for the result from the testing sets of the COVID-19 prevalence around the globe.

Table 1. The identified best ARIMA models to forecast the epidemiological trend of COVID-19 prevalence in the five regions

ARIMA, autoregressive integrated moving average; AR1, autoregressive at lag one day; MA1, moving average at lag one day; MA2, moving average at lag two days; MA4, moving average at lag four days; MA7, moving average at lag seven days; s.e., standard error; NBIC, normalised Bayesian information criterion.

Table 2. The identified best ARIMA models to forecast the epidemiological trend of COVID-19 mortality in the five regions

ARIMA, autoregressive integrated moving average; AR1, autoregressive at lag one day; MA1, moving average at lag one day; MA2, moving average at lag two days; MA3, moving average at lag three days; MA4, moving average at lag four days; MA7, moving average at lag seven days; s.e., standard error; NBIC, normalised Bayesian information criterion.

Developing the α-Sutte Indicator

Applying the α-Sutte Indicator to the prevalence and mortality time series of COVID-19, the resulting forecasts for the testing sets are provided in Figure 2.

Reliability test between models

To see the forecasting accuracy levels of the α-Sutte Indicator method and the ARIMA model, then the comparison of the performance measurement metrics of MAE, MAPE, RMSE, MER and RMSPE from the resulting forecasting results on the testing data using these two models was done. Looking at Table 3, the values of the above-mentioned five indices from the α-Sutte Indicator were smaller than the counterparts from the ARIMA models in both the prevalence and mortality testing sets except for that from the prevalence testing set globally, similar results are also illustrated in Figure 2. In the sense that the reliability level in forecasting, the α-Sutte Indicator is more appropriate for estimating the epidemiological trends of the COVID-19 prevalence and mortality as compared with the ARIMA model in the study regions with an exception of the prevalence around the globe. Consequently, the next 20-day total confirmed cases and deaths from 1 July 2020 to 20 July 2020 in the study regions were predicted using the α-Sutte Indicator on the basis of the data from 27 February 2020 to 30 June 2020 besides the total confirmed cases around the globe, which were done with the ARIMA model (Supplementary Tables S4–S6). The forecasted future 20-day total confirmed cases and deaths may reach 14 153 625 (95% CL 13 293 010 to 15 014 240) and 588 441 (95% CL 587 779 to 589 102) around the globe, respectively, 2 117 890 (95% CL 2 111 135 to 2 124 648) and 74 563 (95% CL 74 365 to 74 761) in Brazil, respectively, 352 946 (95% CL 352 615 to 353 281) and 13 238 (95% CL 13 230 to 13 246) in Peru, respectively, 107 612 (95% CL 107 578 to 107 646) and 8649 (95% CL 8639 to 8659) in Canada, respectively, together with 362 422 (95% CL 357 133 to 367 713) and 8463 (95% CL 8404 to 8532) in Chile, respectively.

Table 3. Comparison of accuracy levels measurement of forecasting for the COVID-19 prevalence and mortality between α-Sutte indicator and ARIMA methods in the five regions

ARIMA, autoregressive integrated moving average method; MAE, mean absolute error; MAPE, mean absolute percentage error; RMSE, root mean squared error; MER, mean error rate; RMSPE, root mean square percentage error; A denotes the α-Sutte Indicator; B represents the ARIMA model.

Discussion

The eruption of COVID-19 has left extensive and profound impacts around the globe. In view of the current serious challenges raised by the COVID-19 outbreak worldwide, feasible and effective countermeasures are required to prevent and control the rapid increases in the numbers of confirmed cases and deaths. Early nowcasting and forecasting the spreading dynamics of the COVID-19 outbreak are significantly vital for defining strategic choices not only in controlling the transmission of this disease, but also in reducing the outbreak-related deaths, moreover, it benefits for national economic development [Reference Ceylan4, Reference Sotgiu8, Reference Li, Feng and Quan41, Reference Ahmar and Del Val42]. As a result, it is necessary to construct the mathematical and statistical models with strong robustness and good reliability to estimate the duration and extent of the COVID-19 outbreak in the most affected countries. Time-series analysis is considerably helpful in forming hypotheses to analyse the epidemiological trends of different diseases and to forecast the epidemic dynamics of the target disease, and subsequently developing a quality control system based on the modelling results [Reference Ceylan4, Reference Singh6, Reference Zeng35, Reference Wang43]. As far as we are aware, this is the only study to perform time-series forecasting for the ongoing trend and extent of the COVID-19 outbreak in the world, Brazil, Peru, Canada and Chile using the advanced α-Sutte Indicator, and its predictive performances on the different prevalence and mortality datasets were compared with the ARIMA model which was recommended as the most frequent and powerful tool in the domain of time-series prediction [Reference Li37, Reference Liu38]. Our experimental results indicated that α-Sutte Indicator has priority over the ARIMA model for forecasting the epidemiological trends of the prevalence and mortality of the COVID-19 outbreak in the mentioned regions except for the epidemiological trends of the COVID-19 prevalence around the globe. Furthermore, the α-Sutte Indicator produced a highly accurate prediction as a value less than 10% in all data was presented in the tested forecasting reliability measure of MAPE that is often used to assess the predictive accuracy level [Reference Pao44]. In summary, the satisfactory results from a series of comparative investigations confirm that the α-Sutte Indicator has an ability to track the dynamic structures of the prevalence and mortality of the COIVD-19 outbreak, which can help policymakers to determine which and when emergency macroeconomic strategies to be formulated and how to allocate the limited medical and health resources. Meanwhile, this prediction model can also be beneficial in estimating when public health interventions take effects in the study population. For example, the actual prevalence and mortality are beginning to recede, whereas we estimated a higher level using this model, implying that the measures are playing a positive role. Otherwise, additional measures may be required. Besides, given its simple structure, good flexibility and excellent potential to evaluate the data of the α-Sutte Indicator, it seems that this method may be transferable to make time-series forecasting for the trends of the epidemiological indicators (such as prevalence, morbidity and mortality) in other countries, territories or areas during the pandemic period or other types of data (such as the data with notable seasonality and periodicity). However, future studies on the additional topic are still required to verify its suitability for the application of the α-Sutte Indicator.

The COVID-19 pandemic has been placing an intolerable burden on the health system capacity worldwide [Reference Nurchis45, Reference Tadesse46]. Currently, there is a great concern on whether the countries severely affected by the COVID-19 pandemic have an ability to provide the sufficient number of materials and resources under dynamic demand for the infected people, such as the increased intensive care unit (ICU), the adequate medical supplies, the eventual vaccine and the like [Reference Ceylan4, Reference Sotgiu8, Reference Ye47]. In this study, the upcoming 20-day total cumulative cases and deaths due to the COVID-19 outbreak were estimated using the ARIMA and α-Sutte Indicator. The resulting results show that the confirmed cases and deaths may still remain high levels around the globe with a daily average of 181 313 and 4229 cases, respectively, in the next 20 days. Brazil, the second-worst-hit country globally, may still witness an exponential trend with daily 38 687 estimated cases and 847 estimated deaths in the future 20 days. The prior experiences from some countries such as China, Republic of Korea, Italy and Germany have demonstrated that, in the absence of vaccines available, were there no strict control actions such as the lockdown and social distancing measures that have been instituted at the national levels, never would we make the outbreak under control well. Thus, given the current outbreak patterns of COVID-19 in Brazil, the government should continue to implement strict preventive and control strategies, and even more strict interventions, such as continued lockdown, keeping social distancing, an optimisation of the current tools, increasing the numbers of the mobile cabin hospitals, avoiding hospital-related infections, increasing medical personnel, increasing ICU availability, preparing isolation wards, enhancing the awareness of the general public etc. [Reference Ceylan4, Reference Chintalapudi, Battineni and Amenta30, Reference Ye47Reference Hu50]. Similar prophylactic measures are also expected to be carried out in Peru and Chile because the daily confirmed cases and deaths have still been noticeably rising in these two countries with daily 3676 and 4321 confirmed cases, coupled with daily 196 and 144 deaths, respectively, and seemingly they required more days to reach the plateau. Contrary to the ongoing trend of the outbreak in the above-mentioned countries, the confirmed cases and deaths are decreasing in Canada with the next 20-day estimates of 218 cases and 6 deaths per day. In all, facing the drastic threats of the COVID-19 pandemic, only under the strict intervention strategies can we hope to tackle such a wide-ranging issue.

Conclusion

Forecasting the epidemiological trends of the prevalence and mortality of the diseases forms the basis for response to epidemics. In this time-series analysis, we focused on exploring the potential of the advanced α-Sutte Indicator and its suitability for the application to the epidemiological trend forecasting of the COVID-19 prevalence and mortality through a series of experiments. Our research suggests that this advanced model can get a more clear perspective of the trends of the epidemiological indicators of the COVID-19 outbreak in the five study regions except for the prevalence data around the globe than the most frequently used ARIMA model. The advanced α-Sutte Indicator can be recommended as a useful tool to nowcast and forecast the prevalence and mortality time series of COVID-19, which will be a useful aid for policymakers to plan and prepare health resources effectively, including medical personnel, medical protection facilities, isolation wards and ICU in response to the epidemic patterns of COVID-19 over the upcoming days or weeks. In addition, under the current outbreak trends, feasible and effective strategies are warranted to mitigate the continued spread of COVID-19.

Supplementary material

The supplementary material for this article can be found at https://doi.org/10.1017/S095026882000237X.

Acknowledgements

We appreciate the WHO and the CSSE for providing these data.

Author contributions

YBW and XHJ performed the data analysis and drafted this original manuscript. SQY and YZZ improved and revised the article. All the authors contributed to the data analysis, drafting or revising the article. All the authors gave final approval of the version to be published, and agreed to be accountable for all aspects of the work.

Financial support

This project was supported by the Innovation and Entrepreneurship Training Project for University Students of Henan Province and Xinxiang Medical University (code: S202010472007 and XYXSKYZ201932) and the Key Scientific Research Project of Universities in Henan (code: 21A330004).

Conflict of interest

None.

Data availability statement

All the data used in this research can be extracted from the WHO website and the Center for Systems Science and Engineering.

Footnotes

*

These authors contributed equally to this paper.

References

World Health Organization (WHO). Coronavirus disease (COVID-2019) situation reports. Available at https://www.who.int/emergencies/diseases/novel-coronavirus-2019/situation-reports/2020 (Accessed 21 May 2020).Google Scholar
Lin, C and Yao, C (2020) Potential role of Nrf2 activators with dual antiviral and anti-inflammatory properties in the management of viral pneumonia. Infection and Drug Resistance 13, 17351741.CrossRefGoogle ScholarPubMed
Wu, JT, Leung, K and Leung, GM (2020) Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study. Lancet (London, England) 395, 689697.Google ScholarPubMed
Ceylan, Z (2020) Estimation of COVID-19 prevalence in Italy, Spain, and France. Science of the Total Environment 729, 138817.CrossRefGoogle ScholarPubMed
Sun, X, Ni, Y and Zhang, M (2020) Rheumotologists' view on the use of hydroxychloroquine to treat COVID-19. Emerging Microbes & Infections 9, 830832.CrossRefGoogle ScholarPubMed
Singh, S et al. (2020) Development of new hybrid model of discrete wavelet decomposition and autoregressive integrated moving average (ARIMA) models in application to one month forecast the casualties cases of COVID-19. Chaos, Solitons, and Fractals 135, 109866.CrossRefGoogle ScholarPubMed
Chen, TM et al. (2020) A mathematical model for simulating the phase-based transmissibility of a novel coronavirus. Infectious Diseases of Poverty 9, 24.CrossRefGoogle ScholarPubMed
Sotgiu, G et al. (2020) Advanced forecasting of SARS-CoV-2-related deaths in Italy, Germany, Spain, and New York state. Allergy 75, 18131815.CrossRefGoogle ScholarPubMed
Chimmula, VKR and Zhang, L (2020) Time series forecasting of COVID-19 transmission in Canada using LSTM networks. Chaos, Solitons, and Fractals 135, 109864.CrossRefGoogle ScholarPubMed
Ayinde, K et al. (2020) Modeling Nigerian Covid-19 cases: a comparative analysis of models and estimators. Chaos, Solitons, and Fractals 138, 109911.CrossRefGoogle ScholarPubMed
Saba, AI and Elsheikh, AH (2020) Forecasting the prevalence of COVID-19 outbreak in Egypt using nonlinear autoregressive artificial neural networks. Process Safety and Environmental Protection 141, 18.CrossRefGoogle ScholarPubMed
Tiwari, S, Kumar, S and Guleria, K (2020) Outbreak trends of coronavirus disease–2019 in India: a prediction. Disaster Medicine and Public Health Preparedness 14, 16. doi: 10.1017/dmp.2020.115.CrossRefGoogle Scholar
Salgotra, R, Gandomi, M and Gandomi, AH (2020) Time series analysis and forecast of the COVID-19 pandemic in India using genetic programming. Chaos, Solitons, and Fractals 138, 109945.CrossRefGoogle ScholarPubMed
Yousaf, M et al. (2020) Statistical analysis of forecasting COVID-19 for upcoming month in Pakistan. Chaos, Solitons, and Fractals 138, 109926.CrossRefGoogle ScholarPubMed
Sarkodie, SA and Owusu, PA (2020) Investigating the cases of novel coronavirus disease (COVID-19) in China using dynamic statistical techniques. Heliyon 6, e03747.CrossRefGoogle ScholarPubMed
Cássaro, FAM and Pires, LF (2020) Can we predict the occurrence of COVID-19 cases? Considerations using a simple model of growth. Science of the Total Environment 728, 138834.CrossRefGoogle Scholar
Wan, K et al. (2020) When will the battle against novel coronavirus end in Wuhan: a SEIR modeling analysis. Journal of Global Health 10, 011002.CrossRefGoogle ScholarPubMed
Al-Qaness, MAA et al. (2020) Optimization method for forecasting confirmed cases of COVID-19 in China. Journal of Clinical Medicine 9, 674. doi: 10.3390/jcm9030674.CrossRefGoogle ScholarPubMed
Bekiros, S and Kouloumpou, D (2020) SBDiEM: a new mathematical model of infectious disease dynamics. Chaos, Solitons and Fractals 136, 109828.CrossRefGoogle ScholarPubMed
Qi, H et al. (2020) COVID-19 transmission in Mainland China is associated with temperature and humidity: a time-series analysis. Science of the Total Environment 728, 138778.CrossRefGoogle ScholarPubMed
Pan, A et al. (2020) Association of public health interventions with the epidemiology of the COVID-19 outbreak in Wuhan, China. JAMA 323, 1915.CrossRefGoogle ScholarPubMed
Cagliani, R and Forni, D (2020) Computational inference of selection underlying the evolution of the novel coronavirus, severe acute respiratory syndrome coronavirus 2. Journal of Virology 94, e00411-20. doi: 10.1128/jvi.00411-20.CrossRefGoogle Scholar
Ahmar, AS (2017) Sutte indicator: a technical indicator in stock market. International Journal of Economics and Financial Issues 7, 223226.Google Scholar
Ahmar, AS et al. (2018) Applied Sutte Indicator method to predicting of stock movement of PT. Astra Agro Lestari Tbk. (AALI). Journal of Physics Conference. p. 1114.Google Scholar
Ansari Saleh, A (2017) SuIndiWeb: a web-based platform of Sutte Indicator predicting movement of stock. 2nd International Conference on Education, Science, and Technology (ICEST 2017). Atlantis Press, pp. 237239.Google Scholar
Ahmar, AS, Rahman, A and Mulbar, U (2018) α-Sutte Indicator: a new method for time series forecasting. Journal of Physics Conference, vol. 1040, p. 012018.CrossRefGoogle Scholar
Caputi, TL and Ayers, JW (2020) Collateral crises of gun preparation and the COVID-19 pandemic: infodemiology study. JMIR Public Health and Surveillance 6, e19369.CrossRefGoogle ScholarPubMed
Singh, RK et al. (2020) Prediction of the COVID-19 pandemic for the top 15 affected countries: advanced autoregressive integrated moving average (ARIMA) model. JMIR Public Health and Surveillance 6, e19115.Google ScholarPubMed
Benvenuto, D et al. (2020) Application of the ARIMA model on the COVID-2019 epidemic dataset. Data in Brief 29, 105340.CrossRefGoogle ScholarPubMed
Chintalapudi, N, Battineni, G and Amenta, F (2020) COVID-19 virus outbreak forecasting of registered and recovered cases after sixty day lockdown in Italy: a data driven model approach. Journal of Microbiology, Immunology and Infection 53, 396403.CrossRefGoogle ScholarPubMed
Bartholomew, D, Box, GEP and Jenkins, GM (2015) Time Series Analysis: Forecasting and Control, 5th Edn. Hoboken, New Jersey: John Wiley and Sons Inc., p. 14.Google Scholar
Chen, Y et al. (2020) Epidemiological features and time-series analysis of influenza incidence in urban and rural areas of Shenyang, China, 2010–2018. Epidemiology and Infection 148, e29.CrossRefGoogle Scholar
Wang, Y et al. (2020) Secular seasonality and trend forecasting of tuberculosis incidence rate in China using the advanced error-trend-seasonal framework. Infection and Drug Resistance 13, 733747.CrossRefGoogle ScholarPubMed
Wang, KW et al. (2017) Hybrid methodology for tuberculosis incidence time-series forecasting based on ARIMA and a NAR neural network. Epidemiology and Infection 145, 11181129.CrossRefGoogle Scholar
Zeng, Q et al. (2016) Time series analysis of temporal trends in the pertussis incidence in Mainland China from 2005 to 2016. Scientific Reports 6, 32367.CrossRefGoogle ScholarPubMed
Wang, Y et al. (2018) Time series modeling of pertussis incidence in China from 2004 to 2018 with a novel wavelet based SARIMA-NAR hybrid model. PLoS ONE 13, e0208404.CrossRefGoogle ScholarPubMed
Li, Z et al. (2019) Application of a hybrid model in predicting the incidence of tuberculosis in a Chinese population. Infection and Drug Resistance 12, 10111020.CrossRefGoogle ScholarPubMed
Liu, Q et al. (2019) Forecasting the seasonality and trend of pulmonary tuberculosis in Jiangsu Province of China using advanced statistical time-series analyses. Infection and Drug Resistance 12, 23112322.CrossRefGoogle ScholarPubMed
Kurniasih, N et al. . (2018) Forecasting infant mortality rate for China: a comparison between α-Sutte Indicator, ARIMA, and Holt-winters. Journal of Physics Conference. p. 1028.CrossRefGoogle Scholar
Ahmar, AS (2018) A comparison of α-Sutte Indicator and ARIMA methods in renewable energy forecasting in Indonesia. International Journal of Engineering & Technology 7, 2022.CrossRefGoogle Scholar
Li, Q, Feng, W and Quan, YH (2020) Trend and forecasting of the COVID-19 outbreak in China. The Journal of Infection 80, 469496.Google ScholarPubMed
Ahmar, AS and Del Val, EB (2020) SutteARIMA: short-term forecasting method, a case: Covid-19 and stock market in Spain. Science of the Total Environment 729, 138883.CrossRefGoogle ScholarPubMed
Wang, Y et al. (2020) Time series analysis of temporal trends in hemorrhagic fever with renal syndrome morbidity rate in China from 2005 to 2019. Scientific Reports 10, 9609.CrossRefGoogle ScholarPubMed
Pao, HT (2009) Forecasting energy consumption in Taiwan using hybrid nonlinear models. Energy 34, 14381446.CrossRefGoogle Scholar
Nurchis, MC et al. (2020) Impact of the burden of COVID-19 in Italy: results of disability-adjusted life years (DALYs) and productivity loss. International Journal of Environmental Research and Public Health 17, 4233.CrossRefGoogle ScholarPubMed
Tadesse, DB et al. (2020) The burden, admission, and outcome of COVID-19 in Africa: protocol for a systematic review and meta-analysis. Emerging Microbes & Infections 9, 13721378.CrossRefGoogle ScholarPubMed
Ye, J et al. (2020) Avoiding hospital-related infections during the COVID-19 epidemic. Critical Care 24, 206.CrossRefGoogle ScholarPubMed
Kumari, P and Toshniwal, D (2020) Impact of lockdown measures during COVID-19 on air quality − A case study of India. International Journal of Environmental Health Research 30, 18. doi: 10.1080/09603123.2020.1778646.CrossRefGoogle Scholar
Sun, C, Wu, Q and Zhang, C (2020) Managing patients with COVID-19 infections: a first-hand experience from the Wuhan Mobile Cabin Hospital. British Journal of General Practice 70, 229230.CrossRefGoogle ScholarPubMed
Hu, D, et al. (2020) More effective strategies are required to strengthen public awareness of COVID-19: evidence from Google Trends. Journal of Global Health 10, 011003.CrossRefGoogle ScholarPubMed
Figure 0

Fig. 1. Time series plots displaying the prevalence and mortality cases of COVID-19. (a) The total confirmed cases and deaths worldwide;(b) The total confirmed cases in Brazil, Peru, Canada, and Chile; (c) The total deaths in Brazil, Peru, Canada, and Chile. Worth noting that manycountries, areas or territories recently reconciliated the reported prevalence and mortality data of the COVID-19 outbreak, and thus the prevalenceand mortality data used to build the ARIMA and α-Sutte Indicator models were retrospectively updated on the basis of the additional detailsprovided by WHO, so that we can develop a reliable model for estimating the epidemiological trends of the prevalence and mortality of the COVID-19 outbreak in the upcoming days or weeks.

Figure 1

Fig. 2. Time series plots displaying the resulting forecasts for the testing sets of COVID-19 prevalence and mortality in the five regions using the α-Sutte Indicator and ARIMA models. (a) The resulting forecasts for the testing sets of the COVID-19 prevalence and mortality globally; (b) The resulting forecasts for the testing sets of the COVID-19 prevalence and mortality in Brazil; (c) The resulting forecasts for the testing sets of the COVID-19 prevalence and mortality in Peru; (d) The resulting forecasts for the testing sets of the COVID-19 prevalence and mortality in Canada; (e) The resulting forecasts for the testing sets of the COVID-19 prevalence and mortality in Chile. Here the forecasts for testing data are plotted as gray shaded area. As seen above, it seemed that the forecasts for the testing sets of both the prevalence and mortality from the α-Sutte Indicator yielded more sufficient prediction accuracy compared with that from the ARIMA model in the five regions except for the result from the testing sets of the COVID-19 prevalence around the globe.

Figure 2

Table 1. The identified best ARIMA models to forecast the epidemiological trend of COVID-19 prevalence in the five regions

Figure 3

Table 2. The identified best ARIMA models to forecast the epidemiological trend of COVID-19 mortality in the five regions

Figure 4

Table 3. Comparison of accuracy levels measurement of forecasting for the COVID-19 prevalence and mortality between α-Sutte indicator and ARIMA methods in the five regions

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