# The Validity of Autoregressive Integrated Moving Average Approach to Forecast the Spread of COVID-19 Pandemic in Africa

Authors: Habtamu Legese Feyisa; Frezer Tilahun Tefera
Journal: Discrete Dynamics in Nature and Society
 (2022)

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## Abstract

Africa’s first COVID-19 case was recorded in Egypt on February 14, 2020. Although it is not as expected by the World Health Organization (WHO) and other international organizations, currently a large number of Africans are getting infected by the virus. In this work, we studied the trend of the COVID-19 outbreak generally in Africa as a continent and in the five African regions separately. The study also investigated the validity of the ARIMA approach to forecast the spread of COVID-19 in Africa. The data of daily confirmed new COVID-19 cases from February 15 to October 16, 2020, were collected from the official website of Our World in Data to construct the autoregressive integrated moving average (ARIMA) model and to predict the trend of the daily confirmed cases through STATA 13 and EViews 9 software. The model used for our ARIMA estimation and prediction was (3, 1, 4) for Africa as a continent, ARIMA (3, 1, 3) for East Africa, ARIMA (2, 1, 3) for West Africa, ARIMA (2, 1, 3) for Central Africa, ARIMA (1, 1, 4) for North Africa, and ARIMA (4, 1, 5) for Southern Africa. Finally, the forecasted values were compared with the actual number of COVID-19 cases in the region. At the African level, the ARIMA model forecasted values and the actual data have similar signs with slightly different sizes, and there were some deviations at the subregional level. However, given the uncertain nature of the current COVID-19 pandemic, it is helpful to forecast the future trend of such pandemics by employing the ARIMA model.


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## Body

## 1. Introduction

Severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) caused a highly contagious disease called coronavirus disease 2019 (COVID-19). The virus was first reported in Wuhan city, People’s Republic of China (PRC), in December 2019 [1–3].Africa is the last continent to be infected by the COVID-19 pandemic. However, Africa, with the most vulnerable populations to infectious diseases, is predicted to be significantly affected by the ongoing COVID-19 outbreak [3]. As of October 30, 2021; CDC Africa reported 8,491,452 cases, 218,175 deaths, and 7,890,021 recoveries out of 76,692,988 COVID-19 tests [4].There is no sustainable economy without a strong health sector [5]. However, the socio-economic conditions in Africa are much less developed than other countries of the world. A series of factors, i.e., the scarcity of medical supplies, low socioeconomic status, lower virus testing efficiency, and poor information and communication technology (ICT) would facilitate the spread of the pandemic [6]. Before the COVID-19 pandemic, most of the healthcare infrastructure in African countries had been deteriorating, and the situation posed unprecedented pressure on the public health systems in many African countries [7]. Currently, the COVID-19 health crisis has already transformed into an economic and labor market shock, impacting not only supply (production of goods and services) but also demand (consumption and investment). In Africa and many low- and middle-income countries, the spread of COVID-19 is translated into economic impacts that will affect the already affected most vulnerable populations [8]. Many people, especially from developing nations, are shifting their focus from the fatal effects of the pandemic to the threats it poses to their daily supply of food [9].What will be the global socio-economic impact of the novel coronavirus (COVID-19)? Answering this question requires accurate forecasting of the spread of confirmed cases as well as analysis of the number of COVID-19-related deaths and recoveries [10]. It is essential to create a reliable and suitable predictive model that is of high importance to understand the current situation, evaluate the severity of the pandemic, and help governments and other stakeholders to control the further spread of novel coronavirus [11, 12]. Until now, several researchers have utilized the ARIMA model to forecast the spread of COVID-19 in many countries. In [13], the researchers employed the ARIMA model to forecast the spread of COVID-19 incidence in Italy, Russia, and the United States of America. In [14–19], ARIMA was used to forecast the spread of the COVID-19 pandemic in Bangladesh, Malaysia, India, Korea, Ethiopia, and Pakistan, respectively. However, the outcome of the aforementioned research depends on the validity of the ARIMA model. Therefore, the general objective of this research is to check the validity of the ARIMA model to forecast the spread of the COVID-19 pandemic in Africa under current testing capacity and public health interventions.Once we started with this brief introduction, the whole paper was organized as follows: In the second part, the study presented the research methodology, in which the specification of the theoretical model and the data issues are included. The third part presents the empirical findings and their interpretations. Finally, in the last part, the study draws possible conclusions and policy implications based on the findings of the study.


## 2. Materials and Methods

### 2.1. Description of the Study Area

Africa is also called the “Mother Continent” due to its being the oldest inhabited continent on Earth and being the homeland for humans and their ancestors for more than five million years. The current population of Africa is 1,382,727,760 as of Tuesday, October 26, 2021, and it is equivalent to 16.72% of the total world population [20]. It can be seen from Table 1 that the UN Statistics Division, Africa, is subdivided into five regions: Northern Africa, Central or Middle Africa, Southern Africa, East Africa, and Western Africa [21].Table 1
African regions with their respective numbers and a list of countries.
RegionsList of countries in the regionNorthern Africa (7)Algeria, Egypt, Libya, Morocco, Sudan, and TunisiaCentral Africa (9)Angola, Cameroon, the Central African Republic, Chad, Congo Republic—Brazzaville, the Democratic Republic of the Congo, Equatorial Guinea, Gabon, and São Tomé and PrincipeSouthern Africa (5)Botswana, Lesotho, Namibia, South Africa, and SwazilandEast Africa (18)Burundi, Comoros, Djibouti, Ethiopia, Eritrea, South Sudan, Kenya, Madagascar, Malawi, Mauritius, Mozambique, Rwanda, Seychelles, Somalia, Tanzania, Uganda, Zambia, and ZimbabweWestern Africa (16)Benin, Burkina Faso, Cape Verde, Côte d’Ivoire, Gambia, Ghana, Guinea, Guinea-Bissau, Liberia, MAli, Mauritania, Niger, Nigeria, Senegal, Sierra Leone, and TogoSource: own computation, 2021.


### 2.2. Data Collection

The official website of Our World in Data was used to collect the daily confirmed new COVID-19 cases from February 15, 2020, to October 16, 2020 [22]. Since the collected data includes the respective daily new confirmed COVID-19 cases of the past few days, it is considered as time series data. STATA 13 and EViews 9 has been used to build and analyze the time-series data.


### 2.3. Description and Development of Econometric Model

The Box-Jenkins approach to modeling ARIMAp,d,q processes is employed in this study, and this methodology is widely regarded as the most efficient forecasting technique and is used extensively [23]. The abbreviation ARIMA stands for autoregressive integrated moving average model, and the model is divided into three components depending on the type of data. The first building block is the autoregressive (AR) models, in which the value of a variable in one period is related to its value in previous periods. ARp is an autoregressive model with p lag.Yt=α+∑i=1Pβiyt−i+εt ; where Yt is the dependent variable, α is a constant, βp is the coefficient for the lagged variable in time t−p and εt is the random or white noise term that represents a shock that cannot be explained.The second component is the moving average (MA) model, which accounts for the possibility of a relationship between a variable and the residuals from previous periods. MA(q) is a moving average model with q lags: Yt=α+εt+∑i=1Pδiεt−i ; where Yt is the dependent variable, α is a constant, δi is the coefficient for the lagged variable in time t-i, and εt is the error term.The combination of the above two models, which are AR (autoregressive) and MA (moving average), gives the ARMA model, and the ARMA model can be used if and only if the data is stationary. The ARMA models combine bothp autoregressive terms and q moving average terms, also called ARMA p,q.(1)Yt=α+∑i=1Pβiyt−i+∑i=1Pδiεt−i+εt.When a variableYt is not stationary, a common solution is to use a differenced variable: ΔYt=Yt−Yt−1, for first-order differences, and by differencing (integrating (I)) the original series before using them will remove any linear time trend. If we include the third component, which is integrated into our ARMA model, it will become ARIMA.The emphasis of these methods is not on constructing single-equation or simultaneous equation models but on analyzing the probabilistic or stochastic properties of economic time series according to their philosophy. Let the data speak for themselves as it allowsYt to be explained by the past, or lagged, values of Y and the stochastic error terms. For this reason, ARIMA models are not derived from any economic theory [24–26].


### 2.4. Model Selection Criteria

Out-of-sample forecasting is concerned with determining how a fitted model forecasts future regress values and given the values of the regressors. To select the best ARIMAp,d,q type of model fitted for Africa and the five African regions, their goodness-of-fit has been compared using the Akaike information criteria (AIC) and Bayesian information criterion (BIC). AIC is an important and leading statistic by which we can determine the order of an autoregressive model. The AIC considers both how well the model fits the observed series and the number of parameters to be used in the fit. The BIC can help in deciding the order of autoregression.AIC=e2k/nRSS/n, where k is the number of regressors (including the intercept), n is the number of observations, and RSS stands for the residual sum of the square. In comparing two or more models, the model with the lowest value of AIC is preferred. One advantage of the AIC is that it is useful for not only in-sample but also out-of-sample forecasting of the performance of a regression model.BIC=−2lnL+klnN; where L is the value of the likelihood function evaluated at the parameter estimates, N is the number of observations, and K is the number of estimated parameters. A lower AIC or BIC value indicates a better fit (a more parsimonious model).


## 2.1. Description of the Study Area

Africa is also called the “Mother Continent” due to its being the oldest inhabited continent on Earth and being the homeland for humans and their ancestors for more than five million years. The current population of Africa is 1,382,727,760 as of Tuesday, October 26, 2021, and it is equivalent to 16.72% of the total world population [20]. It can be seen from Table 1 that the UN Statistics Division, Africa, is subdivided into five regions: Northern Africa, Central or Middle Africa, Southern Africa, East Africa, and Western Africa [21].Table 1
African regions with their respective numbers and a list of countries.
RegionsList of countries in the regionNorthern Africa (7)Algeria, Egypt, Libya, Morocco, Sudan, and TunisiaCentral Africa (9)Angola, Cameroon, the Central African Republic, Chad, Congo Republic—Brazzaville, the Democratic Republic of the Congo, Equatorial Guinea, Gabon, and São Tomé and PrincipeSouthern Africa (5)Botswana, Lesotho, Namibia, South Africa, and SwazilandEast Africa (18)Burundi, Comoros, Djibouti, Ethiopia, Eritrea, South Sudan, Kenya, Madagascar, Malawi, Mauritius, Mozambique, Rwanda, Seychelles, Somalia, Tanzania, Uganda, Zambia, and ZimbabweWestern Africa (16)Benin, Burkina Faso, Cape Verde, Côte d’Ivoire, Gambia, Ghana, Guinea, Guinea-Bissau, Liberia, MAli, Mauritania, Niger, Nigeria, Senegal, Sierra Leone, and TogoSource: own computation, 2021.


## 2.2. Data Collection

The official website of Our World in Data was used to collect the daily confirmed new COVID-19 cases from February 15, 2020, to October 16, 2020 [22]. Since the collected data includes the respective daily new confirmed COVID-19 cases of the past few days, it is considered as time series data. STATA 13 and EViews 9 has been used to build and analyze the time-series data.


## 2.3. Description and Development of Econometric Model

The Box-Jenkins approach to modeling ARIMAp,d,q processes is employed in this study, and this methodology is widely regarded as the most efficient forecasting technique and is used extensively [23]. The abbreviation ARIMA stands for autoregressive integrated moving average model, and the model is divided into three components depending on the type of data. The first building block is the autoregressive (AR) models, in which the value of a variable in one period is related to its value in previous periods. ARp is an autoregressive model with p lag.Yt=α+∑i=1Pβiyt−i+εt ; where Yt is the dependent variable, α is a constant, βp is the coefficient for the lagged variable in time t−p and εt is the random or white noise term that represents a shock that cannot be explained.The second component is the moving average (MA) model, which accounts for the possibility of a relationship between a variable and the residuals from previous periods. MA(q) is a moving average model with q lags: Yt=α+εt+∑i=1Pδiεt−i ; where Yt is the dependent variable, α is a constant, δi is the coefficient for the lagged variable in time t-i, and εt is the error term.The combination of the above two models, which are AR (autoregressive) and MA (moving average), gives the ARMA model, and the ARMA model can be used if and only if the data is stationary. The ARMA models combine bothp autoregressive terms and q moving average terms, also called ARMA p,q.(1)Yt=α+∑i=1Pβiyt−i+∑i=1Pδiεt−i+εt.When a variableYt is not stationary, a common solution is to use a differenced variable: ΔYt=Yt−Yt−1, for first-order differences, and by differencing (integrating (I)) the original series before using them will remove any linear time trend. If we include the third component, which is integrated into our ARMA model, it will become ARIMA.The emphasis of these methods is not on constructing single-equation or simultaneous equation models but on analyzing the probabilistic or stochastic properties of economic time series according to their philosophy. Let the data speak for themselves as it allowsYt to be explained by the past, or lagged, values of Y and the stochastic error terms. For this reason, ARIMA models are not derived from any economic theory [24–26].


## 2.4. Model Selection Criteria

Out-of-sample forecasting is concerned with determining how a fitted model forecasts future regress values and given the values of the regressors. To select the best ARIMAp,d,q type of model fitted for Africa and the five African regions, their goodness-of-fit has been compared using the Akaike information criteria (AIC) and Bayesian information criterion (BIC). AIC is an important and leading statistic by which we can determine the order of an autoregressive model. The AIC considers both how well the model fits the observed series and the number of parameters to be used in the fit. The BIC can help in deciding the order of autoregression.AIC=e2k/nRSS/n, where k is the number of regressors (including the intercept), n is the number of observations, and RSS stands for the residual sum of the square. In comparing two or more models, the model with the lowest value of AIC is preferred. One advantage of the AIC is that it is useful for not only in-sample but also out-of-sample forecasting of the performance of a regression model.BIC=−2lnL+klnN; where L is the value of the likelihood function evaluated at the parameter estimates, N is the number of observations, and K is the number of estimated parameters. A lower AIC or BIC value indicates a better fit (a more parsimonious model).


## 3. Data Presentation and Analysis

### 3.1. Descriptive Statistics

The daily confirmed new COVID-19 case time series plots of African countries initially depict an increasing trend and later a declining trend, but there is a variation in the daily confirmed new COVID-19 case time series plots among African countries and between the five African regions, as shown in Figure1.Figure 1
COVID-19 daily new cases time series plots of African countries and African regions.Source: own computation, 2021.


### 3.2. Econometric Result and Interpretation

#### 3.2.1. Parameter Estimation and Validation

Five models are chosen and tested to find a model with a good fit for Africa and the five African regions, and the model with the lowest AIC is selected for estimation and forecasting. As we can see from Table2, that the ARIMA (3, 1, 4), ARIMA (3, 1, 3), ARIMA (2, 1, 3), ARIMA (2, 1, 3), ARIMA (4, 1, 2), and ARIMA (4, 1, 5) models are selected to estimate the parameters of Africa, East Africa, West Africa, Central Africa, North Africa, and Southern Africa, respectively.Table 2
ARIMA model for forecasting the number of daily confirmed cases according to AIC.
RegionARIMA (p, d, q)AICBICRemarkAfricaARIMA (3, 1, 3)3639.9443666.872ARIMA (3, 1, 4)3595.3213625.615SelectedARIMA (3, 1, 5)3595.3333625.626ARIMA (4, 1, 1)3672.7473696.309ARIMA (4, 1, 3)3619.9153650.209East AfricaARIMA (1, 1, 1)2601.4052614.308ARIMA (3, 1, 1)2598.8182618.173ARIMA (3, 1, 2)2599.3562621.936ARIMA (3, 1, 3)2585.1172610.923SelectedARIMA (3, 1, 4)2586.6252615.657West AfricaARIMA (3, 1, 3)3023.0643049.991ARIMA (2, 1, 1)3022.7223039.552ARIMA (2, 1, 2)3021.7373041.933ARIMA (2, 1, 3)3020.5393044.1SelectedARIMA (1, 1, 3)3021.7373041.933Central AfricaARIMA (3, 1, 1)2965.5262985.721ARIMA (3, 1, 2)2967.5262991.087ARIMA (3, 1, 3)2964.292991.218ARIMA (3, 1, 4)2963.0112989.939ARIMA (2, 1, 3)2962.9822986.544SelectedNorth AfricaARIMA (4, 1, 1)3195.5413219.103ARIMA (4, 1, 2)3195.7623222.69ARIMA (2, 1, 4)3199.0143225.942ARIMA (3, 1, 4)3196.9373227.23ARIMA (1, 1, 4)3193.6483217.21SelectedSouthern AfricaARIMA (3, 1, 3)3482.7383509.666ARIMA (4, 1, 3)3485.7553516.049ARIMA (3, 1, 4)3490.283520.574ARIMA (4, 1, 4)3448.1893481.849ARIMA (4, 1, 5)3446.1523483.178SelectedSource: own computation, 2021.Table 3
The prediction epidemic results of the new COVID-19 in Africa for the next month as predicted by the ARIMA (3, 1, 4) model.
DateExpected casesDateExpected cases17/9/2072562/10/2020580018/9/2073823/10/2020580419/9/2071274/10/2020547820/9/206485/10/2020507021/9/2057796/10/2020488422/9/2053827/10/2020505123/9/2054608/10/2020543824/9/2058389/10/2020575825/9/20614210/10/2020578326/9/20608211/10/2020551327/9/20565812/10/2020516728/9/20515113/10/2020501529/9/20490114/10/2020517330/9/20505715/10/2020552601/10/20546516/10/20205819Source: own computation, 2021.Source: own computation, 2021.Source: own computation, 2021.Source: own computation, 2021.Source: own computation, 2021.Source: own computation, 2021.Source: own computation, 2021.


#### 3.2.2. Forecasting Using the Selected ARIMA Models

Candidate models were obtained based on the respective spikes observed from the autocorrelation function (ACF) and the partial autocorrelation function (PACF). Table3 presents the prediction results of daily confirmed new COVID-19 cases in Africa for the period between 17/9/2020 and 16/10/2020 as predicted by the ARIMA (3,1,4) model, and the result demonstrates that the daily confirmed new cases trend in Africa as the continent may become stable or it will become stagnant (see Figure 2). However, this is the weighted average of the five African regions, and there is significant variation in the spread and trend of COVID-19 among African regions.Figure 2
The plot of actual confirmed cases with the prediction result of the ARIMA model for Africa.Unlike the cases in Africa, the prediction results of daily confirmed COVID-19 cases in East Africa as predicted by the ARIMA (3, 1, 3) model show an increasing trend in the spread of daily cases of the COVID-19 pandemic (as shown in Table4 and Figure 3). Similarly, Table 5 presents the prediction results of daily confirmed COVID-19 cases in Northern Africa for the period between 17/9/2020 and 16/10/2020 as predicted by the ARIMA (1,1,4) model. The prediction results on the plot of actual confirmed cases with the prediction result of the ARIMA model depict the increasing trend and spread of COVID-19 in Northern Africa (see Figure 4).Table 4
The prediction results of daily confirmed COVID-19 cases in East Africa for the next month as predicted by the ARIMA (3, 1, 3) model.
DateExpected casesDateExpected cases17/9/2012862/10/2020145418/9/2014763/10/2020143819/9/2011664/10/2020140820/9/2013235/10/2020144221/9/2014436/10/2020147422/9/2013597/10/2020145423/9/2012678/10/2020144724/9/2013839/10/2020147925/9/20144010/10/2020149226/9/20135111/10/2020147727/9/20133712/10/2020148528/9/20142713/10/2020150929/9/20143414/10/2020151330/9/20137315/10/2020150601/10/20139616/10/20201519Source: own computation, 2021.Figure 3
The plot of actual confirmed cases with the prediction result of the ARIMA model for East Africa.Table 5
The prediction results of daily confirmed new COVID-19 cases in North Africa for the next month as predicted by the ARIMA (1, 1, 4) model.
DateExpected casesDateExpected cases17/9/2035882/10/2020374918/9/2035043/10/2020378319/9/2035714/10/2020378320/9/2035335/10/2020381521/9/2036006/10/2020381822/9/2035707/10/2020384723/9/2036298/10/2020385124/9/2036079/10/2020387925/9/20365910/10/2020388726/9/20364311/10/2020391127/9/20369012/10/2020392028/9/20367813/10/2020394429/9/20372014/10/2020395330/9/20371415/10/2020397601/10/20375216/10/20203987Source: own computation, 2021.Figure 4
The plot of actual confirmed cases with the prediction results of the ARIMA model for North Africa.The prediction results of daily confirmed new COVID-19 cases in West Africa and Central Africa for the next month were estimated by employing the ARIMA (2,1,3) and ARIMA (2,1,3) models, respectively (see Tables6 and 7). The prediction results indicate a slight increasing trend in the number of daily new confirmed cases of COVID-19 in both West Africa and Central Africa (see Figures 5 and 6). On the other hand, Southern Africa is the most infected region in Africa, but Table 8 and Figure 7 confirmed that Southern Africa had an almost decreasing trend in the spread and daily confirmed cases of the COVID-19 pandemic, and this may be the major reason for the stable trend of the African daily confirmed COVID-19 cases as the increase in the daily confirmed cases in the North, East, West, and Central Africa is counterpoised by the decreasing trend of Southern Africa daily confirmed new COVID-19 cases.Table 6
The prediction results of daily confirmed COVID-19 cases in West Africa for the next month as predicted by the ARIMA (2,1,3) model.
DateExpected casesDateExpected cases17/9/205892/10/202064418/9/206433/10/202060719/9/206194/10/202063220/9/205665/10/202067721/9/205846/10/202066722/9/206447/10/202062623/9/206438/10/202063224/9/205909/10/202067825/9/2058510/10/202068626/9/2064011/10/202064927/9/2066112/10/202063828/9/2061713/10/202067729/9/2059314/10/202070030/9/2063515/10/202067201/10/2067216/10/2020649Source: own computation, 2021.Table 7
The prediction results of daily confirmed COVID-19 cases in Central Africa for the next month as predicted by the ARIMA (2,1,3) model.
DateExpected casesDateExpected cases17/9/201842/10/202022018/9/202063/10/202021419/9/202094/10/202020720/9/201895/10/202021821/9/201996/10/202022122/9/2021457/10/202021223/9/202008/10/202021624/9/201959/10/202022525/9/2021410/10/202021826/9/2021111/10/202021627/9/2019812/10/202022528/9/2021013/10/202022529/9/2021814/10/202021930/9/2020515/10/202022501/10/2020616/10/2020230Source: own computation, 2021.Figure 5
The plot of actual confirmed cases with the prediction result of the ARIMA model for West Africa.Figure 6
The plot of actual confirmed cases with the prediction result of the ARIMA model for Central Africa.Table 8
The prediction epidemic results of the new COVID-19 in Southern Africa for the next month as predicted by the ARIMA (4,1,5) model.
DateExpected casesDateExpected cases17/9/2016012/10/2020155718/9/2020633/10/2020164019/9/2021094/10/2020141420/9/2018575/10/2020104721/9/2013466/10/202081022/9/2010267/10/202086523/9/2010378/10/2020115724/9/2013819/10/2020145125/9/20173210/10/2020152226/9/20183111/10/2020131927/9/20157312/10/202099628/9/20115713/10/202079529/9/2087214/10/202085730/9/2091715/10/2020112501/10/20123016/10/20201389Source: own computation, 2021.Figure 7
The plot of actual confirmed cases with the prediction results of the ARIMA model for Southern Africa.Except for Southern Africa, all African regions show an increasing trend in the predicted daily COVID-19 new cases, and specifically East and Northern Africa show a significant increasing trend in the spread of the COVID-19 pandemic.


#### 3.2.3. The Deviation between the Forecasted and Actual Data on the Spread of Covid-19

As shown in Table9, the sign of the forecasted values of COVID-19 cases in Africa and the actual values of the daily confirmed COVID-19-19 cases are similar, which is a positive or an increasing trend. Both values portray the increasing trends of the COVID-19-19 pandemic. However, in all cases, the forecasted values are lower than the actual values, or the ARIMA model prediction results underestimate the spread of COVID-19-19 in Africa.Table 9
The deviation between the actual and forecasted values of the daily confirmed COVID-19 cases in Africa for the period between 17/9/2020–16/10/2020.
DateExpected casesActual casesGapDateExpected casesActual casesGap17/9/207256860313472/10/202058008853305318/9/20738281677853/10/202058048828302419/9/207127872716004/10/202054788089261120/9/20648842077725/10/202050704709-36121/9/20577961463676/10/202048846601171722/9/205382683914577/10/2020505110546549523/9/205460872632668/10/2020543810904546624/9/205838818623489/10/202057588563280525/9/2061427978183610/10/2020578313531774826/9/206082641233011/10/202055138978346527/9/2056588368271012/10/20205167588671928/9/205151566751613/10/202050157834281929/9/2049017508260714/10/2020517311509633630/9/2050578433337615/10/20205526911535891/10/202054657265180016/10/20205819106824863Source: own computation, 2021.At the subregional level, there is a deviation between the actual and the ARIMA model forecasted values of the daily COVID-19 cases, and the deviation is both on the sign and the size of the actual and forecasted values of the daily COVID-19 cases. Tables10–14 present the deviation between the actual and forecasted values of the daily confirmed COVID-19 cases in East Africa, West Africa, Central Africa, North Africa, and Southern Africa for the period between 17/9/2020–16/10/2020, respectively.Table 10
The deviation between the actual and forecasted values of the daily confirmed COVID-19 cases in East Africa for the period between 17/9/2020–16/10/2020.
DateExpected casesActual casesGapDateExpected casesActual casesGap17/9/20128614081222/10/20201454158212818/9/2014761327−1493/10/20201438160416619/9/20116616634974/10/20201408178637820/9/20132315262035/10/20201442970−47221/9/20144315851426/10/202014741076−39822/9/20135916402817/10/20201454161416023/9/2012671351848/10/20201447192647924/9/2013831210−1739/10/20201479163015125/9/2014401178−26210/10/20201492181131926/9/2013511325−2611/10/20201477161513827/9/20133713551812/10/202014851208−27728/9/20142714441713/10/202015091258−25129/9/20143414875314/10/20201513190639330/9/2013731320−5315/10/20201506164614001/10/2013961357−3916/10/202015191456−63Source: own Computation, 2021.Table 11
The deviation between the actual and forecasted values of the daily confirmed COVID-19 cases in West Africa for the period between 17/9/2020–16/10/2020.
DateExpected casesActual casesGapDateExpected casesActual casesGap17/9/20589428−1612/10/2020644525−11918/9/2064364963/10/2020607520−8719/9/20619601−184/10/2020632288−34420/9/20566495−715/10/2020677329−34821/9/20584423−1616/10/2020667378−28922/9/20644407−2377/10/2020626453−17323/9/20643555−888/10/2020632484−14824/9/20590412−1789/10/2020678473−20525/9/20585573−1210/10/2020686468−21826/9/20640372−26811/10/2020649429−22027/9/20661586−7512/10/2020638399−23928/9/20617320−29713/10/2020677585−9229/9/20593454−13914/10/2020700564−13630/9/206356865115/10/2020672494−1781/10/2020672442−23016/10/2020649515−134Source: own computation, 2021.Table 12
The deviation between the actual and forecasted values of the daily confirmed COVID-19 cases in Central Africa for the period between 17/9/2020–16/10/2020.
DateExpected casesActual casesGapDateExpected casesActual casesGap17/9/20184169−152/10/20202202664618/9/20206242363/10/2020214203−1119/9/20209153−564/10/202020743−16420/9/20189119−705/10/2020218163−5521/9/201993231246/10/20202212361522/9/202145157−19887/10/202021235−17723/9/20200257578/10/202021655934324/9/20195163−329/10/2020225149−7625/9/20214157−5710/10/20202182392126/9/20211132−7911/10/2020216150−6627/9/2019869−12912/10/2020225171−5428/9/20210201−913/10/2020225209−1629/9/20218149−6914/10/202021952530630/9/202052201515/10/2020225271461/10/2020206186−2016/10/2020230216−14Source: own computation, 2021.Table 13
The deviation between the actual and forecasted values of the daily confirmed COVID-19 cases in North Africa for the period between 17/9/2020–16/10/2020.
DateExpected casesActual casesGapDateExpected casesActual casesGap17/9/20358842136252/10/20203749464889918/9/20350437462423/10/20203783451473119/9/20357142266554/10/20203783430352020/9/203533458210495/10/202038152283−153221/9/2036003095−5056/10/2020381838422422/9/2035703183−3877/10/202038476387254023/9/20362945749458/10/202038516326247524/9/20360740484419/10/20203879477689725/9/203659446780810/10/202038878391450426/9/2036433530−11311/10/202039115150123927/9/2036904963127312/10/202039202857−106328/9/2036782535−114313/10/20203944456261829/9/203720447475414/10/202039536776282330/9/203714427656215/10/2020397644835071/10/202037523360−39216/10/2020398750171030Source: own computation, 2021.Table 14
The deviation between the actual and forecasted values of the daily confirmed COVID-19 cases in Southern Africa for the period between 17/9/2020–16/10/2020.
DateExpected casesActual casesGapDateExpected casesActual casesGap17/9/20160123827812/10/20201557191836118/9/20206322712083/10/20201640198434419/9/2021092144354/10/20201414166925520/9/2018571698−1595/10/20201047964−8321/9/201346887−4596/10/2020810106525522/9/20102614524267/10/20208652057119223/9/201037208110448/10/20201157188472724/9/20138123719909/10/2020145115358425/9/2017321603−12910/10/202015222622110026/9/2018311072−75911/10/20201319163431527/9/2015731395−17812/10/2020996125125528/9/201157127011313/10/2020795121942429/9/208729437114/10/20208571976111930/9/209171931101415/10/202011252221109601/10/201230191568516/10/2020138934722083Source: own computation, 2021.However, we can tolerate the minor difference between the actual and the ARIMA model forecasted values of COVID-19 daily confirmed cases, given the uncertain nature of the current COVID-19 pandemic and the growing interconnected and complex world, which are ultimately demanding flexibility, robustness, and resilience to cope with unexpected future events and scenarios [27].


## 3.1. Descriptive Statistics

The daily confirmed new COVID-19 case time series plots of African countries initially depict an increasing trend and later a declining trend, but there is a variation in the daily confirmed new COVID-19 case time series plots among African countries and between the five African regions, as shown in Figure1.Figure 1
COVID-19 daily new cases time series plots of African countries and African regions.Source: own computation, 2021.


## 3.2. Econometric Result and Interpretation

### 3.2.1. Parameter Estimation and Validation

Five models are chosen and tested to find a model with a good fit for Africa and the five African regions, and the model with the lowest AIC is selected for estimation and forecasting. As we can see from Table2, that the ARIMA (3, 1, 4), ARIMA (3, 1, 3), ARIMA (2, 1, 3), ARIMA (2, 1, 3), ARIMA (4, 1, 2), and ARIMA (4, 1, 5) models are selected to estimate the parameters of Africa, East Africa, West Africa, Central Africa, North Africa, and Southern Africa, respectively.Table 2
ARIMA model for forecasting the number of daily confirmed cases according to AIC.
RegionARIMA (p, d, q)AICBICRemarkAfricaARIMA (3, 1, 3)3639.9443666.872ARIMA (3, 1, 4)3595.3213625.615SelectedARIMA (3, 1, 5)3595.3333625.626ARIMA (4, 1, 1)3672.7473696.309ARIMA (4, 1, 3)3619.9153650.209East AfricaARIMA (1, 1, 1)2601.4052614.308ARIMA (3, 1, 1)2598.8182618.173ARIMA (3, 1, 2)2599.3562621.936ARIMA (3, 1, 3)2585.1172610.923SelectedARIMA (3, 1, 4)2586.6252615.657West AfricaARIMA (3, 1, 3)3023.0643049.991ARIMA (2, 1, 1)3022.7223039.552ARIMA (2, 1, 2)3021.7373041.933ARIMA (2, 1, 3)3020.5393044.1SelectedARIMA (1, 1, 3)3021.7373041.933Central AfricaARIMA (3, 1, 1)2965.5262985.721ARIMA (3, 1, 2)2967.5262991.087ARIMA (3, 1, 3)2964.292991.218ARIMA (3, 1, 4)2963.0112989.939ARIMA (2, 1, 3)2962.9822986.544SelectedNorth AfricaARIMA (4, 1, 1)3195.5413219.103ARIMA (4, 1, 2)3195.7623222.69ARIMA (2, 1, 4)3199.0143225.942ARIMA (3, 1, 4)3196.9373227.23ARIMA (1, 1, 4)3193.6483217.21SelectedSouthern AfricaARIMA (3, 1, 3)3482.7383509.666ARIMA (4, 1, 3)3485.7553516.049ARIMA (3, 1, 4)3490.283520.574ARIMA (4, 1, 4)3448.1893481.849ARIMA (4, 1, 5)3446.1523483.178SelectedSource: own computation, 2021.Table 3
The prediction epidemic results of the new COVID-19 in Africa for the next month as predicted by the ARIMA (3, 1, 4) model.
DateExpected casesDateExpected cases17/9/2072562/10/2020580018/9/2073823/10/2020580419/9/2071274/10/2020547820/9/206485/10/2020507021/9/2057796/10/2020488422/9/2053827/10/2020505123/9/2054608/10/2020543824/9/2058389/10/2020575825/9/20614210/10/2020578326/9/20608211/10/2020551327/9/20565812/10/2020516728/9/20515113/10/2020501529/9/20490114/10/2020517330/9/20505715/10/2020552601/10/20546516/10/20205819Source: own computation, 2021.Source: own computation, 2021.Source: own computation, 2021.Source: own computation, 2021.Source: own computation, 2021.Source: own computation, 2021.Source: own computation, 2021.


### 3.2.2. Forecasting Using the Selected ARIMA Models

Candidate models were obtained based on the respective spikes observed from the autocorrelation function (ACF) and the partial autocorrelation function (PACF). Table3 presents the prediction results of daily confirmed new COVID-19 cases in Africa for the period between 17/9/2020 and 16/10/2020 as predicted by the ARIMA (3,1,4) model, and the result demonstrates that the daily confirmed new cases trend in Africa as the continent may become stable or it will become stagnant (see Figure 2). However, this is the weighted average of the five African regions, and there is significant variation in the spread and trend of COVID-19 among African regions.Figure 2
The plot of actual confirmed cases with the prediction result of the ARIMA model for Africa.Unlike the cases in Africa, the prediction results of daily confirmed COVID-19 cases in East Africa as predicted by the ARIMA (3, 1, 3) model show an increasing trend in the spread of daily cases of the COVID-19 pandemic (as shown in Table4 and Figure 3). Similarly, Table 5 presents the prediction results of daily confirmed COVID-19 cases in Northern Africa for the period between 17/9/2020 and 16/10/2020 as predicted by the ARIMA (1,1,4) model. The prediction results on the plot of actual confirmed cases with the prediction result of the ARIMA model depict the increasing trend and spread of COVID-19 in Northern Africa (see Figure 4).Table 4
The prediction results of daily confirmed COVID-19 cases in East Africa for the next month as predicted by the ARIMA (3, 1, 3) model.
DateExpected casesDateExpected cases17/9/2012862/10/2020145418/9/2014763/10/2020143819/9/2011664/10/2020140820/9/2013235/10/2020144221/9/2014436/10/2020147422/9/2013597/10/2020145423/9/2012678/10/2020144724/9/2013839/10/2020147925/9/20144010/10/2020149226/9/20135111/10/2020147727/9/20133712/10/2020148528/9/20142713/10/2020150929/9/20143414/10/2020151330/9/20137315/10/2020150601/10/20139616/10/20201519Source: own computation, 2021.Figure 3
The plot of actual confirmed cases with the prediction result of the ARIMA model for East Africa.Table 5
The prediction results of daily confirmed new COVID-19 cases in North Africa for the next month as predicted by the ARIMA (1, 1, 4) model.
DateExpected casesDateExpected cases17/9/2035882/10/2020374918/9/2035043/10/2020378319/9/2035714/10/2020378320/9/2035335/10/2020381521/9/2036006/10/2020381822/9/2035707/10/2020384723/9/2036298/10/2020385124/9/2036079/10/2020387925/9/20365910/10/2020388726/9/20364311/10/2020391127/9/20369012/10/2020392028/9/20367813/10/2020394429/9/20372014/10/2020395330/9/20371415/10/2020397601/10/20375216/10/20203987Source: own computation, 2021.Figure 4
The plot of actual confirmed cases with the prediction results of the ARIMA model for North Africa.The prediction results of daily confirmed new COVID-19 cases in West Africa and Central Africa for the next month were estimated by employing the ARIMA (2,1,3) and ARIMA (2,1,3) models, respectively (see Tables6 and 7). The prediction results indicate a slight increasing trend in the number of daily new confirmed cases of COVID-19 in both West Africa and Central Africa (see Figures 5 and 6). On the other hand, Southern Africa is the most infected region in Africa, but Table 8 and Figure 7 confirmed that Southern Africa had an almost decreasing trend in the spread and daily confirmed cases of the COVID-19 pandemic, and this may be the major reason for the stable trend of the African daily confirmed COVID-19 cases as the increase in the daily confirmed cases in the North, East, West, and Central Africa is counterpoised by the decreasing trend of Southern Africa daily confirmed new COVID-19 cases.Table 6
The prediction results of daily confirmed COVID-19 cases in West Africa for the next month as predicted by the ARIMA (2,1,3) model.
DateExpected casesDateExpected cases17/9/205892/10/202064418/9/206433/10/202060719/9/206194/10/202063220/9/205665/10/202067721/9/205846/10/202066722/9/206447/10/202062623/9/206438/10/202063224/9/205909/10/202067825/9/2058510/10/202068626/9/2064011/10/202064927/9/2066112/10/202063828/9/2061713/10/202067729/9/2059314/10/202070030/9/2063515/10/202067201/10/2067216/10/2020649Source: own computation, 2021.Table 7
The prediction results of daily confirmed COVID-19 cases in Central Africa for the next month as predicted by the ARIMA (2,1,3) model.
DateExpected casesDateExpected cases17/9/201842/10/202022018/9/202063/10/202021419/9/202094/10/202020720/9/201895/10/202021821/9/201996/10/202022122/9/2021457/10/202021223/9/202008/10/202021624/9/201959/10/202022525/9/2021410/10/202021826/9/2021111/10/202021627/9/2019812/10/202022528/9/2021013/10/202022529/9/2021814/10/202021930/9/2020515/10/202022501/10/2020616/10/2020230Source: own computation, 2021.Figure 5
The plot of actual confirmed cases with the prediction result of the ARIMA model for West Africa.Figure 6
The plot of actual confirmed cases with the prediction result of the ARIMA model for Central Africa.Table 8
The prediction epidemic results of the new COVID-19 in Southern Africa for the next month as predicted by the ARIMA (4,1,5) model.
DateExpected casesDateExpected cases17/9/2016012/10/2020155718/9/2020633/10/2020164019/9/2021094/10/2020141420/9/2018575/10/2020104721/9/2013466/10/202081022/9/2010267/10/202086523/9/2010378/10/2020115724/9/2013819/10/2020145125/9/20173210/10/2020152226/9/20183111/10/2020131927/9/20157312/10/202099628/9/20115713/10/202079529/9/2087214/10/202085730/9/2091715/10/2020112501/10/20123016/10/20201389Source: own computation, 2021.Figure 7
The plot of actual confirmed cases with the prediction results of the ARIMA model for Southern Africa.Except for Southern Africa, all African regions show an increasing trend in the predicted daily COVID-19 new cases, and specifically East and Northern Africa show a significant increasing trend in the spread of the COVID-19 pandemic.


### 3.2.3. The Deviation between the Forecasted and Actual Data on the Spread of Covid-19

As shown in Table9, the sign of the forecasted values of COVID-19 cases in Africa and the actual values of the daily confirmed COVID-19-19 cases are similar, which is a positive or an increasing trend. Both values portray the increasing trends of the COVID-19-19 pandemic. However, in all cases, the forecasted values are lower than the actual values, or the ARIMA model prediction results underestimate the spread of COVID-19-19 in Africa.Table 9
The deviation between the actual and forecasted values of the daily confirmed COVID-19 cases in Africa for the period between 17/9/2020–16/10/2020.
DateExpected casesActual casesGapDateExpected casesActual casesGap17/9/207256860313472/10/202058008853305318/9/20738281677853/10/202058048828302419/9/207127872716004/10/202054788089261120/9/20648842077725/10/202050704709-36121/9/20577961463676/10/202048846601171722/9/205382683914577/10/2020505110546549523/9/205460872632668/10/2020543810904546624/9/205838818623489/10/202057588563280525/9/2061427978183610/10/2020578313531774826/9/206082641233011/10/202055138978346527/9/2056588368271012/10/20205167588671928/9/205151566751613/10/202050157834281929/9/2049017508260714/10/2020517311509633630/9/2050578433337615/10/20205526911535891/10/202054657265180016/10/20205819106824863Source: own computation, 2021.At the subregional level, there is a deviation between the actual and the ARIMA model forecasted values of the daily COVID-19 cases, and the deviation is both on the sign and the size of the actual and forecasted values of the daily COVID-19 cases. Tables10–14 present the deviation between the actual and forecasted values of the daily confirmed COVID-19 cases in East Africa, West Africa, Central Africa, North Africa, and Southern Africa for the period between 17/9/2020–16/10/2020, respectively.Table 10
The deviation between the actual and forecasted values of the daily confirmed COVID-19 cases in East Africa for the period between 17/9/2020–16/10/2020.
DateExpected casesActual casesGapDateExpected casesActual casesGap17/9/20128614081222/10/20201454158212818/9/2014761327−1493/10/20201438160416619/9/20116616634974/10/20201408178637820/9/20132315262035/10/20201442970−47221/9/20144315851426/10/202014741076−39822/9/20135916402817/10/20201454161416023/9/2012671351848/10/20201447192647924/9/2013831210−1739/10/20201479163015125/9/2014401178−26210/10/20201492181131926/9/2013511325−2611/10/20201477161513827/9/20133713551812/10/202014851208−27728/9/20142714441713/10/202015091258−25129/9/20143414875314/10/20201513190639330/9/2013731320−5315/10/20201506164614001/10/2013961357−3916/10/202015191456−63Source: own Computation, 2021.Table 11
The deviation between the actual and forecasted values of the daily confirmed COVID-19 cases in West Africa for the period between 17/9/2020–16/10/2020.
DateExpected casesActual casesGapDateExpected casesActual casesGap17/9/20589428−1612/10/2020644525−11918/9/2064364963/10/2020607520−8719/9/20619601−184/10/2020632288−34420/9/20566495−715/10/2020677329−34821/9/20584423−1616/10/2020667378−28922/9/20644407−2377/10/2020626453−17323/9/20643555−888/10/2020632484−14824/9/20590412−1789/10/2020678473−20525/9/20585573−1210/10/2020686468−21826/9/20640372−26811/10/2020649429−22027/9/20661586−7512/10/2020638399−23928/9/20617320−29713/10/2020677585−9229/9/20593454−13914/10/2020700564−13630/9/206356865115/10/2020672494−1781/10/2020672442−23016/10/2020649515−134Source: own computation, 2021.Table 12
The deviation between the actual and forecasted values of the daily confirmed COVID-19 cases in Central Africa for the period between 17/9/2020–16/10/2020.
DateExpected casesActual casesGapDateExpected casesActual casesGap17/9/20184169−152/10/20202202664618/9/20206242363/10/2020214203−1119/9/20209153−564/10/202020743−16420/9/20189119−705/10/2020218163−5521/9/201993231246/10/20202212361522/9/202145157−19887/10/202021235−17723/9/20200257578/10/202021655934324/9/20195163−329/10/2020225149−7625/9/20214157−5710/10/20202182392126/9/20211132−7911/10/2020216150−6627/9/2019869−12912/10/2020225171−5428/9/20210201−913/10/2020225209−1629/9/20218149−6914/10/202021952530630/9/202052201515/10/2020225271461/10/2020206186−2016/10/2020230216−14Source: own computation, 2021.Table 13
The deviation between the actual and forecasted values of the daily confirmed COVID-19 cases in North Africa for the period between 17/9/2020–16/10/2020.
DateExpected casesActual casesGapDateExpected casesActual casesGap17/9/20358842136252/10/20203749464889918/9/20350437462423/10/20203783451473119/9/20357142266554/10/20203783430352020/9/203533458210495/10/202038152283−153221/9/2036003095−5056/10/2020381838422422/9/2035703183−3877/10/202038476387254023/9/20362945749458/10/202038516326247524/9/20360740484419/10/20203879477689725/9/203659446780810/10/202038878391450426/9/2036433530−11311/10/202039115150123927/9/2036904963127312/10/202039202857−106328/9/2036782535−114313/10/20203944456261829/9/203720447475414/10/202039536776282330/9/203714427656215/10/2020397644835071/10/202037523360−39216/10/2020398750171030Source: own computation, 2021.Table 14
The deviation between the actual and forecasted values of the daily confirmed COVID-19 cases in Southern Africa for the period between 17/9/2020–16/10/2020.
DateExpected casesActual casesGapDateExpected casesActual casesGap17/9/20160123827812/10/20201557191836118/9/20206322712083/10/20201640198434419/9/2021092144354/10/20201414166925520/9/2018571698−1595/10/20201047964−8321/9/201346887−4596/10/2020810106525522/9/20102614524267/10/20208652057119223/9/201037208110448/10/20201157188472724/9/20138123719909/10/2020145115358425/9/2017321603−12910/10/202015222622110026/9/2018311072−75911/10/20201319163431527/9/2015731395−17812/10/2020996125125528/9/201157127011313/10/2020795121942429/9/208729437114/10/20208571976111930/9/209171931101415/10/202011252221109601/10/201230191568516/10/2020138934722083Source: own computation, 2021.However, we can tolerate the minor difference between the actual and the ARIMA model forecasted values of COVID-19 daily confirmed cases, given the uncertain nature of the current COVID-19 pandemic and the growing interconnected and complex world, which are ultimately demanding flexibility, robustness, and resilience to cope with unexpected future events and scenarios [27].


## 3.2.1. Parameter Estimation and Validation

Five models are chosen and tested to find a model with a good fit for Africa and the five African regions, and the model with the lowest AIC is selected for estimation and forecasting. As we can see from Table2, that the ARIMA (3, 1, 4), ARIMA (3, 1, 3), ARIMA (2, 1, 3), ARIMA (2, 1, 3), ARIMA (4, 1, 2), and ARIMA (4, 1, 5) models are selected to estimate the parameters of Africa, East Africa, West Africa, Central Africa, North Africa, and Southern Africa, respectively.Table 2
ARIMA model for forecasting the number of daily confirmed cases according to AIC.
RegionARIMA (p, d, q)AICBICRemarkAfricaARIMA (3, 1, 3)3639.9443666.872ARIMA (3, 1, 4)3595.3213625.615SelectedARIMA (3, 1, 5)3595.3333625.626ARIMA (4, 1, 1)3672.7473696.309ARIMA (4, 1, 3)3619.9153650.209East AfricaARIMA (1, 1, 1)2601.4052614.308ARIMA (3, 1, 1)2598.8182618.173ARIMA (3, 1, 2)2599.3562621.936ARIMA (3, 1, 3)2585.1172610.923SelectedARIMA (3, 1, 4)2586.6252615.657West AfricaARIMA (3, 1, 3)3023.0643049.991ARIMA (2, 1, 1)3022.7223039.552ARIMA (2, 1, 2)3021.7373041.933ARIMA (2, 1, 3)3020.5393044.1SelectedARIMA (1, 1, 3)3021.7373041.933Central AfricaARIMA (3, 1, 1)2965.5262985.721ARIMA (3, 1, 2)2967.5262991.087ARIMA (3, 1, 3)2964.292991.218ARIMA (3, 1, 4)2963.0112989.939ARIMA (2, 1, 3)2962.9822986.544SelectedNorth AfricaARIMA (4, 1, 1)3195.5413219.103ARIMA (4, 1, 2)3195.7623222.69ARIMA (2, 1, 4)3199.0143225.942ARIMA (3, 1, 4)3196.9373227.23ARIMA (1, 1, 4)3193.6483217.21SelectedSouthern AfricaARIMA (3, 1, 3)3482.7383509.666ARIMA (4, 1, 3)3485.7553516.049ARIMA (3, 1, 4)3490.283520.574ARIMA (4, 1, 4)3448.1893481.849ARIMA (4, 1, 5)3446.1523483.178SelectedSource: own computation, 2021.Table 3
The prediction epidemic results of the new COVID-19 in Africa for the next month as predicted by the ARIMA (3, 1, 4) model.
DateExpected casesDateExpected cases17/9/2072562/10/2020580018/9/2073823/10/2020580419/9/2071274/10/2020547820/9/206485/10/2020507021/9/2057796/10/2020488422/9/2053827/10/2020505123/9/2054608/10/2020543824/9/2058389/10/2020575825/9/20614210/10/2020578326/9/20608211/10/2020551327/9/20565812/10/2020516728/9/20515113/10/2020501529/9/20490114/10/2020517330/9/20505715/10/2020552601/10/20546516/10/20205819Source: own computation, 2021.Source: own computation, 2021.Source: own computation, 2021.Source: own computation, 2021.Source: own computation, 2021.Source: own computation, 2021.Source: own computation, 2021.


## 3.2.2. Forecasting Using the Selected ARIMA Models

Candidate models were obtained based on the respective spikes observed from the autocorrelation function (ACF) and the partial autocorrelation function (PACF). Table3 presents the prediction results of daily confirmed new COVID-19 cases in Africa for the period between 17/9/2020 and 16/10/2020 as predicted by the ARIMA (3,1,4) model, and the result demonstrates that the daily confirmed new cases trend in Africa as the continent may become stable or it will become stagnant (see Figure 2). However, this is the weighted average of the five African regions, and there is significant variation in the spread and trend of COVID-19 among African regions.Figure 2
The plot of actual confirmed cases with the prediction result of the ARIMA model for Africa.Unlike the cases in Africa, the prediction results of daily confirmed COVID-19 cases in East Africa as predicted by the ARIMA (3, 1, 3) model show an increasing trend in the spread of daily cases of the COVID-19 pandemic (as shown in Table4 and Figure 3). Similarly, Table 5 presents the prediction results of daily confirmed COVID-19 cases in Northern Africa for the period between 17/9/2020 and 16/10/2020 as predicted by the ARIMA (1,1,4) model. The prediction results on the plot of actual confirmed cases with the prediction result of the ARIMA model depict the increasing trend and spread of COVID-19 in Northern Africa (see Figure 4).Table 4
The prediction results of daily confirmed COVID-19 cases in East Africa for the next month as predicted by the ARIMA (3, 1, 3) model.
DateExpected casesDateExpected cases17/9/2012862/10/2020145418/9/2014763/10/2020143819/9/2011664/10/2020140820/9/2013235/10/2020144221/9/2014436/10/2020147422/9/2013597/10/2020145423/9/2012678/10/2020144724/9/2013839/10/2020147925/9/20144010/10/2020149226/9/20135111/10/2020147727/9/20133712/10/2020148528/9/20142713/10/2020150929/9/20143414/10/2020151330/9/20137315/10/2020150601/10/20139616/10/20201519Source: own computation, 2021.Figure 3
The plot of actual confirmed cases with the prediction result of the ARIMA model for East Africa.Table 5
The prediction results of daily confirmed new COVID-19 cases in North Africa for the next month as predicted by the ARIMA (1, 1, 4) model.
DateExpected casesDateExpected cases17/9/2035882/10/2020374918/9/2035043/10/2020378319/9/2035714/10/2020378320/9/2035335/10/2020381521/9/2036006/10/2020381822/9/2035707/10/2020384723/9/2036298/10/2020385124/9/2036079/10/2020387925/9/20365910/10/2020388726/9/20364311/10/2020391127/9/20369012/10/2020392028/9/20367813/10/2020394429/9/20372014/10/2020395330/9/20371415/10/2020397601/10/20375216/10/20203987Source: own computation, 2021.Figure 4
The plot of actual confirmed cases with the prediction results of the ARIMA model for North Africa.The prediction results of daily confirmed new COVID-19 cases in West Africa and Central Africa for the next month were estimated by employing the ARIMA (2,1,3) and ARIMA (2,1,3) models, respectively (see Tables6 and 7). The prediction results indicate a slight increasing trend in the number of daily new confirmed cases of COVID-19 in both West Africa and Central Africa (see Figures 5 and 6). On the other hand, Southern Africa is the most infected region in Africa, but Table 8 and Figure 7 confirmed that Southern Africa had an almost decreasing trend in the spread and daily confirmed cases of the COVID-19 pandemic, and this may be the major reason for the stable trend of the African daily confirmed COVID-19 cases as the increase in the daily confirmed cases in the North, East, West, and Central Africa is counterpoised by the decreasing trend of Southern Africa daily confirmed new COVID-19 cases.Table 6
The prediction results of daily confirmed COVID-19 cases in West Africa for the next month as predicted by the ARIMA (2,1,3) model.
DateExpected casesDateExpected cases17/9/205892/10/202064418/9/206433/10/202060719/9/206194/10/202063220/9/205665/10/202067721/9/205846/10/202066722/9/206447/10/202062623/9/206438/10/202063224/9/205909/10/202067825/9/2058510/10/202068626/9/2064011/10/202064927/9/2066112/10/202063828/9/2061713/10/202067729/9/2059314/10/202070030/9/2063515/10/202067201/10/2067216/10/2020649Source: own computation, 2021.Table 7
The prediction results of daily confirmed COVID-19 cases in Central Africa for the next month as predicted by the ARIMA (2,1,3) model.
DateExpected casesDateExpected cases17/9/201842/10/202022018/9/202063/10/202021419/9/202094/10/202020720/9/201895/10/202021821/9/201996/10/202022122/9/2021457/10/202021223/9/202008/10/202021624/9/201959/10/202022525/9/2021410/10/202021826/9/2021111/10/202021627/9/2019812/10/202022528/9/2021013/10/202022529/9/2021814/10/202021930/9/2020515/10/202022501/10/2020616/10/2020230Source: own computation, 2021.Figure 5
The plot of actual confirmed cases with the prediction result of the ARIMA model for West Africa.Figure 6
The plot of actual confirmed cases with the prediction result of the ARIMA model for Central Africa.Table 8
The prediction epidemic results of the new COVID-19 in Southern Africa for the next month as predicted by the ARIMA (4,1,5) model.
DateExpected casesDateExpected cases17/9/2016012/10/2020155718/9/2020633/10/2020164019/9/2021094/10/2020141420/9/2018575/10/2020104721/9/2013466/10/202081022/9/2010267/10/202086523/9/2010378/10/2020115724/9/2013819/10/2020145125/9/20173210/10/2020152226/9/20183111/10/2020131927/9/20157312/10/202099628/9/20115713/10/202079529/9/2087214/10/202085730/9/2091715/10/2020112501/10/20123016/10/20201389Source: own computation, 2021.Figure 7
The plot of actual confirmed cases with the prediction results of the ARIMA model for Southern Africa.Except for Southern Africa, all African regions show an increasing trend in the predicted daily COVID-19 new cases, and specifically East and Northern Africa show a significant increasing trend in the spread of the COVID-19 pandemic.


## 3.2.3. The Deviation between the Forecasted and Actual Data on the Spread of Covid-19

As shown in Table9, the sign of the forecasted values of COVID-19 cases in Africa and the actual values of the daily confirmed COVID-19-19 cases are similar, which is a positive or an increasing trend. Both values portray the increasing trends of the COVID-19-19 pandemic. However, in all cases, the forecasted values are lower than the actual values, or the ARIMA model prediction results underestimate the spread of COVID-19-19 in Africa.Table 9
The deviation between the actual and forecasted values of the daily confirmed COVID-19 cases in Africa for the period between 17/9/2020–16/10/2020.
DateExpected casesActual casesGapDateExpected casesActual casesGap17/9/207256860313472/10/202058008853305318/9/20738281677853/10/202058048828302419/9/207127872716004/10/202054788089261120/9/20648842077725/10/202050704709-36121/9/20577961463676/10/202048846601171722/9/205382683914577/10/2020505110546549523/9/205460872632668/10/2020543810904546624/9/205838818623489/10/202057588563280525/9/2061427978183610/10/2020578313531774826/9/206082641233011/10/202055138978346527/9/2056588368271012/10/20205167588671928/9/205151566751613/10/202050157834281929/9/2049017508260714/10/2020517311509633630/9/2050578433337615/10/20205526911535891/10/202054657265180016/10/20205819106824863Source: own computation, 2021.At the subregional level, there is a deviation between the actual and the ARIMA model forecasted values of the daily COVID-19 cases, and the deviation is both on the sign and the size of the actual and forecasted values of the daily COVID-19 cases. Tables10–14 present the deviation between the actual and forecasted values of the daily confirmed COVID-19 cases in East Africa, West Africa, Central Africa, North Africa, and Southern Africa for the period between 17/9/2020–16/10/2020, respectively.Table 10
The deviation between the actual and forecasted values of the daily confirmed COVID-19 cases in East Africa for the period between 17/9/2020–16/10/2020.
DateExpected casesActual casesGapDateExpected casesActual casesGap17/9/20128614081222/10/20201454158212818/9/2014761327−1493/10/20201438160416619/9/20116616634974/10/20201408178637820/9/20132315262035/10/20201442970−47221/9/20144315851426/10/202014741076−39822/9/20135916402817/10/20201454161416023/9/2012671351848/10/20201447192647924/9/2013831210−1739/10/20201479163015125/9/2014401178−26210/10/20201492181131926/9/2013511325−2611/10/20201477161513827/9/20133713551812/10/202014851208−27728/9/20142714441713/10/202015091258−25129/9/20143414875314/10/20201513190639330/9/2013731320−5315/10/20201506164614001/10/2013961357−3916/10/202015191456−63Source: own Computation, 2021.Table 11
The deviation between the actual and forecasted values of the daily confirmed COVID-19 cases in West Africa for the period between 17/9/2020–16/10/2020.
DateExpected casesActual casesGapDateExpected casesActual casesGap17/9/20589428−1612/10/2020644525−11918/9/2064364963/10/2020607520−8719/9/20619601−184/10/2020632288−34420/9/20566495−715/10/2020677329−34821/9/20584423−1616/10/2020667378−28922/9/20644407−2377/10/2020626453−17323/9/20643555−888/10/2020632484−14824/9/20590412−1789/10/2020678473−20525/9/20585573−1210/10/2020686468−21826/9/20640372−26811/10/2020649429−22027/9/20661586−7512/10/2020638399−23928/9/20617320−29713/10/2020677585−9229/9/20593454−13914/10/2020700564−13630/9/206356865115/10/2020672494−1781/10/2020672442−23016/10/2020649515−134Source: own computation, 2021.Table 12
The deviation between the actual and forecasted values of the daily confirmed COVID-19 cases in Central Africa for the period between 17/9/2020–16/10/2020.
DateExpected casesActual casesGapDateExpected casesActual casesGap17/9/20184169−152/10/20202202664618/9/20206242363/10/2020214203−1119/9/20209153−564/10/202020743−16420/9/20189119−705/10/2020218163−5521/9/201993231246/10/20202212361522/9/202145157−19887/10/202021235−17723/9/20200257578/10/202021655934324/9/20195163−329/10/2020225149−7625/9/20214157−5710/10/20202182392126/9/20211132−7911/10/2020216150−6627/9/2019869−12912/10/2020225171−5428/9/20210201−913/10/2020225209−1629/9/20218149−6914/10/202021952530630/9/202052201515/10/2020225271461/10/2020206186−2016/10/2020230216−14Source: own computation, 2021.Table 13
The deviation between the actual and forecasted values of the daily confirmed COVID-19 cases in North Africa for the period between 17/9/2020–16/10/2020.
DateExpected casesActual casesGapDateExpected casesActual casesGap17/9/20358842136252/10/20203749464889918/9/20350437462423/10/20203783451473119/9/20357142266554/10/20203783430352020/9/203533458210495/10/202038152283−153221/9/2036003095−5056/10/2020381838422422/9/2035703183−3877/10/202038476387254023/9/20362945749458/10/202038516326247524/9/20360740484419/10/20203879477689725/9/203659446780810/10/202038878391450426/9/2036433530−11311/10/202039115150123927/9/2036904963127312/10/202039202857−106328/9/2036782535−114313/10/20203944456261829/9/203720447475414/10/202039536776282330/9/203714427656215/10/2020397644835071/10/202037523360−39216/10/2020398750171030Source: own computation, 2021.Table 14
The deviation between the actual and forecasted values of the daily confirmed COVID-19 cases in Southern Africa for the period between 17/9/2020–16/10/2020.
DateExpected casesActual casesGapDateExpected casesActual casesGap17/9/20160123827812/10/20201557191836118/9/20206322712083/10/20201640198434419/9/2021092144354/10/20201414166925520/9/2018571698−1595/10/20201047964−8321/9/201346887−4596/10/2020810106525522/9/20102614524267/10/20208652057119223/9/201037208110448/10/20201157188472724/9/20138123719909/10/2020145115358425/9/2017321603−12910/10/202015222622110026/9/2018311072−75911/10/20201319163431527/9/2015731395−17812/10/2020996125125528/9/201157127011313/10/2020795121942429/9/208729437114/10/20208571976111930/9/209171931101415/10/202011252221109601/10/201230191568516/10/2020138934722083Source: own computation, 2021.However, we can tolerate the minor difference between the actual and the ARIMA model forecasted values of COVID-19 daily confirmed cases, given the uncertain nature of the current COVID-19 pandemic and the growing interconnected and complex world, which are ultimately demanding flexibility, robustness, and resilience to cope with unexpected future events and scenarios [27].


## 4. Conclusion

The pattern of daily confirmed new cases of the COVID-19 pandemic is forecasted by using the ARIMA model strategy to help the efforts of the World Health Organization, African Union, Africa Centers for Disease Control and Prevention (CDC Africa), African regional organizations (IGAD, ECOWAS, COMESA, ECCAS, SADC), and other stakeholders to control the further spread of coronavirus in Africa. The prediction of the number of infections would assist policymakers in a specific region to assess their current healthcare capacity and decide which measures need to be taken to curb and control the spread of COVID-19 [28].Based on the available data, the study found that the best prediction models for forecasting the trend of daily new confirmed COVID-19 cases are ARIMA (3,1,4), ARIMA (3,1,3), ARIMA (2,1,3), ARIMA (2,1,3), ARIMA (1,1,4), and ARIMA (4,1,5). The prediction models are considered best for Africa as a continent, East Africa, West Africa, Central Africa, North Africa, and Southern Africa, respectively. By adopting this model, we were able to predict the daily confirmed new COVID-19 cases for the period between 17/9/2020 and 16/10/2020.Given the uncertain nature of the current COVID-19 pandemic and the world’s growing interconnectedness and complexity, the proposed method’s experimental results match the actual COVID-19 daily case data to demonstrate the proposed model’s realistic nature. As a result, the ARIMA model’s forecasting will help in prioritizing and promoting regional cooperation in formulating policies to address the COVID-19 pandemic and employing effective strategies to control the virus by incorporating the experience of those regions that have seen a declining trend, such as Southern Africa.



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*Source: 2211512-2022-09-30.xml*