Forecast number of new cases of Corona Virus Disease (COVID-19) in Ethiopia, using the case-based autoregressive integrated moving average model

As the most common, SARS COV-1 infection had a wide range of respiratory and gastrointestinal symptoms and the last confi rmed case was reported in 2004. The second outbreak in 2012 was caused by Middle East respiratory coronavirus syndrome (MERS-CoV), and case fatality was substantially higher than that of SARS-COV-1. MERS-CoV has a wide variety of mild, moderate to serious physical symptoms and some patients have acute respiratory distress syndrome. On December 2019 the third and most recent outbreak of serious acute respiratory syndrome coronavirus-2 (SARS-CoV-2) began, leading to a global pandemic. Patients with SARS-CoV2 infection may be asymptomatic or have the most typical signs Abstract


Introduction
It is understood that human coronavirus infections are responsible for mild respiratory diseases. The three global coronavirus outbreaks that contributed to signifi cant mortality and morbidity were SARS CoV-1, MERS-CoV and SARS-CoV2.
The fi rst outbreak of the twenty fi rst century caused by coronavirus was SARS CoV-1.

Abstract
After the initial outbreak in Ethiopia, the dispersion of SARS-CoV-2 is elevated number of cases. Literally, reported results for confi rmed cases peaked in August 2020 and declined after that time, as evidenced by the contestd responses that have invested in pandemic control in the country.
ARIMA models are a most widely used approaches to time series forecasting and provide harmonizing approaches to the problem of forecasting. ARIMA models aim to describe autocorrelations in the data. Thus, in this study, the Autoregressive Integrated Moving Average (ARIMA) method is used to predict the number of new coronavirus cases. In short, Auto regression uses the dependent relationship between observation and lagged observations; Integrated using the difference in raw observations; and Moving Average relies on the dependency between observation and residual error. ARIMA (2, 2, 2) predicts the number of confi rmed cases of COVID-19, based on the period between March 2020 and December 2020 at 95% confi dence intervals. The result revealed that the maximum expected new case per day was 807 and the minimum forecast was 410 cases per day in the next two months. In addition, the total number of confi rmed COVID-19 expected cases could reach about 160585 by end-February 2021. of fever, cough, and shortness of breath. SARS-Cov-2, literally called COVID-19 [1], was the subject of this study.
The latest outbreak (COVID-19) became a global pandemic as of 4 May 2020 and is still ongoing [2]. The pandemic was identifi ed in Wuhan, China in December 2019 [3]. Later, the rapid spread of this pandemic from corner to corner was a sudden shock to the entire planet. As of 31 December 2020, more than 83.8 million cases of COVID-19 have been registered in about 2010 countries and regions, resulting in more than 1.8 million deaths, while more than 59.3 million people have recovered [4].
In Africa, the fi rst case of coronavirus was reported in Egypt on 14 [4,5].
While well known, interventions such as hand washing, maintaining social distances and wearing face masks suggested by public health workers to monitor the spread of coronavirus,it's transmission never stopped still in Ethiopia [6]. In the fi rst three months, the case confi rmed, and the rate of death in the country grew over the initial three months [7,8]. Since COVID-19 continues to be a global public health concern and requires the utmost effort to track the prevalence of the virus, it is argued that the fundamental prerequisite for successful monitoring of the prevalence rate is the use of pandemic predictive methods [9]. Thus, the study predicted a new case of COVID-19 in Ethiopia for the next 60 days with the goal of notifying all concerned entities to monitor the prevalence, and hazard of this pandemic.

Data set
Across the world, researchers and policy makers are looking at confi rmed cases and deaths to understand and compare the spread of the COVID-19. In this study, data of COVID-19 were

Analytical methods
ARIMA modeling is one of the best modeling techniques in the time series [2,9]. ARIMA methods with the help of a number of parameters and a model expressed as ARIMA (p, d, q). Here, p stands for the order of self-regression, d stands for the degree of difference in trends, and q stands for the order of the moving average [10]. For the confi rmed COVID-19 cases in Ethiopia, I have used ARIMA (2,2,2) technique. The model for predicting possible reported cases of COVID-19 was shown as;

Descriptive statistics
The description of the corona virus spread in Ethiopia by months was displayed on Table 1 and Figure 1. There were 13905, new cases in November, raising the total number of confi rmed cases to 110,074. The death toll rose to 1706. The number of recovered patients increased to 73,815, at the end of the month. In the last month of 2020, there were 14190 new cases and 217 additional deaths. The pandemic case increased to 124,264, and the death toll rose to 1,923. The total number of new cases, deaths and recoveries was shown in Table 1.
The line of new case report decreased after it peaked in August 2020. The pattern of case is not obvious from the fuigure1. The death chart is somewhat constant while the recovery chart show increase with month.

Measures of model accuracy
In this study, the time series model encompasses to forecast COVID-19 cases in the coming 60 days. The results for the measure of model accuracy for ARIMA, Linear Trend, Quadratic Linear, and S-Curve Trend, Moving Average, and Exponential model had displayed in Table 2 Then, parameters are estimated for the ARIMA (2, 2, 2) model and displayed in Table 3. Then it is observed that AR (2) and MA (2) parameters have a p-value of 0.000, 0.000, 0.000, and 0.0001 respectively, indicating that the parameters are signifi cant in the model at a 5% level of signifi cance except for intercept.
The prediction of new cases of COVID-19 in Ethiopia, shown in Table 4, with a 95% confi dence interval. According to the expected result, the number of confi rmed COVID-19 new cases will increase slightly over the next 60 days. This increase is evidenced by the unrestricted response that has been invested in pandemic control in the country. However, the estimated predicted values were high, requiring more effort to minimize the spread of this pandemic across the country. The key problem of the outbreak is the explanation why a few people have not shown any signs of the virus spreading the virus to others without understanding the test.
The outcome of the forecasted maximum and minimum number of new Covid-19 cases will be 410 and 807 in one day. In addition, the cumulative confi rmed cases reached 160,585 at the end of February 2021. Basically, it is displayed in Table   4. Thus, more prevention measures and more resources will be introduced by the government; unless the coronavirus relapses and affects the country more.
Trend analysis presents the related statistics for reported COVID-19 data in Figure 2 (Figure 4). This also implies that the errors are somewhat near normal due to  25  106  1041  4674  11684  34601  23237  20801  13905  14190  124264   New deaths  0  3  8  92  171  535  389  271  237  217  1923   Recovery  2  57  150  2221  4520  11792  12210  21701  21162  38281    a few outliers, such as the August report. Thus, the normality assumption may be slightly followed, but the residual histogram followed the normality assumption ( Figure 5). The graph between the residuals and fi tted values shows a small dispersion at very early times, and about 19 percent of the new case values are zero (See Figure 3). This implies that the assumption of constant variance is also satisfi ed, except the smaller (zero) data values are dropped. is connected to its previous values ( Figure 6). PACF is a partial auto-correlation function, fi nds a residual correlation (remaining after removing the effects that have already been explained by the earlier lag(s)). Then next lag value, therefore 'partial' and not 'complete' as we remove the found variations before we fi nd the next correlation ( Figure 7).     in Ethiopia in the fi rst three months has been shown to increase [9].
The scholars disprove the effect of geographical difference and temperature in reducing the distribution of COVID-19 (16). However, Covid-19 has caused serious global social and economic distress. Thus, COVID-19, regulated only by preprotective strategies. However, no aspect is evaluated in this study due to the unavailability of exposure data.
Pandemic patterns in the US and India have risen from 12 July 2020 to 11 September 2020 [10,13]. Countries are now the fi rst and second highly confi rmed cases of the pandemic. In the case of India, the case of COVID-19 was predicted using the ARIMA method and suggested the implementation of lockdown [9]. The security measures proposed were not, however, well implemented, and now the possibility of a pandemic in that country is uncontrollable. Ethiopia was 5th in the number of COVID-19 confi rmed cases in Africa, according to the WHO report [5]. It is presumed that if and only if the standard WHO disease prevention and control measures are not taken [9], the worst-case scenario could occur. This study therefore showed slight elevate in cases Ethiopia.
Like other scholars, this research was carried out to forecast the potential estimation of cases of COVID-19 using the ARIMA model [9][10][11][12]. In line with this analysis, the scholars have found that ARIMA technique is suitable for predicting the prevalence of Covid-19 [13][14][15][16]. The ARIMA model predicted a pandemic outbreak in India and indicated important corona viruses in the country prior to a rise in confi rmed cases [10]. Since the same model used in this analysis, the ARIMA model is useful in predicting potential cases of COVID-19. Ethiopia must also introduce controlling mechanisms and establish even more pandemic prevention policies.

Conclusion
Since the study shows a small increase in the number of cases in Ethiopia, more attention has been paid to the control of Covid-19. Unless the Government of Ethiopia implements a mechanism to control the pandemic, it may relapse and affect the country more. The study therefore suggested that proactive and control mechanisms should be implemented on a continuous basis. Since ARIMA model is an effort to predict the future forecast of the distribution of COVID-19, based on current data, so that the institutions have to formulate policies from now on the result of the study.