Indo-Pak Comparison Of COVID-19 By ARIMA Model: A Secondary Analysis

Background: Historically, the world has faced and recovered from many pandemics. The most recent global pandemic facing the entire world is Covid-19. India and Pakistan can be considered to be in the same phases of development and health spending relative to their GDP and also have similar climatic conditions. The main aim of the study is to forecast cumulative cases and deaths in Pakistan and India, which will be helpful for policy makers to plan accordingly. Methods: The data set was obtained from the World Health Organization (WHO) website (https://covid19.who.int). The time period we have considered since the first corona related case and death were observed in both countries. The dataset for Pakistan covered the time period from 28th February 2020 to 28th February 2021 and for India 30th January to 28th February 2021. The Auto-Regressive integrated moving average (ARIMA) model was applied for forecasting using R-package. Results: Our results forecasted that cumulative COVID-19 cases at the end of June 2021, at the end of September 2021 and at the end of December 2021 will be 13065792, 14704450, and 16481122 respectively in India while for Pakistan, we forecasted that at the end of June 2021, at the end of September 2021 and at the end of December 2021 will be 746963.5 873557.3and 999766.5 respectively. Cumulative deaths were also forecasted for Pakistan and India. We predicted cumulative deaths as at the end of June 2021 at the end of June 2021, at the end of September 2021 and at the end of December 2021 will be 170586.5, 181153.4 and 192017.5 respectively in India while for Pakistan, we forecasted that cumulative deaths at the end of June 2021, at the end of September 2021 and at the end of December 2021 will be 17890.98, 21825.26 and 25849.4 respectively. Conclusion: Corona related cumulative cases and deaths are on the rise in both countries. The pandemic situation in India is worse than in Pakistan nevertheless both countries are at high risk. There is a sudden increasing pattern in the number of corona related cases in both countries.


Background
The world has historically faced and recovered from many pandemics. The most recent global pandemic that the whole world is facing is Novel Coronavirus -Covid-19. The Virus has spread almost in every country at a rapid pace after initiating from China 1 . Although the virus has a low mortality rate, it is highly contagious due to which the response of the country dealing with the Covid-19 pandemic can be termed as a significant determinant of the consequences of this disease 2 . There are many articles for different countries around the world in regard to their responses to Covid-19. The current article has been aimed at sketching a comparison between the prevalent situation of Covid-19 in India and Pakistan which has resulted from their response to the pandemic.
Both the countries, India and Pakistan, can be regarded as being in the same phases of development and expenditure on healthcare with respect to their GDPs and they also have similar climatic condition 3 . India and Pakistan had their first cases within a month of each other as Pakistan had its first case on 26 th February 2020 in Karachi whereas India got its first case on 30 th January 2020 in Kerala 3 . Comparing the response of the two countries, it is known that India was quick to ban travels starting from early February and the country also issued the orders of a rapid lockdown in March for the purpose of containing the spread of Coronavirus 4 . In contrast, Pakistan responded slowly to the threat of Covid-19 as it's Prime Minister Imran Khan did not see the virus as a potential life-endangering threat and addressed the country downplaying the danger of Covid-19 stating that only old age people are affected by it 5 . He also encouraged the people to return to their work and mentioned that most cases of the virus can be resolved through self-quarantine. Nevertheless, realizing the danger of the virus, lockdown in Pakistan was imposed in late March.
Moving on, it can be observed that the fast response of India to the Covid-19 pandemic was significantly effective in containing the danger and destruction of the virus as in May, the reported cases of India were one-third and morality was almost half than that of Pakistan 6 . If a comparison is drawn between the stimulus package of India and Pakistan, it can be noted that the stimulus of Pakistan was much larger than that of India in terms of GDP percentage as Pakistan offered a stimulus of 2.5% of GDP and India offered a stimulus of 0.8% of GDP 7 . However, the economic situation of Pakistan has been estimated to be more affected than that of India as according to IMF 8 , the economy of Pakistan is estimated to contract by 1.5% whereas India's economy is estimated to grow by 1.9% in the year 2020. Hence, it can be stated by comparing both the countries that India dealt with the Covid-19 pandemic in a quick and effective manner while Pakistan was slow in taking actions due to which India's situation is comparatively that of Pakistan.

Data Collection Methodology
The data set for this research is obtained from the World Health Organization (WHO) online repository (https://covid19.who.int/). The time period we have considered since the first corona related case and death were observed in both countries. The dataset for Pakistan covered the time period from 28th February to 28th February 2021 and for India 30th January to 28th February 2021. The following table 1 provides the summary of corona infected cases and deaths in both countries up to 28 th February 2021.

Data Analysis
The R-package "Forecast" is used to forecast the number of corona infected cases and deaths in Pakistan and India. R is an open-source programming platform that is used for analysis and model development 9,10 . The Auto-Regressive integrated moving average (ARIMA) model, available in the package, is run on our dataset. The analysis and results are given in the next sections. The ARIMA model is the mixture of autoregressive and moving average processes and is specified by three parameters (p, d, q); where 'p' represents the order for an autoregressive part, 'd' represents the degree of integrated order difference I(d), and 'q' represents the order for Moving average part.

Model Estimation and Analysis
In this study, four separate ARIMA models are run for countries Pakistan and India. Two is for the number of corona infected cumulative cases and two for the number of coronae related cumulative deaths. Fig. 1 below is the graph of confirmed cumulative corona cases in Pakistan and India for the period January 2020 to February 2021.

Figure-1: Number of corona infected cumulative cases in Pakistan and India
The above Fig. 1 represents the graph of cumulative corona infected cases in both countries. The corona infected cases are growing faster in India than Pakistan that is clearly seen in the above figure. The same pattern is observed in the variable of death in both countries.

Results
The Forecast package in R is used to estimate the four ARIMA models for the number of corona related cumulative cases and deaths. Table 2 represents the best-fitted models based on minimum AIC and BIC criterion. Table 3 represents the estimates of accuracy parameters for the best-fitted models.  The 306 days forecast graph (1st March 2021 to 31st December 2021) of cumulative corona cases and death are given in Figure 2. The grey shaded area represents 80% confidence interval and white shaded area represents a 90% confidence interval in the figure  The standardized Q-Q plot and histograms for all models reflect normal curve distribution. The Ljung-Box test for all models indicates independence of residuals at 1% level of significance.
The accuracy of the forecast is assessed by the following formula:

Discussion
We used the WHO COVID-19 dataset for Pakistan and India. The purpose is to forecast the number of cumulative corona related cases and deaths in both countries. The AUTOARIMA technique is used, that is available in the R package "forecast". The forecast model ARIMA is simple to use and more predictive than other regression models. It is due to the fact that the ARIMA model only considers the past lag values of dependent variables 12 such that cumulative cases and deaths in this research.
After the emergence of a number of cases and deaths due to coronavirus, both governments imposed lockdown to make people at home. All markets, marriage halls, restaurants, schools and universities were closed to avoid overcrowding and make lockdown effective. Schools and universities are encouraged to adopt e-learning methods. Several quarantine centres were established to treat corona infected patients. Besides the government's effort, several nongovernment organizations (NGOs) provided food and some amount door-to-door to needy families.
Currently, the citizens in both countries are being encouraged to take more protective measures and practice social distancing to control the COVID-19 pandemic 13 --15 . Social media campaigns are being run to educate the public about this pandemic. Consequently, the spread of coronavirus is being expected to be decreased soon in the future. 16 After this analysis, we are of the view that COVID-19 pandemic situation in Pakistan is much better than India, nevertheless, both governments must take serious measures to cope with COVID-19 pandemic. Effective lockdown, self-isolation and public awareness are necessary to further control this pandemic.

Conclusion
This research found that corona related cumulative cases and deaths are on the rise in both countries. The pandemic situation in India is worse than in Pakistan nevertheless both countries are at high risk. There is a sudden increasing pattern in the number of corona related cases in both countries. Both governments must impose effective policies to control this pandemic.