key: cord-0918719-5xj64geb authors: Khan, Nasrullah; Arshad, Asma; Azam, Muhammad; Al‐marshadi, Ali Hussein; Aslam, Muhammad title: Modeling and forecasting the total number of cases and deaths due to pandemic date: 2021-12-18 journal: J Med Virol DOI: 10.1002/jmv.27506 sha: 273c78b6302dbf82431639b5138105f01c75fc1b doc_id: 918719 cord_uid: 5xj64geb The COVID‐19 pandemic has appeared as the predominant disease of the 21st century at the end of 2019 and was a drastic start with thousands of casualties and the COVID‐19 victims in 2020. Due to the drastic effect, COVID‐19 scientists are trying to work on pandemic diseases and Governments are interested in the development of methodologies that will minimize the losses and speed up the process of cure by providing vaccines and treatment for such pandemics. The development of a new vaccine for any pandemic requires long in vitro and in vivo trials to use. Thus the strategies require understanding how the pandemic is spreading in terms of affected cases and casualties occurring from this disease, here we developed a forecasting model that can predict the no of cases and deaths due to pandemic and that can help the researcher, government, and other stakeholders to devise their strategies so that the damages can be minimized. This model can also be used for the judicial distribution of resources as it provides the estimates of the number of casualties and number of deaths with high accuracy, Government and policymakers on the basis of forecasted value can plan in a better way. The model efficiency is discussed on the basis of the available dataset of John Hopkins University repository in the period when the disease was first reported in the six countries till the mid of May 2020, the model was developed on the basis of this data, and then it is tested by forecasting the no of deaths and cases for next 7 days, where the proposed strategy provided excellent forecasting. The forecast models are developed for six countries including Pakistan, India, Afghanistan, Iran, Italy, and China using polynomial regression of degrees 3–5. But the models are analyzed up to the 6th‐degree and the suitable models are selected based on higher adjusted R‐square (R (2)) and lower root‐mean‐square error and the mean absolute percentage error (MAPE). The values of R (2) are greater than 99% for all countries other than China whereas for China this R (2) was 97%. The high values of R (2) and Low value of MAPE statistics increase the validity of proposed models to forecast the total no cases and total no of deaths in all countries. Iran, Italy, and Afghanistan also show a mild decreasing trend but the number of cases is far higher than the decrease percentage. Although India is expected to have a consistent result, more or less it depicts some other biasing factors which should be figured out in separate research. In this advanced area of science, man is enjoying the luxurious life that seems to be a dream in the early Twenty century. Science, technology, and artificial intelligence have dramatically improved every field of life. Similarly, the health sector has witnessed an intense improvement in methodologies, medicine, and Treatment. With all this advancement, humankin is facing the challenge to find out a treatment for new viruses, Parasites, and Microbes. In December 2019, an unprecedented disease similar to pneumonia-like clinical symptoms emerged in Wuhan, the biggest city of central China. It is said to be connected with wet-market dealing of victims with fish, bats and poultry. 1 Further research revealed that it has very clear clinical characteristics of fever, cough, fatigue, loss of smell or taste, sore throat, labored breathing, and pneumonia. 2, 3 Recent studies further demonstrated that age is a predisposing factor in victimizing through this virus so older people with underlying disease conditions such as diabetes and hypertension are at higher risk of advanced symptoms 4 which can lead to a casualty. The disease was later named COVID-19 by World Health Organization 5 and the virus responsible for the disease was named SARS-CoV2. 6 As of May 15th, 2020, the disease has been reported in 216 countries causing infections in >4. 4 Million people and >0.35 million deaths. In the absence of effective vaccination and therapeutics, social distancing and movement restriction through partial and complete lockdowns remained the key approach to tackle this pandemic. 7-10 On one hand, movement restriction has negative impacts on the economy while easing restrictions may increase the number of cases. Therefore, understanding the future trends of this disease through a statistical model could be highly useful in policymaking. In this regard, Pandey 11 developed a mathematical SIER model and a regression model for forecasting the total confirmed cases in India. Tan et al. 12 used a method of differential equations system to forecast the cumulative cases counts in China. Recently, Li et al. 13 has conducted a retrospective study to forecast the number of future COVID-19 confirmed cases by observing the correlation between internet researches estimated results and daily actual reported cases. Remuzzi 14 and Yang et al. 15 accessed the situation of Italy and suggested the possible trend of the disease to overcome the pandemic. Yang et al. 15 uses a modification of the SEIR model to forecast the disease patterns along with the AI method for forecasting the trend of the epidemic of COVID-19 in China. Panwar et al. 16 developed a mathematical model using CF and ABC nonsingular derivate to model the COVID- 19 . Hu et al. 17 using modeling techniques access the risk of COVID transmission in train passengers. Anzum and Islam 18 have given a mathematical modeling approach for the production rate of COVID with the effect of policies and behaviors. In the current study, using the probabilistic approach polynomial regression model is used to model the future scenario of any pandemic in terms of the number of deaths and the number of cases using R programming software. We applied a polynomial regression approach to model COVID-19's prevalence in Pakistan and 5 other countries (India, Afghanistan, Iran, Italy, and China) and forecasted by using a polynomial regression model of degrees 3-5. Recently, Li et al. 19 proposed the chaotic cloud quantum bats algorithm algorithm for optimization problems. Zhang and Hong 20 a forecasting modeling approach for electric loads using a support regression vector is discussed. The SAR modeling approach and using the CF and ABC nonsingular approach are mathematical models using the deterministic approach to model the number of cases, in the current study we assumed that the numbers of cases and number of deaths follow random behaviors, we applied the probabilistic approach to the model number of cases and number of deaths. Furthermore, these models are analyzed up to the 6th-degree and the suitable models are selected based on higher adjusted R-square (R 2 ) and lower root-mean-square error 24 Verity, 25 and Tang et al. 26 The rest of the formation of the paper is as under in Section 2 the applied methodology is discussed in detail, the result and discussion are carried out in Section 3 for each of the six countries. Section 4 provides the interpretation of the proposed methodology. University, United States has been used for analysis and forecasting of the total no of cases and total no of deaths in Pakistan, India, Afghanistan, Iran, Italy, and China. In the current study, we used the data of total no cases and total no deaths from the date when the first time a case is reported in these countries from the time of emergence to mid-May 2020. The understudy countries cover approximately 42% of the world population and they are neighboring or adjoining to neighboring countries to China from where this pandemic started, as it is supposed. These factors are the main motivation for our research. The key limitation of this study is that this modeling strategy can be used only where data is exponentially increasing where the infection rate is very high as it is in the case of pandemics used to see. In the following section, the models used for analysis and forecast purposes are illustrated. The multiple regression model with k independent variables regressing on the dependent variable Y is defined as are polynomial regression coefficients related to k th power of predictor X. 27 The interpretation of the regression coefficients of the polynomial regression model is the same as of multiple regression. The mean square error (MSE) is an unbiased estimator of σ 2 and is defined as The quantity MSE measures the average square of the difference between observed and predicted values and is used as how well a model is fitted to data. The quantity RMSE MSE = as although a biased estimator of σ but is widely used to measure the size of the error. The MAPE is a widely used statistic to compare the accuracy of different models to compare the relative performance of models. 28 This measure MAPE is defined as: The Coefficient of Determination R 2 and adjustedR * 2 are used to measure how much variation a model explains of the total variation. It ranges from 0 to 1, i.e., R 0 ≤ ≤ 1 2 and is defined as: Whereas the adjusted R-square (adj. R 2 ) is defined as The spread of the COVID-19 pandemic is undeniable as is evident Available data about these countries is analyzed through the Polynomial Regression Model technique to peep into the depth of data. Pakistan is the target forecast country while the rest of the countries are included to observe the difference on relative grounds. In Table 1 the polynomial regression analysis for the confirmed COVID-19 cases counts is presented along with the fitted model coefficients. The possible significance of each coefficient with respect to individual countries is observed at 1% significance level. Similarly, in Table 2 Tables 1 and 2 , respectively. In the following paragraphs, individual countries along with the fitted models have been discussed (Table 2a ). The dataset of Pakistan has been taken since the emergence of the Table 1 ). The mathematical form of polynomial regression equation in the case of Pakistan to get a forecast about the total number of confirmed cases is as follows: Table 2 ). The mathematical form of polynomial regression equation in the case of Pakistan to get a forecast about the total number of deaths is as follows: , therefore, the equation of the fitted polynomial regression model is: The facts and figures of Iran have been analyzed for the period of the emergence of COVID-19 till 15th May 2020 and significantly revealed drastic results through a suitable model whose results are tabulated in Table 1 for the cases and Table 2 The forecasting of the number of cases and Deaths can be performed by using polynomial regression modeling. Tables 3 and 4 Similarly, a comparative Forecast Trend Analysis based on the proportion of fatalities computed for each country relative to China is presented in Table 6 and Figure 11 . However, the analysis performed in Table 2 T A B L E 3 COVID-19 average forecast cases of next week (95% confidence interval limits) Conclusive data analysis of forecasts for each country in the upcoming week is performed with the death rates per COVID-19 cases. The average death rate among COVID-19 cases in Pakistan is 2.1% which is the least one amongst the others such as Afghanistan has 2.4%, India has 3.3%, Iran has 5.3%, China 5.8%, and Italy attains the highest expected Forecast for the deaths is 13.5%. The results are mentioned in the percentage in Table 7 for ease of understanding. On the other hand, it can also be seen that whether the expected number of cases is greater in Pakistan but still Table 7 We are thankful to the editor and reviewers for their valuable suggestions to improve the quality of the paper. This work was supported by King Abdulaziz University. There are no conflict of interests. 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