Modeling and forecasting the total number of cases and deaths due to pandemic.

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 (R2 ) and lower root-mean-square error and the mean absolute percentage error (MAPE). The values of R2 are greater than 99% for all countries other than China whereas for China this R2 was 97%. The high values of R2 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.

INTRODUCTION

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. 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. , 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 which can lead to a casualty. The disease was later named COVID‐19 by World Health Organization and the virus responsible for the disease was named SARS‐CoV2.

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. , , , 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 developed a mathematical SIER model and a regression model for forecasting the total confirmed cases in India. Tan et al. used a method of differential equations system to forecast the cumulative cases counts in China. Recently, Li et al. 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 and Yang et al. , accessed the situation of Italy and suggested the possible trend of the disease to overcome the pandemic. Yang et al. 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. developed a mathematical model using CF and ABC nonsingular derivate to model the COVID‐19. Hu et al. using modeling techniques access the risk of COVID transmission in train passengers. Anzum and Islam  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. proposed the chaotic cloud quantum bats algorithm algorithm for optimization problems. Zhang and Hong 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 (RMSE) & the mean absolute percentage error (MAPE) which satisfied these statistical checks at their maximum. The total no of cases and total no of deaths in Pakistan, India, Afghanistan, Iran, Italy, and China are from an open data source of Our World in Data and John Hopkins University, United States , . In the study we have discussed the possible modeling strategy in case of a pandemic, for this, the data of the COVID‐19 dataset of John Hopkin University repository is taken and we have selected 6 countries that cover approximately 42% of the world population and are neighboring countries to China from where the Pandemic as firstly reported whereas to test the efficacy of our proposed model for predicting the total no of effective cases and the number of deaths , and MAPE are used. The short time forecast comprised of 7 days of the week is presented to assist the Government and Medical practitioners to formulate their policies and tackle with COVID‐19 challenge of the century. Verity et el. provided the model‐based analysis for COVID‐19. Some more details can be seen in Ruan, Verity,  and Tang et al. 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.

PROPOSED METHODOLOGY AND RESULTS

Time series data provided by Our World in Data and John Hopkins 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.

Polynomial regression model

The multiple regression model with independent variables regressing on the dependent variable is defined as Where represents the number of observations in the sample. The is the intercept of multiple regression lines while are regression coefficients related to predictors of the regression line. The polynomial regression model is the extension of the multiple regression model where the predictor , , …… is replaced with , respectively, to study pandemics areas of research like COVID‐19 which have an exponential spread by each passing unit of time. Hence, the polynomial regression model becomes Where represents the number of observations in the sample. The is the intercept of the polynomial regression model and are polynomial regression coefficients related to power of predictor 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 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 as although a biased estimator of 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. This measure MAPE is defined as:

The Coefficient of Determination and adjusted are used to measure how much variation a model explains of the total variation. It ranges from 0 to 1, i.e., and is defined as: Whereas the adjusted R‐square (adj. ) is defined as

Algorithm for model selection

We applied the cyclical model approach for the selection of an appropriate model for the forecasting of the number of cases and the number of deaths. In the first step, we proposed a model, and after checking the data validity and assumption of the model we fitted the model, the efficacy statistic MAPE, R 2, and adj. R 2 for each of the proposed models is computed, if the proposed selected model outperforms the existing model then that is selected and the previous is dropped. This process is replicated till the selection of the most appropriate model. The flow chart of the process is illustrated in Figure 1.

Figure 1

Flow chart of model selection

Results and discussion

The spread of the COVID‐19 pandemic is undeniable as is evident from the drastic increase in the number of confirmed patients and death count in the whole world as shown in Figures 2 and 3. By the time of writing this manuscript, >4 million are the victims of this disease with approx. The mortality rate varies from country to country and climate to climate. None of the countries is saved from its effects but more or less in some countries due to various factors. In this study, the discussion is comprised of the dataset for the number of confirmed COVID‐19 patients and the number of deaths reported till mid of May 2020 from the emergence of the COVID‐19 pandemic through authentic sources for the respective six countries specifically: Afghanistan, Pakistan, India, China, Iran, and Italy. As the target is to analyze the COVID‐19 situation in Pakistan so its neighboring countries are selected for the comparison relative to the countries with severe spread of the COVID‐19 pandemic in China and Italy. This study is an effort to give a forecast about the number of deaths and the expected number of new COVID‐19 confirmed cases in the next weeks with statistical modeling. It is important to break the strength of the rumors spreading around through the encouraging effective facts and figures based on analytical output in favor of a decreased number of deaths and the expected number of COVID‐19 cases as well. Analysis of the data is performed through Polynomial Regression up to 6th degree to fit the best model on the basis of lower value of RMSE and MAPE along with the higher value of as a measure of the reliability and accurate forecast obtained through fitted polynomial regression model with the suitable degree. The analysis is performed and presented in such a way that one can understand by depicting results separately in the percentage for individual countries along with most concerning China for elaborating details about the sensitivity of the conditions at the risk of level of significance.

Figure 2

Total no of cases reported in the world

Figure 3

Total no of deaths in world

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 COVID‐19 deaths count is analyzed by fitting a polynomial regression model and related information about coefficients and possible significance is presented. By putting the values of coefficients in above‐mentioned equation along with the time period as an independent variable provides the predicted number of cases and deaths. Similarly, forecasts about the future cases and deaths are provided in Tables 1 and 2, respectively. In the following paragraphs, individual countries along with the fitted models have been discussed (Table 2a).

Table 1

Polynomial regression analysis for COVID‐19 cases counts dataset (model coefficients)

Country		Estimate	SE	t Value	p Value
Pakistan	Intercept = β_0	273.907	144.757	1.892	0.063
	Poly (1) = β_1	−107.329	26.362	−4.071	0.01
	Poly (2) = β_2	8.978	1.416	6.341	0.01
	Poly (3) = β_3	−0.185	0.028	−6.550	0.01
	Poly (4) = β_4	0.002	0.000	12.735	0.01
India	Intercept = β_0	267.300	230.472	1.160	0.249
	Poly (1) = β_1	−91.723	29.548	−3.104	0.003
	Poly (2) = β_2	7.732	1.116	6.932	0.01
	Poly (3) = β_3	−0.230	0.016	−14.684	0.01
	Poly (4) = β_4	0.002	0.000	30.398	0.01
Afghanistan	Intercept = β_0	50.838	32.721	1.554	0.125
	Poly (1) = β_1	−18.875	6.203	−3.043	0.003
	Poly (2) = β_2	1.612	0.347	4.647	0.01
	Poly (3) = β_3	−0.041	0.007	−5.675	0.01
	Poly (4) = β_4	0.001	0.000	10.582	0.01
	Poly (5) = β_5	−2651.252	1005.239	−2.637	0.010
Iran	Intercept = β_0	1069.996	228.728	4.678	0.01
	Poly (1) = β_1	−109.041	16.059	−6.790	0.01
	Poly (2) = β_2	5.231	0.465	11.252	0.01
	Poly (3) = β_3	−0.078	0.006	−13.258	0.01
	Poly (4) = β_4	0.000	0.000	13.980	0.01
Italy	Intercept = β_0	−11749.338	2136.873	−5.498	0.01
	Poly (1) = β_1	4165.197	396.887	10.495	0.01
	Poly (2) = β_2	−341.070	22.718	−15.014	0.01
	Poly (3) = β_3	9.675	0.536	18.068	0.01
	Poly (4) = β_4	−0.098	0.006	−17.736	0.01
	Poly (5) = β_5	0.000	0.000	16.174	0.01
China	Intercept = β_0	19561.665	3096.381	6.318	0.01
	Poly (1) = β_1	−5063.443	447.607	−11.312	0.01
	Poly (2) = β_2	272.330	19.918	13.673	0.01
	Poly (3) = β_3	−4.385	0.364	−12.031	0.01
	Poly (4) = β_4	0.030	0.003	10.142	0.01
	Poly (5) = β_5	0.000	0.000	−8.565	0.01

Table 2

Polynomial regression analysis for COVID‐19 deaths counts dataset (model coefficients)

Country		Estimate	SE	t Value	p Value
Pakistan	Intercept = β_0	−3.199	3.294	−0.971	0.335
	Poly (1) = β_1	1.291	0.378	3.416	0.001
	Poly (2) = β_2	−0.119	0.012	−10.178	0.01
	Poly (3) = β_3	0.003	0.000	33.250	0.01
India	Intercept = β_0	3.279	11.665	0.281	0.779
	Poly (1) = β_1	−2.013	1.496	−1.346	0.181
	Poly (2) = β_2	0.217	0.057	3.840	0.01
	Poly (3) = β_3	−0.007	0.001	−9.054	0.01
	Poly (4) = β_4	0.000	0.000	19.453	0.01
Afghanistan	Intercept = β_0	0.755	1.264	0.597	0.552
	Poly (1) = β_1	−0.115	0.151	−0.763	0.448
	Poly (2) = β_2	−0.004	0.005	−0.847	0.400
	Poly (3) = β_3	0.001	0.000	10.691	0.01
Iran	Intercept = β_0	383.983	50.806	7.558	0.01
	Poly (1) = β_1	−114.987	7.992	−14.387	0.01
	Poly (2) = β_2	7.117	0.371	19.208	0.01
	Poly (3) = β_3	−0.084	0.006	−13.083	0.01
	Poly (4) = β_4	0.000	0.000	8.413	0.01
Italy	Intercept = β_0	−1969.319	358.019	−5.501	0.01
	Poly (1) = β_1	644.370	66.496	9.690	0.01
	Poly (2) = β_2	−48.476	3.806	−12.736	0.01
	Poly (3) = β_3	1.265	0.090	14.101	0.01
	Poly (4) = β_4	−0.012	0.001	−12.905	0.01
	Poly (5) = β_5	0.000	0.000	11.014	0.01
China	Intercept = β_0	790.834	161.565	4.895	0.01
	Poly (1) = β_1	−186.224	23.356	−7.974	0.01
	Poly (2) = β_2	9.295	1.039	8.944	0.01
	Poly (3) = β_3	−0.147	0.019	−7.705	0.01
	Poly (4) = β_4	0.001	0.000	6.613	0.01
	Poly (5) = β_5	0.000	0.000	−5.760	0.01

Table 2a

Comparison of proposed with exponential and linear regression model

Country	Exponential regreesion			Linear regression			Proposed poly nomial regression
	R 2	Adj. R 2	Mape	R 2	Adj. R 2	Mape	R 2	Adj. R 2	Mape
Pakistan	0.8621	0.8602	853.8	0.7908	0.7879	0.5871	0.9995	0.9995	0.2422
India	0.9615	0.9611	1132.2	0.6007	0.5969	0.787	0.9995	0.9995	0.9099
Afghanistan	0.9191	0.9179	144	0.751	0.7474	0.6213	0.9989	0.9988	0.6465
Iran	0.6939	0.6903	4426.1	0.973	0.9727	0.3035	0.9959	0.9957	0.5506
Itly	0.811	0.8092	7239.3	0.9174	0.9166	0.4782	0.9985	0.9985	0.4446
China	0.5945	0.5915	5415.5	0.7422	0.7403	0.4205	0.9747	0.9737	0.2781

Pakistan

The dataset of Pakistan has been taken since the emergence of the pandemic COVID‐19 till mid‐May 2020. The data are fitted with the 4th‐degree of the polynomial regression model and found significant except the intercept. As the best‐fitted model is chosen with the lowest value of RMSE & MAPE and the higher value of among all other fitted polynomial regression models with varying degrees for the forecast of the number of cases regarding outbreak and the spread of COVID‐19 pandemic disease among humans in the upcoming week (see 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:

, So the fitted polynomial regression model is stated as: . Here an estimate of which is 273.91 explains that the total number of cases of COVID‐19 patient independent from time period are initially around 274. Similarly, estimated values of the rest of the regression coefficients, i.e., are reported (−107.33, 8.9784, −0.1852, and 0.002382) respectively explain the impact of each day as linear, quadratic, cubic and quadrant in the additive model. In addition, some of the factors have an additive or negative impact on the composite output (prediction or forecast). Now one can use this fitted model to get the desired forecast about the total number of COVID‐19 cases for the upcoming days or period. But it is recommended that the forecast period should not be far from the period of the fitted model. Pakistan's forecasted data is depicting the significant increase in upcoming days which is apparently because of ease in lockdown and opening of markets 4 days a week. Similarly, data on the total number of deaths that occurred in patients of the COVID‐19 pandemic is analyzed and results are presented in Table 2. Here, a most suitable polynomial regression model with degree 3 is chosen on the basis of the lowest value of RMSE & MAPE and the higher value of among all other fitted polynomial regression models for the forecast of death counts regarding outbreak and the spread of COVID‐19 pandemic disease among humans in the upcoming days or period (see 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: . Here an estimate of which is −3.199. This negative sign shows that there was initially no impact on the total number of deaths due to COVID‐19 independent from the time period. But as time passed, an impact is observed in the form of estimated values of the rest of the regression coefficients, i.e., are reported (1.291, 0.119, and 0.003) respectively, explain the impact of each day as linear, quadratic, and cubic in the additive model. In addition additive as well as negative impact on various factors is observed on the composite output (predicted or forecasted deaths). Now a fitted model is ready to be utilized to get the desired forecast about the total number of COVID‐19 deaths for the upcoming days or period.

Both of these fitted models explain the current scenario of Pakistan making it obvious that the current situation is under control but it could be dangerous or alarming if the government fails to maintain the current situation of lockdown in the country. So, necessary actions taken well in time are the need of the hour to mitigate the spread of this pandemic among the masses.

India

the neighboring country of Pakistan is selected for the comparison due to the climatic, cultural, and infrastructural similarities. India's data has been taken since the start of the pandemic COVID‐19 till mid‐May 2020. The data are fitted with the 4th‐degree polynomial regression model and found significant except the intercept as in the case of Pakistan. Similar conditions for the selection of the final model are imposed to get the desired model, i.e., Here an estimate of which is 267.30 explains that a total number of cases of COVID‐19 patients without an impact of the time periods are initially around 267. Similarly, estimated values of the rest of the regression coefficients, i.e., are reported (−91.723, 7.732, −0.230, and 0.002) respectively, explain the impact of each day as linear, quadratic, cubic, and quadrant in the additive model. In addition, some of the factors have additive or negative impacts on the composite output (prediction or forecast). Now one can use this fitted model to get the desired forecast about the total number of COVID‐19 cases for the upcoming days or period. India's forecasted data is depicting the continuous and significant rise in upcoming days similarly, data on the total number of deaths that occurred in patients of the COVID‐19 pandemic is analyzed and results are presented in Table 2. An appropriate model fitted to get a forecast about the total number of deaths is as follows: . Here is an estimate of which is 3.279. This shows that initially almost 3 deaths were reported due to COVID‐19 irrespective of the time period. Similarly, the estimated values of the rest of the regression coefficients, i.e., are reported (−2.013, 0.217, and 0.007) respectively, explain the impact because each successive day is linear, quadratic, and cubic in the composite model. Furthermore, additive/negative impacts on various factors are observed on the response

Afghanistan

it is another neighboring country of Pakistan on the west and has a serious impact on the spread of the pandemic in Pakistan, if not get controlled. That's why to have an eye on its ground realities, it is selected for the comparison. An appropriate fitted model from the data about the total number of cases is . Intercept is found insignificant while the remaining three coefficients are found significant with p 0.01. The second model is fitted on the total number of deaths that occurred due to COVID‐19. This fitted model is described in mathematical form as: . The first three coefficients are found insignificant while the fourth coefficient is observed significantly. From the fitted model, it is clear that there is a low impact of this pandemic on Afghanistan. The reason may be the unavailability of testing kits and other tools to judge the accurate number of affected ones.

Iran

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 for the deaths, to efficiently forecast the upcoming number of cases and the deaths due to the COVID‐19. The estimated model . All coefficients are found significant. Similarly, a fitted model for the forecast of the number of deaths is obtained as: . These models present higher values of the total number of cases and deaths reported at the initial stage as compared to Pakistan, India, and Afghanistan.

Italy

Italy is included in the analysis because of the higher number of cases and deaths in Europe. The data is analyzed for the same span of time from the emergence of COVID‐19 to Mid‐May, 2020 and results are analyzed with a fitted polynomial regression model of degree 5 as: . Similarly, another model for the forecast of the total number of deaths in Italy is . The above mentioned models present a vulnerable situation of Italy at the initial stage in the form of a larger number of cases as well as a total number of deaths in the country. This indicates that no preventive measures were taken after the outbreak of this pandemic in China. But the forecasts show that the increase in the total number of cases and deaths has been slowed down due to very strict measures taken by the government of Italy.

China

It is included in the analysis because cases of COVID‐19 appeared first time in China. The data is analyzed for the same period of time from the start of COVID‐19 to Mid‐May, 2020 and results are analyzed with a fitted polynomial regression model of degree 5 as: . Similarly, another model for the forecast of the total number of deaths in China is . The above mentioned models present a vulnerable situation of China at the initial stage in the form of a larger number of cases (around 19 562) as well as a total number of deaths (around 791) independent of the time period in the country. This shows how rapidly Wuhan city of China was affected by this pandemic. The forecasts show that the increase in the total number of cases and deaths has been almost stopped due to the very strict lockdown by the government of China.

In Tables 1 and 2, a declining trend in coefficients estimated value shows that there is a significant effect of all preventive and the treatment measures taken during lockdown conditions to overcome the outbreak of pandemic virus COVID‐19, proved a success story in this regard.

INTERPRETATION OF FITTED MODEL TRENDS

Figures 4 and 5 show the impact of prevalence with the number of cases and the deaths per day for all respective periods mentioned along the x‐axis. The y‐axis represents the frequency of the counts with the blue color for the observed dataset and the red color for the estimated best‐fitted trend of respective polynomial regression models of the appropriate degrees. Each adjusted value is greater than , revealing the accuracy and goodness‐of‐fit of the model for each country respectively with the appropriate degree to forecast. Interpretation of the derived results, about the prevalence of cases per day, is discussed above in detail subject to the parametric behaviors of the polynomial regression models; which is also shown in Tables 1, 2 and Figures 6, 7 the coefficients graphical understanding. The data is analyzed using the R language.

Figure 4

Fitted curve against the observed data with adjusted R 2 for total no of case

Figure 5

Fitted curve against the observed data with adjusted R 2 for total no of death

Figure 6

Behavior of regression coefficients of no of cases of COVID‐19

Figure 7

Behavior of regression coefficients of no of deaths due to COVID‐19

Forecast of total number of cases and deaths

The forecasting of the number of cases and Deaths can be performed by using polynomial regression modeling.

Tables 3 and 4 present the projected total number of cases and deaths for the upcoming week from May 16–22, 2020. These forecasts are based on fitted polynomial regression models. Along with forecasts, the data within parenthesis gives 95% confidence interval limits. These limits give an overview that our forecasted values may lie somewhere between these limits with high confidence. Strict measures can slow down the increase in cases while the ease in lockdown or other such measures may cause an increased opening of the markets etc. The data is hereby arranged in ascending order of prevalence forecast report in the respective countries. The least case counts are a forecast in Afghanistan, followed by Pakistan, India, China, Iran; and the highest cases are in Italy for the coming week shown through Figures 8 and 9. Comparative Forecast Trend Analysis Relative to China is hereby presented to forecast the proportionate increase of case counts for all countries under study based on facts and figures caused by the significant outbreak and the prevalence of pandemic virus COVID‐19, and are mentioned in Table 5 and Figure 10. There is a drastically increasing trend of COVID‐19 confirmed cases in Italy depicting an average proportion of , (Iran), and (India) relative to China. But in Pakistan, the number of cases emergence forecast on the average around with a slow increase in comparison with Italy. However, a slightly increasing trend of prevalent COVID‐19 confirms cases in Afghanistan are as an average relative to China. In contrast, a significant declining trend itself is occurring in China of at a base period of May 16, 2020. However, this declining impact may be attributed to the significant effect of the preventive and treatment measures taken during lockdown conditions to overcome the outbreak of pandemic virus COVID‐19.

Table 3

COVID‐19 average forecast cases of next week (95% confidence interval limits)

May 2020	Afghanistan	Pakistan	India	China	Iran	Italy
16	5906	39 973	86 610	82 546	119 277	226 532
	(5819–5993)	(39 590–40 357)	(86 005–87 215)	(74 452–90 640)	(116 625–121 930)	(220 921–232 143)
17	6277	42 156	91 172	81 792	122 789	228 716
	(6175–6380)	(41 706–42 605)	(90 495–91 849)	(72 609–90 974)	(119 552–126 025)	(222 116–235 316)
18	6667	44 437	95 909	80 903	126 727	231 165
	(6547–6788)	(43 912–44 961)	(95 154–96 664)	(70 511–91 296)	(122 807–130 647)	(223 437–238 894)
19	7077	46 820	100 825	79 870	131 135	233 917
	(6937–7217)	(46 212–47 428)	(99 985–101 666)	(68 143–91 597)	(126 426–135 843)	(224 915–242 919)
20	7507	49 308	105 926	78 679	136 056	237 012
	(7345–7670)	(48 607–50 009)	(104 993–106 858)	(65 489–91 870)	(130 447–141 665)	(226 584–247 440)
21	7959	51 904	111 214	77 319	141 538	240 492
	(7771–8146)	(51 100–52 709)	(110 182–112 247)	(62 531–92 107)	(134 910–148 166)	(228 478–252 505)
22	8432	54 613	116 696	75 776	147 630	244 399
	(8217–8646)	(53 696–55 530)	(115 556–117 835)	(59 252–92 301)	(139 855–155 405)	(230 631–258 167)

Table 4

COVID‐19 average forecast deaths next week (95% confidence interval limits)

May 2020	Afghanistan	Pakistan	India	China	Iran	Italy
16	148	860	2850	4741	6815	31 214
	(145–151)	(852–869)	(2819–2880)	(4319–5163)	(6681–6949)	(30 274–32 154)
17	155	902	3001	4722	6848	31 370
	(151–158)	(892–911)	(2966–3035)	(4243–5201)	(6695–7002)	(30 264–32 476)
18	162	945	3157	4697	6880	31 535
	(158–166)	(934–955)	(3119–3196)	(4155–5239)	(6705–7056)	(30 240–32 830)
19	169	989	3320	4665	6911	31 712
	(164–173)	(977–1000)	(3277–3363)	(4053–5276)	(6711–7111)	(30 203–33 220)
20	176	1034	3489	4625	6941	31 904
	(171–181)	(1021–1047)	(3441–3536)	(3937–5313)	(6714–7168)	(30 157–33 651)
21	184	1081	3664	4578	6970	32 115
	(178–189)	(1067–1095)	(3611–3716)	(3806–5349)	(6714–7226)	(30 102–34 128)
22	192	1129	3845	4522	6998	32 350
	(186–198)	(1114–1145)	(3787–3902)	(3660–5384)	(6710–7285)	(30 043–34 656)

Figure 8

Comparative forecast trend analysis of COVID‐19 cases in next week

Figure 9

Comparative forecast trend analysis of COVID‐19 deaths/fatalities in next week

Table 5

COVID‐19 forecast cases relative to china (%age)

May 2020	Afghanistan	Pakistan	India	China	Iran	Italy
16	7.2%	48.4%	104.9%	100.0%	144.5%	274.4%
17	7.7%	51.5%	111.5%	99.1%	150.1%	279.6%
18	8.2%	54.9%	118.5%	98.0%	156.6%	285.7%
19	8.9%	58.6%	126.2%	96.8%	164.2%	292.9%
20	9.5%	62.7%	134.6%	95.3%	172.9%	301.2%
21	10.3%	67.1%	143.8%	93.7%	183.1%	311.0%
22	11.1%	72.1%	154.0%	91.8%	194.8%	322.5%
Average	9.0%	59.3%	127.7%	96.4%	166.6%	295.4%

Figure 10

Percentage reported COVID‐19 confirmed cases relative to China

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 and shown in Figure 5 discussed in detail in the previous section, proved that there is a drastically significant outbreak with the fatalities of pandemic COVID‐19 forecast and can be viewed in Figures 5 and 11. The highest no. of fatalities/deaths (30 274–32 154) per day is expected to occur in Italy; which shows an increasing trend in fatalities/deaths in Italy with an average proportion of , in Iran 148.6% and India 71.8%, in Pakistan 21.4% relative to China. However, a slightly increasing trend of prevalent deaths forecasts an average proportion of 3.6% in Afghanistan relative to China. In contrast, a slightly declining trend itself is occurring in China 98.1% on average with a base period of May 16, 2020. However, this declining impact may be attributed in favor of the significant effect of all preventive and treatment measures taken during lockdown conditions to overcome the outbreak of pandemic virus COVID‐19.

Table 6

COVID‐19 forecast deaths relative to China (%age)

May 2020	Afghanistan	Pakistan	India	China	Iran	Italy
16	3.1%	18.1%	60.1%	100.0%	143.7%	658.4%
17	3.3%	19.1%	63.6%	99.6%	145.0%	664.3%
18	3.4%	20.1%	67.2%	99.1%	146.5%	671.4%
19	3.6%	21.2%	71.2%	98.4%	148.1%	679.8%
20	3.8%	22.4%	75.4%	97.6%	150.1%	689.8%
21	4.0%	23.6%	80.0%	96.6%	152.2%	701.5%
22	4.2%	25.0%	85.0%	95.4%	154.8%	715.4%
Average	3.6%	21.4%	71.8%	98.1%	148.6%	682.9%

Figure 11

Percentage reported COVID‐19 fatalities/deaths relative to China

The comparison of the proposed methodology with the existing Simple linear and Exponential regression model reveals that the polynomial regression model does better in terms of R 2, Adjusted R 2, and MAPE. The model significance was determined by F‐statistic at p < 0.05 is considered as a significant model and only such models are considered for forecasting of no of cases and deaths.

Forecast of death counts per COVID‐19 cases for the next week (%age)

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 depicts the decreasing percentage from 2.2% to 2.1% which can be taken as an overwhelming for the effectiveness of the preventive measures to control the epidemic. Iran, Italy, and Afghanistan also show a mild decreasing trend but the number of cases is far higher than the decrease percentage. However, 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.

Table 7

Next week deaths forecast per COVID‐19 cases (%age)

May 2020	Afghanistan	Pakistan	India	China	Iran	Italy
16	2.5%	2.2%	3.3%	5.7%	5.7%	13.8%
17	2.5%	2.1%	3.3%	5.8%	5.6%	13.7%
18	2.4%	2.1%	3.3%	5.8%	5.4%	13.6%
19	2.4%	2.1%	3.3%	5.8%	5.3%	13.6%
20	2.3%	2.1%	3.3%	5.9%	5.1%	13.5%
21	2.3%	2.1%	3.3%	5.9%	4.9%	13.4%
22	2.3%	2.1%	3.3%	6.0%	4.7%	13.2%
Average	2.4%	2.1%	3.3%	5.8%	5.3%	13.5%

CONCLUSIONS

Polynomial regression of appropriate degree found a best‐fitted forecast model approach for prediction of no effective cases and no of deaths in case of any pandemic, as here for COVID‐19 prevalent cases as well as fatalities/deaths for each country, respectively. The value of adjusted  > 0.99, can be described as a benchmark for the accuracy and goodness‐of‐fit of the fitted or proposed model for each country pandemic forecast. The average death rate per COVID‐19 prevalent cases in Pakistan is at the least 2.1%, following Afghanistan (2.4%), India (3.3%), Iran (5.3%), China (5.8%), and the highest death rate is 13.5% in Italy. A slightly declining trend in deaths among COVID‐19 cases is occurring in China 98.1% itself with a base period of May 16, 2020, showing a decline in forecasted fatalities of 4741 with 95% confidence limits as (L = 4319, U = 5163) but still with a 4% increase. The number of fatalities/deaths in Italy is forecasted on May 16, 2020, is 31 214 with 95% confidence limits as (L = 30274, U = 32154); which shows an average proportion of 658.4% times relative to that in China. The respective datasets also show that the severity of the pandemic in Pakistan occurred after the months in comparison with other countries. As it can be easily seen in March for other countries, whereas in Pakistan it started at that time. This declining impact of analysis in China and Italy is attributed to the significant effect of the preventive and treatment measures taken during lockdown conditions to overcome the outbreak of pandemic virus COVID‐19. So, it can be concluded to opt for such methodologies for prediction of no of cases and casualties, so that the sensible and early steps can be taken to avoid economic losses and human life can be protected by making wise decisions using modeling based upon data‐driven methods. The limitation of the study is the data for the number of cases reported and the number of deaths is assumed random, the case reported count or death count may be influenced by the Government prevention steps, Society behaviors, Environment, Disease pattern and, another unexplored effect. More detailed investigation/studies could be carried out to see the influence of these factors on the counts of reported and death cases. The current study using neutrosophic statistics can be extended in future research.

CONFLICT OF INTERESTS

There are no conflict of interests.

AUTHOR CONTRIBUTIONS

Nasrullah Khan, Asma Arshad, Muhammad Azam, Ali Hussein AL‐Marshadi, and Muhammad Aslam wrote the paper.