Role of meteorological parameters with the spread of Covid-19 in Pakistan: application of autoregressive distributed lag approach

Abstract

This research focuses on the impacts of different meteorological parameters (temperature, humidity, rainfall, and evapotranspiration) on the transmission of Covid-19 in the administrative regions and provinces of Pakistan, i.e., Azad Jammu and Kashmir, Gilgit Baltistan, Khyber Pakhtunkhwa, Islamabad, Punjab, Sindh, and Balochistan from June 10, 2020, to August 31, 2021. This study analyzes the relation between Covid-19-confirmed cases and the meteorological parameters with the help of the autoregressive distributed lag model. In this research, additional tools (t-statistics, f-statistics, and time series analysis) are used for the motive of examining the linear relationship, the productivity of the model, and for the significant association between dependent and independent variables, lnccc and lnevp, lnhum, lnrain, lntemp, respectively. Values of t-statistics and f-statistics reveal that variables have a connection and individual significance for the model exist. Time series display that the Covid-19 spread increased from June 10, 2020, to August 31, 2021, in Pakistan. Temperature positively influenced the Covid-19-confirmed cases in all provinces of Pakistan in the long run. Evapotranspiration and rainfall influenced positively, while specific humidity influenced negatively on the confirmed Covid-19 cases in Azad Jammu Kashmir, Khyber Pakhtunkhwa, and Punjab. Specific humidity had a positive impact, while evapotranspiration and rainfall had the negative impact on the Covid-19-confirmed cases in Sindh and Balochistan. Evapotranspiration and specific humidity influenced positively, while rainfall influenced the Covid-19-confirmed cases negatively in Gilgit Baltistan. Evapotranspiration influenced positively, while specific humidity and rainfall influenced negatively on the Covid-19-confirmed cases in Islamabad.

Supplementary Information

The online version contains supplementary material available at 10.1007/s13762-023-04997-4.

Introduction

Pandemics and outbreaks caused many problems in the aspect of life as well as in the lifestyle roots of people around the world. While reading about the history of pandemics in the literature, it is enriched with diseases similar to the Covid-19 pandemic. Some famous pandemics brought destruction and catastrophe around the world in which some are, including cholera, plague, dengue, AIDS, influenza, severe acute respiratory syndrome (SARS), West Nile disease, and tuberculosis are some major names that come to the front page (Qiu et al. 2017). Humankind has faced two enormous outbreaks in the past, named severe acute respiratory syndrome (SARS) (Shahzad et al. 2020; Drosten et al. 2003) the Middle East Respiratory Syndrome coronavirus (MERS) (Zaki et al. 2012; Ramadan and Shaib 2019). Around the 1500 s or approximately every 10–50 years, there were moments when Influenza pandemics struck about three times in the specified regions around the world. In the twentieth century, there were 3 influenza pandemics which were named “Spanish flu” from 1918 to 1919, “Asian flu” from 1957 to 1958,s and “Hong Kong flu” from 1968 to 1969. Out of these three large pandemics, 20 million death number crossed around the world by the pandemic influenza from 1918 to 1919 and it was declared the most disastrous epidemic in world history (Gasparini et al. 2005; Version 2011). Furthermore, talking about H5N1 influenza, H1N1 influenza, and Ebola (Gostin et al. 2016), Influenza H1N1 2009 virus (A/2009/H1N1) had affected the whole world, and 18,000 confirmed deaths confirmed by this pandemic alone (Rewar et al. 2015). On the other hand, the death rate of Ebola crossed the 11,000 figure, and around USD $2 billion was utilized, according to World Bank calculations (Maurice 2016). If we focus on the Plague pandemics, Justinian plague, Black Death plague, and the third plague were caused by the Yersinia Pestis (Piret and Boivin 2021; Zietz and Dunkelberg 2004). Between 541 and 543, Egypt faced the Justinian plague which eventually consumed the Eastern Roman Empire and its neighbors, and an estimated 100 million people were eliminated by the plague in the Roman Empire and specifically talking, in Constantinople (Cunha and Cunha 2008). On the other hand, the Black Death plague showed its origin in East Asia and affected Central Asia and Europe. Historians stated that the Black death used the medieval Silk routes, which consisted of land and sea trade routes (Zietz and Dunkelberg 2004). As long as it stayed in Europe (early nineteenth century), around 200 million death figure was accomplished by the black death plague. Historians stated that from 1347 to 1351, the Black Death wiped 30% of the European population out of 100% and more destruction was caused by the Milan plague (1630), the great plague of London (1665–1666), and the Marseille plague, which came after the black death from 1720 to 1722 (Seifert et al. 2016). In 1817, when the first cholera pandemic affected India and then left its destructive impact on the other regions of the world, physicians and doctors recommended changing it from endemic to pandemic. Cholera did not stop there, in fact, five additional cholera pandemics showed their origin in India and left their destructive footprints on different continents during the nineteenth and twentieth centuries (Faruque et al. 1998). The seventh cholera was the most extensive one in cholera history. It began in Indonesia in 1961 and caused major epidemics in many countries from Zimbabwe to Mexico, and from South Soudan, Ghana to Yemen (Mutreja et al. 2011; Hu et al. 2016).

Specifically talking about Covid-19, many susceptibilities in communities emerged due to this outbreak itself. For example, decision-makers & specific community planers faced challenges with local pliability. (Newell and Dale 2020; Josef Settele, 2020) clarifies that ‘[r]ampant deforestation, an uncontrolled extension of agribusiness, serious breeding, mining and substructure advancement, as well as the black market dealing of wild species, have made an “exemplary absolute storm” for the overflow of infections & diseases.’ For medical professionals, mega-level shortages of individual defensive appliances and problems related to labor deficiency as well as insufficient food for everyone, ‘on the dot’ inventory management, etc., are some examples of issues that emerged due to Covid-19 (Hobbs 2020).

Fast forward to the last week of December 2019, 27 to 31 were the days when World Health Organization (WHO) first faced the unknown outbreak (yet to be declared Covid-19) reports from Wuhan, Hubei, China (Atri et al. 2020; Zhu et al. 2020; Bashir et al. 2020). During the first five days of the epidemic, Wuhan experienced an outbreak of the virus which left around 1800 people on their deathbeds and left around 70,000 people in very critical health situations (Ilyas et al. 2020). The main thing in the reports which got the attention of the WHO was the mentioning of symptoms in the patients who were suffering from mysterious respiratory contamination. Then, later in January 2020, WHO decided to go public with the information that the mysterious contamination in Wuhan is none other than part of the family of coronaviruses, and on February 11, 2020, the unknown outbreak got the name Covid-19 (Cascella et al. 2022). Novel coronavirus disease 2019 (2019-nCOV) was the name given by Chinese researchers. The International Committee on Taxonomy of Viruses (ICTV) named the virus SARS-CoV-2 and the disease COVID-19 (Lai et al. 2020). When cross-referenced with the respiratory coronavirus ancestors, all characteristics, for example, mechanisms, infections, and replications, COVID-19 works just like its ancestors, but it can bind tighter to the host receptor and increase its transmissibility due to some mutations. When studies were conducted, it was found by the researchers that (SARS-CoV-2) showed sticky behavior with the aerosols for three hours, in the case of copper, four hours, cardboard provided the 24-h time for their stay, and plastic and stainless steel provided 3 to 4 days of stay of SARS-CoV-2 (Lanese 2020). The stability of SARS-CoV-2 proven by the information extracted from the previous results suggested that the virus affected the people through the air and after touching objects that were directly exposed to the virus (van Doremalen et al. 2020).

Breathing and pneumonia were the prime symptoms in the Covid-19 patients at that time (Holshue et al. 2020; Perlman 2020). Moreover, Covid-19 showed promising similarities with the past decade’s outbreaks, e.g., SARS & MERS accord with the symptoms starting from cough, pyrexia, muscle pain, drowsiness, blood loss through coughing, dysentery, hyperventilation, and deficiency of circulating lymphocytes (Chen et al. 2020). Last but not least, kidney failure, pneumonia, and even death were the worst-case scenario related to Covid-19 (D. Wang et al. 2020). Some careful studies highlighted the possible transmission course of SARS-CoV-2 between humans (National Health Commission of China 2020) and 1) direct inbreathe of bronchial driblet (from the infected patient); 2) exposure of a surface as well as object infected with the Covid-19 virus, and 3) limited spaces exposed to aerosol transmission.

Specifically talking about earth and the earth’s surface, many phenomena, and events that happened in the atmosphere, climate, or weather, as well as the environment around us, are highly correlated to the meteorological parameters, and they are known as critical factors of the climate. Daily activities can be significantly affected by the meteorological parameter variations at different spatiotemporal scales. Values like unnatural highs and lows leave their influence on everyday life and especially in the daily life sectors. Moreover, the safety of both inland and sea transportation can be disturbed by the high/low values of meteorological parameters, often causing a huge impact on the environment (Karvelis et al. 2017). In recent years, an alarming situation that caught the attention of scientists community was the close relationship between climatic change and the wide spread of dangerous diseases. In the future, preparations and cautions must be done to timely dominate the disease, if any occurs. An example of Covid-19 is the most bitter lesson for us to analyze the humankind mistakes (Wang et al. 2020; Yi et al. 2019; Shi et al. 2020). The literature also gives us numerous study work where researchers found the meteorological variables were majorly involved in the scarlet fever spread (Lu et al. 2019), tuberculosis (Koh et al. 2013), dengue fever (Xiang et al. 2017), hemorrhagic fever with renal syndrome (HFRS) (Wei et al. 2018), bacillary dysentery (Hao et al. 2019), and human brucellosis (Cao et al. 2020), hand, foot and mouth disease (HFMD) (Wei et al. 2015), etc.

The literature has refined information when it comes to finding the relation between Covid-19 and meteorological parameters. While reading some high-yielding work in the literature, information regarding the change in temperature which play its role in spreading the SARS outbreak. In that research work, variables were used to find the possible relation between weather variability, and the transmission of infection through hospitals. For this, a structured multiphase regression analysis was utilized. Lin and cols. discussed that mean air temperature with other factors draw a parallel with SARS transmission (Lin et al. 2006). Tan et al. (2005) discovered the important finding that temperature was significantly lower in the 2003 SARS epidemic and daily incidence was much higher at higher temperatures, i.e., 18.18 times higher frequency was noticed at higher temperatures when compared to normal conditions or temperatures in Hong Kong as well as in Guangzhou, Beijing, and Taiyuan. A simple correlation with time lags (0, 1, 3, 5, 7, 10, 14) was used between the daily number of SARS patients and average values for meteorological variables.

When Kimberly Bloom-Feshbach and cols. used the time series models with peak time and by utilizing both latitudinal and longitudinal gradients specified in the time frame, periodical amplitude, and between-year variability of large-scale diseases were confirmed in the 85 countries with the help of the time series model applied to influenza data (Bloom-Feshbach et al. 2013). Moreover, temperature, as well as humidity, showed their role in the spreading of some diseases. For example, influenza virus and viruses related to respiratory, when researchers used the GraphPad Prism 5 software for the Statistical analyses.

To prove the dependency of Influenza Virus Transmission on some meteorological parameters such as relative humidity and temperature, guinea pigs as an experiment was used by the Lowen and cols. Twenty experiments support that relative humidity from 20 to 80% and 5 °C, 20 °C, or 30 °C favor transmission in both cold and dry conditions. In contrast, they also verified that increases in the value of both temperature and relative humidity caused influenza transmission to lose its activity (Lowen et al. 2007). Studies related to epidemics present the conclusion that both SARS and MERS tend to show activity at lower temperatures (Lin et al. 2006). Emma G. Gardner and cols. generated results by using univariable conditional logistic regression and case-crossover design suggest that Saudi Arabia faced primary MERS human cases when conditions were relatively cold and dry (Gardner et al. 2019). Xu et al. (2020 used the time series Poisson regression model between air quality index (AQI) and confirmed cases of Covid-19 in 33 locations in China. Several cities such as Jinzhong and Beijing showed results that the AQI showed a positive relationship with the confirmed cases of COVID-19. From lag day 1 to 3, the AQI effect on COVID-19 spread was statistically significant and the Covid-19 spread tends to occur under dry conditions.

The literature also reveals that when it comes to the spread of the disease, environmental conditions played a major role in the spread of the outbreak in the past. For instance, in the infection of influenza, Tamerius, and cols. emphasize that the strong activity of the virus increases in temperate regions as follows: When talking about the southern hemisphere, advancing from May to September is most critical and in contrast, the northern hemisphere can be affected from November to March. These results unfolded with the help of exploratory rank analyses, univariate and multivariate regression, and 78 study sites included in this study. Some were Italy, the Republic of Korea, Michigan, USA or Victoria, Australia, homogeneous climatic regions in Peru, some Thailand provinces; northern Argentina or Taiwan cities; and a subtropical island in Japan (Tamerius et al. 2013). In the research conducted by them, they strongly point out the factor that the high temperatures left a strong effect on the elimination of the virus.

Moving forward to SARS-CoV, Chan, and cols. used virus strain and cell line, stock virus harvest action, and the effect of drying, heat, and relative humidity and eventually found some interesting results. Chan and cols found the minimum and maximum lifetime of the virus. Results showed that when the temperature hits 22–25 °C and relative humidity vary between 40 and 50%, 5 days was the period when the virus was active and showing its effectiveness. In contrast, when they increased the temperature to 38 °C and relative humidity touched 95% saturation, the spreading activity of the virus was completely out of order (Méndez-arriaga 2020). While reaching up to 56 °C, the maximum time analyzed for the virus life was 15 min approximately (Pei et al. 2020; Chan et al. 2011).

Out of many possible meteorological parameters, three environmental parameters were highlighted by Yuan and cols., which were air temperature, humidity, and wind speed. Statistical tests between dependent and independents (temperature, humidity, and wind velocity) in the regression equation authenticate a significant SARS transmission in correlation with these meteorological parameters (Yuan et al. 2006). One prediction which was highly noticed in the above-mentioned studies points to the fact that if SARS has to reoccur, suitable environmental conditions are likely to be present in the spring season.

When talking about the recent Covid-19 disease, researchers used different approaches like ERA-5 reanalysis, Real-Time Reverse Transcriptase–Polymerase Chain Reaction Specimens, Decision Tree (DT), Random Forests (RF), Logistic Model Trees (LMT), and Naive Bayes (NB) classifiers, and gave a demonstration that why several countries faced the Covid-19 cases with the cold–dry environment conditions that occurred in during January and February 2020 (Sajadi et al. 2020; Wang et al. 2020; Keshavarzi 2020; Harmooshi et al. 2020). Authors also suggested that out of many factors and possibilities that contribute to the spread of the Covid-19 virus, the latitude and longitude play a major role in the spread (Wang et al. 2020; Keshavarzi 2020).

Araujo and cols used 200 environmental ideal models throughout a climatological year to check the spread of SARS-CoV-2. Their results also verified the fact that temperate climates tend to generate a high correlation bond where cold–dry weather conditions meet and Covid-19 transferral tends to occur (Araújo and Naimi 2020). Similarly, as the usual warm–humid environmental conditions dominate in tropical countries, Bukhari and cols. stated that the tropical countries tend to show a low number of positive Covid-19-confirmed cases which point to the explanation of how warm–humid environmental conditions minimized the Covid-19 spread. They also evaluate that countries that encountered the humidity of more than 10 g/m3 could visualize the slowdown in the Covid-19 transmissions (Qasim Bukhari 2020). Ma and cols. pointed out that the major reason for mortality in Wuhan, China was related to the temperature and humidity in accord with Covid-19 (Shereen et al. 2020).

Basheeruddin Asdaq and co used the SPSS-IBM 25 software where they used the bivariate regression analysis as well as Spearman’s Rho correlation in order to find the relation and association between the environmental parameters and Covid-19 cases in Saudi Arabia. Their study concluded that cases of virus tend to increase in following weather conditions; hot, less humid, and steady wind flow. In their research, temperature was one of the important characteristics that directly disturbed the host system where decrease in temperature resulted in the low infection rate, and as the temperature increased, the infection rate also rose to higher values (Asdaq et al. 2022).

Covid-19 strikes in Pakistan on the date of Feb 26, 2020, where 2 cases were confirmed by the Ministry of National Health Services Regulations and Coordination Islamabad, Pakistan. In Islamabad and Karachi, cases jumped to twenty (Sindh gave 14 cases, Gilgit Baltistan cases were 5, 1 in Baluchistan 12-yr.-old boy showed the symptoms of Covid-19) by March 12, 2020. After checking the travel history of these patients, it portrayed that Iran, London, and Syria were their recent visited places (Saqlain et al. 2020). On March 18, 2020, Peshawar, Pakistan reported the first death by Covid-19. Many strict actions were taken by the government of Pakistan at that time to control this pandemic including screening procedures for the passengers who recently traveled and came from other countries, restricting transportation services from one city to another, taking quick action to new cases, quarantining, and restricting unnecessary mobility of people, etc. (Noreen et al. 2020).

There were a lot of studies and research done around the world including many major cities and provinces of the countries like China & its provinces, New York, the USA, Mexico, Brazil, India, etc. However, no study has looked into the possible high relationship between the cases of Covid-19 and meteorological variables on entire Pakistan. In the literature, some studies were done on the local level in Pakistan. For example, (Rehman et al. 2021) did research regarding Covid-19 and meteorological parameters nexus in Islamabad, Pakistan where the researchers used Pearson, Spearman, and Kendall’s correlations. Batool and Tian (2021) determined the correlation between Covid-19 and weather parameters using time series forecasting on Pakistan cities by using simple machine learning models, i.e., ARIMA, linear regression, SVM, MLP, RNN, LSTM, GRU, etc. (Shahzadi et al. 2020) used Spearman’s rank (rs) correlation coefficient test for the influences of meteorological parameters on Covid-19 spread in those cities of Pakistan where contamination rose high (Karachi, Lahore, and Peshawar). Syed et al.(2021) focuses on the impact of the Covid-19 lockdown on urban mobility, atmospheric pollutants, and Pakistan’s climate, in Pakistan’s three major cities (Islamabad, Lahore, and Karachi) by using satellite remote sense data and different models and tests like Pearson, Kruskal–Wallis H test (KWt), Wilcoxon signed rank sum test (WRST), generalized linear models (GLM), etc. Covid-19 cases in Lahore, Pakistan, and the impact of climate (Manzoor and Sharif 2021) used the stepwise linear regression model. From biological science, (Uzair et al. 2022) did a case study on Pakistan with the help of charts and graphs, showing the relation between Covid-19 cases and temperature, precipitation, etc.

So keeping in mind all the above-mentioned studies, this paper intends to investigate the association between the cases of Covid-19 and parameters correlated with the environment by using the autoregressive distributed lag (ARDL) approach for the long-run test for all the provinces of Pakistan. This study focus on the effects of daily air temperature, precipitation rate, humidity, and evapotranspiration on the daily local confirmed Covid-19 positive cases in Pakistan from June 10, 2020, to August 31, 2021. This research work distinct itself from other research studies done on Pakistan by using a different approach as they used methods like Pearson, Spearman, and Kendall’s correlations, time series models, (KWt) and (WRST) tests, etc., whereas this research used ARDL model with t-statistics, f-statistics which are considered for Pakistan and used for the total number of accumulated confirmed cases of Covid-19 and meteorological parameters, i.e., temperature, humidity, rainfall, evapotranspiration. Also, this research focuses on entire Pakistan, whereas others mostly focused on the local level and cities of Pakistan. As the objective of this study is to check the role of meteorological variables mentioned previously in the spread of the Covid-19 epidemic in Pakistan, the above-mentioned studies related to outbreaks and disease have inspired us to research meteorological parameters and Covid-19 behavior.

Materials and methods

Study area

In the countries list, Pakistan rank as the 33rd largest country by area covering around 881,913 square kilometers and a population almost touching the number 226, 992, 332 approximately (2021 estimate). Four provinces and three administrative boundaries are part of Pakistan: Punjab, Sindh, Khyber Pakhtunkhwa, Balochistan, Azad Jammu & Kashmir, Gilgit Baltistan, and Islamabad, respectively (Syed et al. 2021) (Fig. 1 with the demographic data). Pakistan is geographically part of South Asia. While talking about its extent, it starts from the Arabian Sea in the south to the north, where the Himalayan Mountains are present. This can tell us that Pakistan has a long latitudinal extent stretch. While talking in zone division, it is located in the sub-tropics and partially in the temperate region. Moreover, Köppen–Geiger climate classification for Pakistan are; Cwa, Cwb, Cfa, Csa, BWh, BSh, BWk, BSk, Dwb, Dfa, Dsa, and Dsb. A dominant hydro-meteorological re-source is responsible for 59% of annual rainfall in Pakistan due to monsoon rains (Farooqi et al. 2005).

Fig. 1.

Study area map of Pakistan showing distribution of population

Datasets

Daily Covid-19 data

Covid-19 accumulative data with the number of positive confirmed Covid cases (CCC), positive Covid death cases (CDC), positive Covid recovered cases (CRC), Covid active cases (CAC) from June 10, 2020, to August 31, 2021, along with Covid incident rate (CIR) and Covid case fatality ratio (CCFR) per province were collected from the Covid-19 Data Repository by the Center for System Science and Engineering (CSSE) at John Hopkins University GitHub website (https://github.com/CSSEGISandData/COVID-19). CCC got priority in accord with all provinces of Pakistan, and an increase in the CCC was observed throughout the provinces of Pakistan on the specified date.

Meteorological statistical data

Full meteorological statistical data (daily minimum temperature (MIN-T), daily mean temperature (MEAN-T), daily maximum temperature (MAX-T), daily surface temperature (DST), daily total evapotranspiration (EVP), daily specific humidity (SH), daily rainfall (R)) were obtained from Giovanni Earthdata (https://giovanni.gsfc.nasa.gov/giovanni/). Excel spreadsheets were made for the compilation of the Covid-19 data and meteorological parameters separately for every province. Eviews 10 software is used for the statistical processing of the data.

Methodology

P-value, F-test, F-value

To measure and judge the result of the model, probability (P-value) is utilized in the statistical analyses because P-value identifies the probability of having results that are nearly at the limit as well as the actual results, presuming that the null hypothesis is error-free. On the other hand, F-test is highly specialized in inspecting the group of the independent variable, in this case lntemp, lnevp, lnrain, lnhum (natural log of meteorological parameters through Eviews) are collectively significant or not. To check whether a regression model gives better-fitted data than a model having no independent variable, F-value got priority (Manzoor and Sharif 2021).

Unit root and breakpoint unit root tests

Generate series by equation used for the variables under the research which was essential for the processing (ln(variable) = log(variable)). Unit root and breakpoint unit root tests were conducted for all the variables. In the unit root test, the following methods were used for the test; augmented Dicky–Fuller (ADF) test type, intercept test equation, lag length of 17 with Schwarz Info Criterion (by default), and for level and 1st difference, respectively, for each variable. Same for the breakpoint unit root test, intercept test equation, same lag length (17 with Schwarz Info Criterion), break type of innovation outlier, breakpoint selection of Dicky–Fuller min-t, and for level and 1st difference, respectively, for each variable. The output generated by both unit root and breakpoint unit root gave the variables described as follows; t-statistics and probability for each variable individually.

For this study and the results to be achieved, the unit root test with level, and 1st difference was used alongside the long-run and bound test in accord with the error estimation/correction term (ECT) (Pesaran 2008). ECT plays a major role in the analysis of short- and long-term dynamics and the Coint Eq. (-1) is of specific interest (Liu et al. 2020).

While talking about the unit root test, its need in this research is for the arrangement of integration and indication of variables used in the research with the ability to examine the validity of the co-integration test and to sure that when the model run, it runs based on pre-requirements defined earlier. The outcomes of unit root test confirm that all the variables (lnccc, lnevp, lnhum, lnrain, and lntemp) are not stationary at level or at 1st difference which allows us to run the model.

Autoregressive distributed lag models (ARDL)

After the unit root test, the next work was the equation estimation with the ARDL. The ARDL model of co-integration developed by (Pesaran 2008) was used to observe the relationship between the Covid-confirmed cases and meteorological parameters. ARDL technique is vital as it has numerous benefits. One major and noticeable benefit is the long-run estimation of reliable and powerful deduction with a single well-defined equation (Mehmood et al. 2021). In particular, the ARDL model holds one of the key prerequisites for the analysis of time series known as variable stationarity (Mehmood et al. 2021). One can utilize the ARDl approach when all variables are stationary at I(0), I(1), or a mixture of I(0) and I(1) (Ibrahim & Law 2016; Meo et al. 2018). One limitation which is important to keep in mind is that none of the model variables should be stationary at I(2) (Meo et al. 2018). Results of the long-run test are presented in Table 10 of the results section.

Table 10.

Long-run estimated results

Province	Variable	Coefficient	t-statistic	Prob. value
AJAK	lnccc (−1)	− 0.063***	− 10.22	0.0000
	lnevp	0.021**	1.219	0.2234
	lnhum	− 0.046*	− 1.933	0.0539
	lnrain	0.0548*	1.915	0.0561
	lntemp	0.012***	5.683	0.0000
	ECT (−1)	− 0.0063***	− 18.685	0.0000
Balochistan	lnccc (−1)	− 0.0655***	− 7.314	0.0000
	lnevp	− 0.0730*	− 1.726	0.0852
	lnhum	0.0230**	2.389	0.0174
	lnrain	− 0.0239*	− 1.855	0.0644
	lntemp	0.0117***	7.198	0.0000
	ECT (−1)	− 0.0065***	− 14.63	0.0000
Gilgit Baltistan	lnccc (−1)	− 0.0609***	− 10.157	0.0000
	lnevp	0.0713	0.809	0.4190
	lnhum (−1)	0.0411***	3.739	0.0002
	lnrain	− 0.0150	− 0.950	0.3425
	lntemp	0.0155***	9.730	0.0000
	ECT (−1)	− 0.0060***	− 24.474	0.0000
Islamabad	lnccc (−1)	− 0.0628***	− 6.059	0.0000
	lnevp	0.0702	0.390	0.6966
	lnhum	− 0.0650*	− 1.937	0.0537
	lnrain	− 0.0539	− 1.643	0.1014
	lntemp	0.0774***	3.184	0.0016
	ECT (−1)	− 0.0062***	− 10.400	0.0000
Khyber Pakhtunkhwa	lnccc (−1)	− 0.055***	− 9.381	0.0000
	lnevp	0.056***	6.337	0.0000
	lnhum (−1)	− 0.099***	− 6.921	0.0000
	lnrain (−1)	0.0581***	2.989	0.0030
	lntemp	0.01545***	9.500	0.0000
	ECT (−1)	− 0.0055***	− 18.970	0.0000
Punjab	lnccc (−1)	− 0.0513***	− 7.456	0.0000
	lnevp	0.0257***	3.249	0.0013
	lnhum	− 0.0703***	− 5.012	0.0000
	lnrain (−1)	0.0532***	2.936	0.0035
	lntemp	0.0122***	6.699	0.0000
	ECT (−1)	− 0.00513***	− 15.892	0.0000
Sindh	lnccc (−1)	− 0.01186***	− 11.850	0.0000
	lnevp (−1)	− 0.04149***	− 6.077	0.0000
	lnhum (−1)	0.01310***	5.386	0.0000
	lnrain	− 0.0446	− 1.567	0.1182
	lntemp	0.0262***	11.538	0.0000
	ECT (−1)	− 0.0118***	− 17.081	0.0000

***, **, and * show the significance at 1%, 5%, and 10%, respectively

Dependent and independent variables

The dependent variable can be indicated as a level or as a first difference. Assuming that the first difference exhibits the dependent variable and if the right-hand side variable is the lagged level, the null hypothesis is that its boundary is zero. Consequently, the null manifests that the time-series variable has a unit root and the alternative is that the series is stationary. The equation can be estimated by OLS, but the test statistic (tau) prefers the non-standard likelihood distribution. Dickey and Fuller provide critical values for the test (Wang and Tomek 2007).

All variables were selected once and the following conditions were applied; no trend specification with 1 lag for both the dependent variable and regressors. In this test, two methods were used in the coefficient diagnostics which are named: error correction form, and long-run form/bounds test. Error correction form helped in the analysis of F-statistics in accord with the significance and value, while long-run and bound test gave the value coefficient, t-statistics, and the probability of all variables.

In mathematical terms,

$$\text{lnccc}=F\left(\text{lnevp};\text{lnhum};\text{lnrain};\text{lntemp}\right)$$ 1

ln is a natural logarithm and is used with the variables for the equation. lnccc is the number of confirmed Covid patients with ln scale. lnevp is evapotranspiration, lnhum is specific humidity, lnrain is rainfall and lntemp is the daily surface temperature (with ln scale). In this model, lnccc is a dependent variable, while lnevp, lnhum, lnrain, and lntemp are the independent variables (Qayyum et al. 2021).

Results and discussion

Below-mentioned tables show the CCC, CDC, CRC, CAC, CIR, CCFR cases, daily surface temperatures (min, max, mean), daily total evapotranspiration, daily specific humidity, daily rainfall in monthly format for each province and also for administrative territories, e.g., Gilgit Baltistan, Azad Jammu and Kashmir, and Islamabad from June 10, 2020, to August 31, 2021. By visualizing the tables, we can see the increasing trend in the confirmed Covid-19 cases over time while meteorological parameters changes in either increase or decrease trend.

Meanwhile, time series charts are supporting and backing the numbers in tables, as you can see the trend and relation between Covid-19 cases and the meteorological parameters. CCC can be identified by grey long bars, which are increasing throughout time and meteorological parameters are in line format with different colors.

Time series analysis

Azad Jammu and Kashmir

In Azad Jammu and Kashmir, CCC increased from 807 to 29,155. As confirmed cases increase, CDC also increased from 19.14 to 666.41. While these numbers increased abruptly, CRC also goes up thanks to quick medical facilities in various health departments.

While looking at the meteorological parameters, the minimum temperature touched the − 18.77 °C, as Azad Jammu and Kashmir are located in the north–east direction, adjacent to Gilgit Baltistan. The maximum temperature reached the value of 19.05 °C. Other parameters varied differently in different environments and seasonal conditions (Fig. 2).

Fig. 2.

CCC versus temperatures chart for Azad Jammu and Kashmir administered territory

Balochistan

CCC in Balochistan took an abrupt increase trend from 9122.86 to 31,549.52, which indicates the high number of cases. The number of CDC goes from 97.86 to 333.90 which was low as compared to recovered cases. CAC also decreased from June 2020 to January 2021, but then again increased from February 2021 to August 2021.

The minimum temperature was recorded at a value of 3.15 °C, and the maximum temperature was 40.27 °C. As located in the bottom part of Pakistan and mostly a mountainous cover area with adjacent to Afghanistan and Iran, temperatures revolved around high values, which may produce an impact on Covid-19 cases number (Fig. 3).

Fig. 3.

CCC versus temperatures chart for Balochistan province during June 2020–August 2021

Gilgit Baltistan

Gilgit Baltistan is part of the northern areas and while keeping this in mind, the minimum temperature touched the value of − 25.85 °C and the maximum temperature went to 12.23 °C. Death cases went from 20.10 to 162.87 and recovered cases reached 7350.25 from 868.29 (Fig. 4).

Fig. 4.

CCC versus temperatures chart for Gilgit Baltistan administered territory during June 2020–August 2021

Islamabad

Islamabad is suited in between the Khyber Pakhtunkhwa and Azad Jammu and Kashmir. It also touches the boundary with Punjab and is known as a well-developed area. The minimum temperature was around 4.81 °C, and the maximum temperature touched the 38.49 °C figure. Confirmed cases were already around the figure 10,187.95 in June 2020 and went to 94,069.81 in August 2021 (Fig. 5).

Fig. 5.

CCC versus temperatures chart for Islamabad administered territory during June 2020–August 2021

Khyber Pakhtunkhwa

Khyber Pakhtunkhwa also showed the highest number of CCC starting from 21,198 to 153,420. These numbers were alarming and it lead to serious death tolls from 792 to 4699. As active cases first decreased and then increased, consequences were done in the form of confirmed and dead cases (Fig. 6).

Fig. 6.

CCC versus temperatures chart for Khyber Pakhtunkhwa province during June 2020–August 2021

Punjab

Punjab province showed the second-highest cases as the population is enormous and increasing day by day. 374,500.84 cases were confirmed from June 2020 to August 2021 and that figure was not small. At the end of August, 11,431.52 death cases were reported. An important thing to notice was active cases which vary throughout the time as it decreased and increased randomly. The minimum temperature recorded was 4.35 °C in January 2021, and the maximum temperature was 39.80 °C in June 2021 (Fig. 7).

Fig. 7.

CCC versus temperatures chart for Punjab province during June 2020–August 2021

Sindh

While talking about the top on the chart, Sindh generated the highest numbers even higher than the Punjab province. Increasing from 65,262 to 411,959, confirmed cases in Sindh were quite alarming. Same as Punjab, active cases changed randomly and this allows the death cases and recovered cases side by side. The minimum temperature was 8.88 °C in January 2021, and the maximum was 41.26 °C in June 2020 (Fig. 8).

Fig. 8.

CCC versus temperatures chart for Sindh province during June 2020–August 2021

All tables contain so much information regarding Covid-19 in accord with meteorological parameters. While looking at tables of Punjab, Sindh, Kpk, and Balochistan, those specific tables show the highest numbers of Covid-19 cases from June 2020 to August 2021. Aside from the technical statistical results, common logical results can be made by visualizing these tables.

Punjab and Sindh have the highest population numbers in general if comparison made between the provinces on a population basis. Covid-19 spread fast in congested populated areas or regions thanks to person to person spreading technique of Covid-19. It is safe to assume and say that other provinces with less population got Covid-19 cases from high populated provinces as people from the less developed area or provinces prioritize doing business in more developed areas to earn well for their families. First, Covid-19 was imported into the high-density areas or provinces, i.e., Punjab, Sindh, etc., by the people who came from abroad with the symptoms of Covid-19, and then, it spread one too many with the person to person spreadability and the help of environmental conditions. People from other provinces were also affected by that and when they returned to their homeland, the virus spread there also.

Northern areas, especially Gilgit Baltistan and Azad Jammu & Kashmir, which plays a major role in tourism would face the highest cases also but thanks to local authorities they close the gates on time as following the lockdown procedures around the world, which leads to the least cases in GB and AJAK compared to other regions or provinces.

Aside from CCC, the relation between CDC/CAC/CIR/CCFR and meteorological parameters is also important to note in all provinces and results can be generated based on Tables 1, 2, 3, 4, 5, 6 and 7 (including ST), as they play a major role in finding the solutions regarding Covid and environmental parameters also aside from CCC. Although this research more focuses on the relation between CCC & meteorological parameters, we cannot simply ignore the other cases. Aside from CCC, there is one interesting case which is CAC. While focusing on CCC, CDC, CRC, and CIR, all increase with time, but CAC shows irregular behavior. Many assumptions and results can be generated by visualizing the CAC pattern compared with meteorological parameters or by general theories. An increase in the active cases may be due to (i: People failed to follow the lockdown procedures or did not take the cautions seriously (ii: Environmental conditions favor the spread of Covid at that particular time (iii: Resources were not enough or limited supplies available at that time in hospitals or care centers, etc.

Table 1.

Summary of Covid-19 cases and temperatures (Azad Jammu and Kashmir)

Date	CCC	CDC	CRC	MIN-T (C)	MAX-T (C)	MEAN-T (C)	DST (K)
2020-06-01	807.57	19.14	351.28	3.47	15.76	9.78	283.45
2020-07-01	1713.35	44.12	1103.16	5.75	17.71	11.83	285.76
2020-08-01	2188.67	58.96	1960.51	6.76	18.60	12.63	286.67
2020-09-01	2471.73	67.33	2237.4	2.60	14.66	8.28	282.50
2020-10-01	3386.09	81.61	2693.64	− 2.97	9.34	2.56	276.49
2020-11-01	5510.03	128.4	4141.23	− 11.02	0.95	− 5.27	268.89
2020-12-01	7770.35	197.48	6526.41	− 17.93	− 4.44	− 11.52	262.34
2021-01-01	8637	242.83	8079.29	− 18.77	− 4.37	− 11.91	261.36
2021-02-01	9561.71	281.96	8774.42	− 14.56	− 0.85	− 7.69	265.07
2021-03-01	11,332.6	326.41	10,059.4	− 11.31	2.01	− 4.29	269.10
2021-04-01	15,179.6	422.26	12,623.3	− 8.08	4.35	− 1.21	271.87
2021-05-01	18,312.8	515.74	16,003.7	− 0.28	10.45	5.36	277.44
2021-06-01	19,831.0	567	18,708.6	3.74	15.47	9.74	282.31
2021-07-01	21,947.4	601.16	19,982.7	6.78	19.05	13.04	286.48
2021-08-01	29,155.4	666.41	21,349.5	5.38	17.64	11.46	285.33

Table 2.

Summary of Covid-19 cases and temperatures (Balochistan)

Date	CCC	CDC	CRC	MIN-T (C)	MAX-T (C)	MEAN-T (C)	DST (K)
2020-06-01	9122.86	97.86	3378.05	24.11	40.09	32.21	306.19
2020-07-01	11,263.45	129.48	8047.03	25.50	39.49	32.48	305.91
2020-08-01	12,229.65	138.58	10,875.61	24.30	37.32	30.63	304.42
2020-09-01	13,990.43	144.70	12,697.90	18.86	34.49	26.37	300.87
2020-10-01	15,633.45	147.19	15,166.81	13.17	30.28	21.05	294.90
2020-11-01	16,493.37	157.73	15,904.10	9.31	24.35	16.13	289.68
2020-12-01	17,783.52	176.00	17,178.48	4.93	19.13	11.21	285.75
2021-01-01	18,546.06	189.81	18,087.97	3.15	19.03	10.03	284.25
2021-02-01	18,937.07	198.04	18,645.39	8.79	25.12	16.36	290.12
2021-03-01	19,276.26	202.81	18,907.42	13.40	30.18	21.56	295.47
2021-04-01	20,806.20	221.53	19,710.23	17.35	34.04	25.73	299.73
2021-05-01	23,936.52	260.26	22,461.32	21.52	37.05	29.49	303.09
2021-06-01	26,353.90	296.87	25,140.53	24.29	40.27	32.40	305.78
2021-07-01	28,724.77	319.06	27,283.97	25.75	39.29	32.45	306.21
2021-08-01	31,549.52	333.90	29,034.00	23.30	38.52	30.77	304.38

Table 3.

Summary of Covid-19 cases and temperatures (Gilgit Baltistan)

Date	CCC	CDC	CRC	MIN-T ( C)	MAX-T (C)	MEAN-T ( C)	DST (K)
2020-06-01	1258.95	20.10	868.29	− 3.26	7.42	2.33	274.54
2020-07-01	1774.74	39.29	1406.87	− 0.90	10.14	4.92	277.81
2020-08-01	2495.06	60.29	2101.71	0.31	12.23	6.36	279.89
2020-09-01	3327.13	78.30	2914.03	− 3.42	7.44	1.74	274.85
2020-10-01	4027.00	89.94	3700.97	− 9.20	0.52	− 4.75	267.41
2020-11-01	4462.67	93.83	4204.83	− 16.68	− 6.61	− 11.70	260.04
2020-12-01	4792.71	99.10	4581.97	− 24.00	− 12.51	− 18.42	253.56
2021-01-01	4887.84	101.42	4751.26	− 25.85	− 12.63	− 19.49	252.19
2021-02-01	4936.07	102.00	4811.68	− 21.15	− 8.58	− 14.79	256.90
2021-03-01	4973.19	102.77	4855.81	− 17.90	− 6.11	− 11.56	260.04
2021-04-01	5168.00	103.73	4964.27	− 14.40	− 3.74	− 8.47	262.60
2021-05-01	5440.45	107.00	5230.19	− 6.78	2.76	− 1.88	269.12
2021-06-01	5785.00	108.60	5537.33	− 3.56	6.67	1.80	273.38
2021-07-01	7223.65	118.61	6408.87	0.20	11.90	6.30	278.59
2021-08-01	9264.48	162.87	7350.25	− 1.14	10.41	4.68	277.14

Table 4.

Summary of Covid-19 cases and temperatures (Islamabad)

Date	CCC	CDC	CRC	MIN-T (C)	MAX-T ( C)	MEAN-T (C)	DST (K)
2020-06-01	10,187.95	98.33	4008.62	23.48	35.45	29.23	307.22
2020-07-01	14,264.06	152.45	10,995.4	24.48	34.04	29.40	305.90
2020-08-01	15,356.61	172.26	13,616.6	24.87	32.72	28.71	302.82
2020-09-01	16,051.93	178.60	15,438.77	21.83	32.41	26.64	301.33
2020-10-01	18,018.19	197.06	16,763.74	15.71	30.02	21.76	297.16
2020-11-01	24,741.37	263.47	20,652.10	9.71	21.76	14.81	289.88
2020-12-01	35,055.52	375.42	29,204.68	5.97	18.23	11.07	285.93
2021-01-01	39,876.55	452.06	37,507.35	4.81	18.11	10.63	285.08
2021-02-01	42,818.86	485.96	40,857.79	9.82	21.95	15.18	289.96
2021-03-01	50,018.74	532.29	44,715.32	11.93	24.85	17.85	293.22
2021-04-01	68,296.90	628.13	55,181.77	14.16	28.75	21.22	295.93
2021-05-01	79,101.29	728.42	69,540.74	20.43	35.52	28.05	301.87
2021-06-01	82,157.13	771.33	79,486.37	24.29	38.49	31.94	305.91
2021-07-01	84,601.48	787.55	81,858.48	25.53	36.24	31.06	305.26
2021-08-01	94,069.81	835.65	83,673.50	24.17	33.52	28.88	302.99

Table 5.

Summary of Covid-19 cases and temperatures (Khyber Pakhtunkhwa)

Date	CCC	CDC	CRC	MIN-T (K)	MAX-T (K)	MEAN-T (K)	DST (K)
2020-06-01	21,198.05	792.05	7584.00	287.68	301.36	294.86	297.60
2020-07-01	30,993.65	1109.00	22,327.29	289.37	302.60	296.22	297.95
2020-08-01	35,134.06	1233.74	32,031.16	289.93	302.43	296.10	297.19
2020-09-01	37,095.03	1256.93	35,161.23	285.31	298.60	291.69	293.69
2020-10-01	38,613.16	1265.97	36,836.81	279.70	293.95	286.24	287.99
2020-11-01	42,872.80	1314.80	39,349.27	273.00	285.74	278.79	280.56
2020-12-01	53,435.65	1505.94	47,689.94	268.47	280.93	274.00	276.08
2021-01-01	63,165.32	1780.39	58,154.48	267.73	281.83	273.97	275.44
2021-02-01	69,869.89	1999.82	65,620.64	272.63	286.08	279.01	280.15
2021-03-01	78,264.32	2189.39	71,548.94	275.29	288.78	281.92	283.36
2021-04-01	103,946.03	2817.73	88,518.73	277.87	292.50	285.48	286.46
2021-05-01	126,808.52	3766.68	114,931.90	284.54	298.14	291.69	292.27
2021-06-01	136,115.27	4229.20	128,765.37	288.08	302.78	295.92	296.79
2021-07-01	140,503.97	4384.26	133,999.52	290.69	303.82	297.48	298.38
2021-08-01	153,420.29	4699.10	136,572.50	288.74	301.84	295.31	296.80

Table 6.

Summary of Covid-19 cases and temperatures (Punjab)

Date	CCC	CDC	CRC	MIN-T (C)	MAX-T (C)	MEAN-T (C)	DST (K)
2020-06-01	63,329.76	1342.05	18,951.10	26.24	39.67	33.30	309.71
2020-07-01	87,655.45	2022.45	62,166.87	26.76	38.49	32.76	308.19
2020-08-01	95,178.00	2177.58	88,210.00	26.23	36.96	31.48	306.20
2020-09-01	98,071.37	2220.23	94,374.37	21.87	35.26	28.41	304.30
2020-10-01	101,578.52	2292.32	96,875.13	16.28	32.73	23.95	298.97
2020-11-01	111,237.83	2624.63	97,858.50	9.88	24.26	16.32	291.36
2020-12-01	129,526.19	3522.23	114,593.71	5.76	19.66	11.86	287.33
2021-01-01	149,012.29	4414.48	133,916.06	4.35	19.44	11.09	286.32
2021-02-01	164,716.64	5075.14	152,229.25	9.10	25.14	16.60	291.49
2021-03-01	192,687.35	5864.52	173,742.06	13.56	29.86	21.45	296.21
2021-04-01	264,011.07	7371.30	215,708.60	16.30	33.28	24.94	299.80
2021-05-01	325,911.13	9398.03	285,436.97	22.42	37.50	30.40	304.58
2021-06-01	344,111.40	10,522.67	322,135.93	26.12	39.80	33.40	307.68
2021-07-01	350,363.87	10,876.23	329,683.23	27.61	38.93	33.43	307.30
2021-08-01	374,500.84	11,431.52	333,728.50	25.88	38.07	31.98	306.23

Table 7.

Summary of Covid-19 cases and temperatures (Sindh)

Date	CCC	CDC	CRC	MIN-T (C)	MAX-T (C)	MEAN-T (C)	DST (K)
2020-06-01	65,262.24	1030.67	33,896.76	28.84	41.26	34.74	308.58
2020-07-01	107,510.42	1867.19	78,630.26	28.87	39.02	33.68	307.71
2020-08-01	125,647.77	2313.77	118,233.10	27.77	36.26	31.61	305.62
2020-09-01	132,946.13	2452.27	127,423.97	24.56	35.58	29.67	305.40
2020-10-01	141,516.61	2569.65	134,397.94	20.27	35.54	27.46	303.02
2020-11-01	157,721.03	2762.33	143,836.67	14.82	29.98	21.78	296.58
2020-12-01	198,076.81	3248.26	173,803.42	10.96	26.52	18.02	292.60
2021-01-01	232,966.16	3788.16	211,303.39	8.88	25.83	16.60	290.81
2021-02-01	253,630.50	4206.61	234,076.39	14.58	31.61	22.68	295.91
2021-03-01	261,973.55	4455.48	252,444.58	19.54	36.63	27.87	301.07
2021-04-01	272,547.10	4554.23	259,726.53	22.58	39.42	30.94	304.54
2021-05-01	300,680.94	4830.00	275,927.58	26.32	40.76	33.42	306.73
2021-06-01	329,337.60	5269.33	302,407.37	28.23	40.56	33.99	306.86
2021-07-01	355,729.94	5698.90	320,679.13	28.00	38.46	32.74	306.24
2021-08-01	411,959.03	6459.74	334,751.75	26.36	38.94	32.11	305.12

Autoregressive distributed lag models (ARDL)

Unit root and breakpoint unit root test

The findings of the unit root test presented in Tables 8 and 9 confirm that none of the variables are stationary at I(1) and I(2) and therefore long- and a short-term association between the proposed variables for the ARDL model can be used for further model tests. f-statistic values for all variables including dependent and independent variables for all provinces of Pakistan are more than the upper bound value which gives the green light and confirms that the long-run association between the parameters is sustainable. ADF technique was used and applied to inspect the integration sequence of variables used in the ARDL model.

Table 8.

Unit root test

Province	Variables	Unit root at level		Unit root at 1st difference
		t-statistic	Probability	t-statistic	Probability
AJAK	lnccc	− 1.038*	0.7406	− 2.896***	0.0466
	lnevp	− 1.553*	0.5058	− 28.338***	0.0000
	lnhum	− 2.085*	0.2507	− 18.406***	0.0000
	lnrain	− 8.631***	0.0000	− 11.706***	0.0000
	lntemp	− 1.159*	0.6932	− 15.256***	0.0000
Balochistan	lnccc	− 0.774*	0.8247	− 7.206***	0.0000
	lnevp	− 2.852**	0.0519	− 13.942***	0.0000
	lnhum	− 2.189*	0.2104	− 13.257***	0.0000
	lnrain	− 7.207***	0.0000	− 15.359***	0.0000
	lntemp	− 1.410*	0.5778	− 17.864***	0.0000
Gilgit Baltistan	lnccc	− 1.283*	0.6386	− 5.587***	0.0000
	lnevp	− 1.364*	0.6005	− 15.742***	0.0000
	lnhum	− 2.107*	0.2420	− 15.922***	0.0000
	lnrain	− 7.557***	0.0000	− 13.164***	0.0000
	lntemp	− 1.302*	0.6298	− 15.285***	0.0000
Islamabad	lnccc	− 0.819*	0.8122	− 3.095***	0.0276
	lnevp	− 2.520*	0.1112	− 21.850***	0.0000
	lnhum	− 2.374*	0.1497	− 12.974***	0.0000
	lnrain	− 9.083***	0.0000	− 7.593***	0.0000
	lntemp	− 1.368*	0.5982	− 12.912***	0.0000
Khyber Pakhtunkhwa	lnccc	− 0.134*	0.9435	− 8.767***	0.0000
	lnevp	− 1.742*	0.4091	− 20.505***	0.0000
	lnhum	− 2.448*	0.1292	− 12.582***	0.0000
	lnrain	− 6.837***	0.0000	− 13.645***	0.0000
	lntemp	− 1.369*	0.5977	− 14.561***	0.0000
Punjab	lnccc	0.156*	0.9695	− 13.257***	0.0000
	lnevp	− 2.102*	0.2440	− 15.969***	0.0000
	lnhum	− 2.375*	0.1495	− 15.204***	0.0000
	lnrain	− 6.808***	0.0000	− 11.505***	0.0000
	lntemp	− 1.710*	0.4253	− 17.060***	0.0000
Sindh	lnccc	− 0.346*	0.9150	− 4.489***	0.0002
	lnevp	− 2.762**	0.0645	− 13.952***	0.0000
	lnhum	− 1.339*	0.6121	− 13.323***	0.0000
	lnrain	− 7.063***	0.0000	− 12.413***	0.0000
	lntemp	− 1.569*	0.4976	− 16.794***	0.0000

***, **, and * show the significance at 1%, 5%, and 10%, respectively

Table 9.

Breakpoint unit root test

Province	Variables	Unit root with break at level		Unit root with break at 1st difference
		t-statistic	Probability	t-statistic	Probability
AJAK	lnccc	− 8.959***	0.01	− 21.118***	0.01
	lnevp	− 2.238*	0.9573	− 30.096***	0.01
	lnhum	− 2.810*	0.7826	− 19.259***	0.01
	lnrain	− 9.798***	0.01	− 23.270***	0.01
	lntemp	− 1.915*	0.9866	− 15.710***	0.01
Balochistan	lnccc	− 6.191***	0.01	− 29.895***	0.01
	lnevp	− 3.412*	0.4343	− 15.834***	0.01
	lnhum	− 3.241*	0.5404	− 14.009***	0.01
	lnrain	− 7.613***	0.01	− 18.719***	0.01
	lntemp	− 2.325*	0.9420	− 18.520***	0.01
Gilgit Baltistan	lnccc	− 11.139***	0.01	− 18.039***	0.01
	lnevp	− 2.796*	0.7891	− 23.420***	0.01
	lnhum	− 2.834*	0.7706	− 17.059***	0.01
	lnrain	− 8.815***	0.01	− 22.556***	0.01
	lntemp	− 2.066*	0.9780	− 15.749***	0.01
Islamabad	lnccc	− 7.454***	0.01	− 29.255***	0.01
	lnevp	− 3.053*	0.6543	− 23.874***	0.01
	lnhum	− 3.042*	0.6612	− 16.532***	0.01
	lnrain	− 9.682***	0.01	− 16.805***	0.01
	lntemp	− 2.422*	0.9214	− 18.614***	0.01
KPK	lnccc	− 6.399***	0.01	− 19.787***	0.01
	lnevp	− 2.491*	0.9051	− 22.881***	0.01
	lnhum	− 3.204*	0.5643	− 16.676***	0.01
	lnrain	− 11.783***	0.01	− 23.040***	0.01
	lntemp	− 2.166*	0.9669	− 15.070***	0.01
Punjab	lnccc	− 4.682***	0.0259	− 18.161***	0.01
	lnevp	− 2.656*	0.8477	− 17.607***	0.01
	lnhum	− 3.153*	0.5951	− 15.614***	0.01
	lnrain	− 10.357***	0.01	− 22.442***	0.01
	lntemp	− 2.427*	0.9201	− 17.465***	0.01
Sindh	lnccc	− 10.298***	0.01	− 23.011***	0.01
	lnevp	− 3.842*	0.2172	− 15.087***	0.01
	lnhum	− 3.052*	0.6549	− 15.122***	0.01
	lnrain	− 8.039***	0.01	− 16.379***	0.01
	lntemp	− 2.258*	0.9537	− 17.483***	0.01

***, **, and * show the significance at 1%, 5%, and 10%, respectively

Both Tables 8 and 9 show the outputs of the unit root test which represents the stability in the variables under research. If variables are stationary and probability is significant, variables are forward to the long-run test.

Long-run test

Long-run and bound test with ECT, among the dependent variable (lnccc) and independent variables (lnevp, lnhum, lnrain, lntemp) for all the provinces of Pakistan.

Table 10 is the most important, as it shows the association between Covid-19-confirmed cases and the meteorological parameters. The long-run association is established between the lnccc, and the meteorological parameters as shown in table. The coefficient for Coint Eq. (-1) are − 0.0063, − 0.0065, − 0.0060, − 0.0062, − 0.0055, − 0.00513, − 0.0118 from AJAK to SINDH for Covid-19-confirmed cases, respectively. In the ECM/ECT, the Coint Eq. (-1) is of specific interest. With the help of a long-run association test, significance is confirmed and points to the fact that association does exist among the dependent and independent parameters. The output shows that, in the long run, lnccc (Covid-confirmed cases) is statistically significant with the meteorological parameters (evapotranspiration, specific humidity, rainfall, and temperature) and influences the number of Covid-19 patients.

In Azad Jammu and Kashmir, evapotranspiration, rainfall, and temperature are positively associated, while humidity is negatively associated with Covid-19-confirmed cases. In Balochistan province, humidity and temperature are positively associated and evapotranspiration and rainfall are negatively associated with Covid-19-confirmed cases. In Gilgit Baltistan, except for the rainfall, which shows a negative association, all other parameters (temperature, evapotranspiration, humidity) show a positive association with the covid-19-confirmed cases. In Islamabad, evapotranspiration and temperature are positively associated, while humidity and rainfall are negatively associated with the Covid-19-confirmed cases. In Khyber Pakhtunkhwa, except for the humidity, all other parameters (temperature, evapotranspiration, rainfall) positively influenced the Covid-19-confirmed cases. The same results followed the Punjab province where (temperature, evapotranspiration, and rainfall) positively influenced the Covid-19-confirmed cases. In Sindh, temperature and humidity positively influenced the Covid-19-confirmed cases, while evapotranspiration and rainfall negatively influenced the Covid-19-confirmed cases.

Positive association means that a particular environmental parameter or parameters play a positive role in the increase/decrease confirmed cases of Covid-19, i.e., an increase/decrease in the value of meteorological parameters generate increase/decrease number of Covid-19-confirmed cases. Negative association means that increase/decrease in the value of meteorological parameters produce negligible effect on the Coivd-19-confirmed cases.

These long-run test results agree with the results generated by (Rehman et al. 2021), who found a significant association between temperatures and the Covid-19-confirmed cases in Islamabad, Pakistan. Another research by (Batool and Tian 2021) confirms the relationship between meteorological parameters and Covid-19 with results that agree with this research that meteorological parameters, especially temperature, plays a major role in an increase in Covid-19 cases. Another research on Pakistan focusing on the influences of meteorological parameters on Covid-19 spread by (Shahzadi et al. 2020) backs up this research findings where they find the relation. A case study by (Syed et al. 2021) is the situation of urban mortality in Pakistan due to Coid-19 also supports this research work by identifying the influences of temperature and rainfall on Covid-19 cases. Impact of climate on Covid-19 cases in Lahore by (Manzoor and Sharif 2021) made a model with Stepwise regression which assists the findings also. From the biological science view, research by (Uzair et al. 2022) supports this unique research work by finding the similarities between Covid-19 and meteorological parameters.

Discussion

There was (and still at the current time) a lot of discussion and questions arise at the time when Covid-19 was at its peak and was out of control, is there a relationship exist between environmental parameters and Covid-19? A lot of discussions have already been done on this but we are interested in the discussion which exists in the literature. Although the literature openly and strongly agrees with the “low temperature and low humidity light up the Covid spread”, the thing which is still missing is that what are the limits (High or Low) and what are the key factor that favors the Covid-19 quick spread information is still missing. All the findings related to Covid-19 origin and its nature were extracted from the laboratory experiments which we already discussed in the introduction part. The point which has so much weight is that the experiments which done in the laboratory were always performed under the “controlled situation and environment” where conditions were optimal throughout the entire process and no change introduced in that environment either from inside or outside except when needed. So keeping in mind this statement, those experiments still failed to answer those unique Covid cases in such areas where reverse situations present (reverse of low temperature and low humidity situations). But we cannot just underestimate the results from controlled environments, as they are the fundamental measurements against the Covid and problems always tend to generate new solutions.

Conclusion

This research aims to find the relationship between Covid-19 spread and meteorological parameters in Pakistan with the help of the time series analysis, unit root test, and the long-run bound test in accord with ECM/ECT. Moving forward from time series analysis, unit root, to long run, every step and analysis helps in the generation of the successful relationship between dependent and independent variables. For example, unit root helps in the integration order of the parameters and variables under research. Long-run test with ARDL was solely used for finding the association between dependent and independent variables. For the dependent variable, Covid-19-confirmed cases (lnccc) are used. For the independent variables, evapotranspiration, specific humidity, rainfall, and daily surface temperature (lnevp, lnhum, lnrain, lntemp), respectively. Positive and negative impacts between the meteorological parameters and Covid-19 with the help of ARDL long-run test in Eviews software. In all provinces, temperature showed a positive association with the Covid-19-confirmed cases. Evapotranspiration and rainfall influence positively, while specific humidity influences negatively Covid-19-confirmed cases in Azad Jammu Kashmir, Khyber Pakhtunkhwa, and Punjab. Specific humidity influences positively, while evapotranspiration and rainfall influence negatively the Covid-19-confirmed cases in Sindh and Balochistan. Evapotranspiration and specific humidity influence positively, while rainfall influences negatively the Covid-19-confirmed cases in Gilgit Baltistan. Evapotranspiration influences positively, while specific humidity and rainfall influence negatively the Covid-19-confirmed cases in Islamabad.

For future research, more work can be done and models can be generated with the help of other Covid variables like Covid death cases, recovered Covid cases, active Covid cases, etc. Secondly, the limited daily testing magnitude may also govern the number of Covid-19-confirmed cases.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

Zia ul-Haq conceptualized the work and wrote the manuscript, Usman Mehmood conducted the analysis, Salman Tariq wrote the manuscript, Anas Hanif conducted the analysis and wrote the manuscript, and Hasan Nawaz wrote the manuscript.

Funding

Not applicable.

Declarations

Conflict of interest

The authors declare no competing interests.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.

Consent to participate

All authors participate in this research.

Consent for publication

Not applicable.