Introduction

Coronavirus (SARS-COV-2)-related viral pneumonia with an unidentified agent was reported in Wuhan, China, toward the end of December 2019 (Comito and Pizzuti 2022). As a result of the virus’ rapid global spread and border crossings, 196 countries were afflicted on March 25, 2020. (Lu et al. 2020). The virus is an organ of the coronavirus family of the order Nidovirales and is a giant single-stranded RNA virus (Wang et al. 2010). The United Nations has explained COVID-19 as a leading social, human, and economic catastrophe that affects even developed countries; continuing the outbreak of this pandemic will cause problems for the global health community system, which will result in a population crisis of the world (Mollalo et al. 2020; Wu et al. 2020). The outbreak and intensity of an infectious disease epidemic significantly depend on the “infectious power of the disease” (Bailey and Gatrell 2015; Kandwal et al. 2009). In order to assess the risk of COVID-19 and identify areas that are now at high risk, all necessary information should be immediately available.

More than 185 countries being affected shows how quickly the coronavirus is spreading, necessitating cutting-edge technologies to evaluate the danger in particular areas. The spatial investigation of this pandemic virus can significantly benefit from using geographic information systems (GIS) (Zhou et al. 2020). One of the primary uses of epidemiology is to make it easier to identify areas and groups of people in danger and to offer the best medical and social options for reducing risk factors in such areas (Zhou et al. 2020). For 150 years, medical professionals have used maps for spatial disease analysis (WHO 2020). Anatomical epidemiology’s study of the regional distribution of infection and mortality includes geographic epidemiology (Gatto et al. 2020). Data visualization and representation as geographic maps are the first stage of analyzing geographical data (Kandwal et al. 2009). For years, GIS has extensively been modeling different diseases, businesses, the environment, and natural resources (WHO 2011). The administrators of this industry must be proficient in GIS because of the healthcare service centers’ extensive geographic reach and high activity levels. GIS’s geospatial analysis capabilities directly benefit modeling diseases’ spatial distribution and their relationships with environmental characteristics and the healthcare system. Currently, GIS technology is thought to be crucial in infectious disease study and control (Kistemann et al. 2015).

Understanding the Spatiotemporal dynamics of the prime wave of the diseases and analyzing the results of inhibitory measures have received much attention in the inquiry since Covid-19 was first reported in January 2020. In epidemiology, standard analytical and numerical models were used. For instance, Leung et al. (2020) assessed the COVID-19 immediate reproduction number and confirmed case-fatality danger in central Chinese urban and provinces, which used a Sensitive-Infectious-Recovered (SIR) model to assess the potential effects of measures following the prime wave of infection. Fanelli and Piazza’s (2020) SIR was employed to undertake a comparative analysis in China, Italy, and France. Both Danon et al. (2020) and Peixoto et al. (2020) used population models to dissect and forecast the illness extension among England and Wales, as well as the Brazilian states of So Paulo and Rio de Janeiro in the meantime, spatial statistical models were used to analyze the illness space-time dynamics. Guliyev (2020), for instance, used a spatial panel data model to study the subject of transmission dissemination in China, discovering spatial effects such as the dispensation of confirmed fatalities and recovery. To dissection and forecast the space-time dispersion of the illness in Italy, Giuliani et al. (2020) made an endemic–epidemic multivariate time-series mixed-effects GLM for regional counts of COVID-19 confirmed.

Rahnama and Bazargan (2020) used descriptive-analytical techniques and spatial distribution modeling to investigate the spatiotemporal patterns of the COVID-19 epidemic in Iran. Their research findings revealed that the most critical geographic parameter for the COVID-19 distribution in Iran is the distance between and the vicinity of the provinces affected by the disease, which follows the pattern of the spatial distribution of adaptation. The regional distribution of COVID-19 and its fluctuation throughout the United States were modeled by Abolfazl et al. in 2020. They investigated the virus’s spread using GWR and multi-geographically weighted regression (MGWR). According to the findings of their study, GWR performs reasonably well in the spatial analysis of COVID-19 prevalence compared to the MGWR model. Pourghasemi et al. (2020) examined the COVID-19 outbreak risk indicators to pinpoint areas in Iran’s Fars region that were highly vulnerable to infection and gauge infection patterns there.

For this reason, a GIS-based machine learning system was used to evaluate the danger of a coronavirus outbreak in the province of Fars. Coronavirus infection impacts tourism and pilgrimage provinces such as Mazandaran and Qom. Qom is a pilgrimage province with many places of pilgrimage. In contrast, Mazandaran province has tourist attractions that cause heavy human traffic, contributing to a higher rate of spread in urban areas. It has been shown that citizens migrate to these provinces from different parts of Iran, which has caused the spread of the disease to dense urban areas in Iran (Patel et al. 2019). Jia et al. (2021) presented a dynamic model to describe coronavirus transmission by analyzing the relationship between virus spread and air quality conditions. They concluded that the air quality index is the most important climatic factor in virus diffusion.

Ibrahim (2020) looked at the volume and density of the risk of coronavirus pollution in Makkah, Saudi Arabia, using the GWR model. According to the findings of this study, the correlation between coronavirus pollution size and pollution density was positive, with a coefficient of 0.96. The relationship between the spatial dispersion of COVID-19 and population migration was investigated using a Bayesian spatiotemporal model during the early stage of the outbreak in Wuhan, China (Chen et al. 2020). Their investigation revealed that the Bayesian spatiotemporal model could be beneficial for rapid warning distribution and preventing the future dispersion of the virus.

Geographically weighted regression (GWR), ordinary least squares (OLS), and spatial autocorrelation (Moran’s) modeling methods are some of the most widely used in various fields of research. The spatial distribution of the PM2.5 was modeled using GWR in china’s cities, and the findings of this research revealed the proper functionality of this modeling approach (Gu et al. 2021). The GWR and OLS were employed in central java, Indonesia, to evaluate the impact of the human development index and population size on poverty. This study’s outcomes reported good performance of these models (Mahara and Fauzan 2021). The OLS and GWR methods are used to assess the influences of geographical parameters on forming land surface temperature (Kashki et al. 2021). The results from this research exposed feasible functionalities of this modeling approach’s spatial distribution of land surface temperature. Explanatory of Urban Expansion was assessed in Kolkata city using the geographically weighted regression (GWR) technique; the outputs of this study exposed the practical applicability of GWR in urban planning and management (Mondal et al. 2015). In order to investigate the effects of urbanization and landscape patents, habitat quality (Zhu et al. 2020) employed OLS and GWR models. According to the results of this study, rapid urbanization has a significant and negative influence on habitat quality within the study area. Jiao et al. (2021) used GWR and OLS models to research the disparities in COVID-19 infections’ temporally varying demographics and economic conditions, and their findings indicated the significance of the demographic and economic disparities. El Deeb (2021) used spatial autocorrelation (Moran’s I) to determine the dynamic and mean center for the COVID-19 pandemic in Lebanon. The results of this investigation revealed the adoptable functionality of spatial autocorrelation in disease modeling. To evaluate the spatial distribution and relationship neighboring the regions in terms of the COVID-19 outbreak, Amaliah et al. (2021) used Moran’s I Index. Considering the results of this research, a spatial autocorrelation of the confirmed cases is detected.

Following the rapid outbreak of COVID-19, public places and events, including schools and universities, movie theaters, concerts, theater shows, and national sports leagues, were closed, and office hours were decreased. Body temperature screening stations began operating at the entrance of different places. The “Stay at Home” campaign was implemented nationwide, asking people not to leave their homes to break the coronavirus transmission chain between the country’s provinces and reduce social mobilization. Consequently, after a while, the government implemented the “social distancing” plan with increased active cases. Following the implementation of social distancing, the confirmed cases and mortality of coronavirus in the provinces of Qom and Mazandaran decreased. Today, the study of the distribution and pandemic diseases using modeling techniques is globally considered essential to discover the sources and conditions causing the spread of the disease in any geographical location. Since 1993, the World Health Organization (WHO) has initiated applying GIS and modeling approaches to create disease maps. This paper intends to compare the spatiotemporal distribution of COVID-19 pandemic outbreaks utilizing the GWR model and the outcomes with the OLS model from February 24, 2020, to late October 2021, in Mazandaran and Qom provinces in Iran. This study aims to investigate the spatiotemporal distribution of COVID-19 based on three indicators (confirmed cases, deaths, and recovered) utilizing GWR and least-square models in Qom and Mazandaran provinces of Iran, from February 3, 2020, to late October 2021. Spatial autocorrelation (Global Moran’s I) was used to analyze the three indicators (confirmed cases, deaths, and recovered cases).

Area of ​​study

The study area comprises two provinces of Iran (Qom and Mazandaran). Qom province is situated between the latitudes of 34° 9″ and 35° 15″ N and between the longitudes of 50° 6″ and 51° 58″ E, sharing borders with Tehran Province to the north, Semnan Province to the east, Isfahan Province to the south and Markazi Province to the west. It has an area of 11,238 km2 in the central corridor of Iran and has a population of 1.06 million (Fig. 1). Mazandaran province is located in northern Iran along the coast of the Caspian Sea, between the latitudes of 35° 45′ 49′′, 36° 57′ 42″ N, and longitudes 50° 21′ 5″, 54° 7′ 55″ of E. Mazandaran province shares borders with Tehran and Qazvin in the south, Semnan to the southeast, Gilan to the west, Golestan province to the east and with Caspian Sea to the North (Fig. 1). According to the 2016 census, Mazandaran has a population of 3,283,577 (Statistical yearbook of Mazandaran Province, 2016).

Fig. 1
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Location of the study area. Provinces of Iran (A), Mazandaran province (B), and Qom province (C)

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Materials and methods

This study is based on secondary data, precisely information on confirmed deaths retrieved from hospitals and the National Institute of Health website for the provinces of Qom and Mazandaran between March 2, 2019, and November 30, 2021. The ALOS PALSAR digital terrain model (DTM) was acquired from (https://search.asf.alaska.edu). To assess the impact of elevation on the COVID-19 pandemic outbreak. The monthly average data for two chosen Iranian provinces were divided into three indicators using the Excel program (Tables 1 and 2).

Table 1 Monthly average of COVID-19 pandemic indicators in Mazandaran province by percentage
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Table 2 Monthly average of COVID-19 pandemic indicators in Qom province by percentage
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Following that, in the ArcGIS 10.8.1 environment, statistical models of GWR, OLS, and spatial autocorrelation (Moran I) were employed to examine the spatiotemporal distribution of three indicators: confirmed cases, deaths, and recovered. Three indicators, confirmed cases, deaths, and recovered, were added to the research area’s shapefile to implement the GWR and OLS models. The ArcGIS 10.8.1 spatial modeling module was used to develop the GWR and OLS statistical models. The shapefile of the research areas was chosen as the input for these models, and three indicators of confirmed cases, deaths, and recovered causes, were introduced to the GWR and OLS models. The spatial data for three indicators, confirmed cases, deaths, recovered cases, and a digital elevation model of the provinces of Qom and Mazandaran, are provided in (Fig. 2).

The three indicators were interpolated using the inverse distance weighting (IDW) approach to apply the GWR and OLS models. The interpolated COVID-19 pandemic indicators and digital elevation models were converted into feature polygons to suit the model implementation. An intersection overlay was employed to overlay the elevation maps and create polygons. An intersection overlay was employed to overlay the elevation maps and created polygons. Higher elevation areas received higher values after the weights were added to the attribute tables.

Fig. 2
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Spatial data points for three indicators and digital elevation model, a Mazandaran province, b Qom province

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Fig. 3
figure 3

Workflow of the methodology

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Geographically weighted regression (GWR model)

Brunsdon et al. (1996) introduced the concept of geographically weighted regression (GWR) to the geography literature to investigate the possibility of correlations in a regression model being spatially variable, or what is known as parametric nonstationarity. GWR is based on the locally weighted regression method, established in statistics for curve-fitting and smoothing applications. The novel aspect of GWR uses a subset of data close to the model calibration point in geographic space instead of variable space. GWR is based on the non-parametric locally weighted regression approach created in statistics for curve-fitting and smoothing applications, where local regression parameters are calculated using subsets of data close to a model estimation point in variable space (Gilbert and Chakraborty 2010). The novel aspect of GWR uses a subset of data close to the model calibration point in geographic space instead of variable space (Fotheringham et al. 2002; Wang et al. 2010). GWR has been proposed as a technique to perform inference on spatially changing connections to extend the initial focus on prediction to confirmatory analysis, while the emphasis in conventional locally weighted regression in statistics has been on curve-fitting, that is, estimating or predicting the response variable (Páez and Wheeler 2009).

Although the model calibration sites are not limited to observation locations, any observation location in the dataset may have a regression model fitted using GWR. The weights that indicate the geographical dependency between observations are calculated using the inter-point distances, which are obtained from the spatial coordinates of the data points—either individual data points or areal centroids—and then entered into a kernel function. Geographically weighted regression forms separate equations with the participation of independent and dependent variables placed inside a “distance” bar of each phenomenon and also allows parameter values to change continuously in geographic space. Equation 1 shows the GWR model (Hu et al. 2012):

$$Y_{i} = \beta _{{i0}} + \sum\limits_{1}^{P} {\beta _{{ik}} } x_{{ik}} + \varepsilon _{i}$$
(1)

where βik and xik are the factors and observed values of the independent variable k (k = 1,…,p) for observation i; εi is the error term for observation i.

Ordinary least squares (OLS)

One of the most famous regression analysis techniques involving identifying mechanisms operating within the real estate market is the ordinary least squares (OLS) approach (Hutcheson et al. 2019). The relationship between the dependent and independent variables can be defined by a simple straight line for which the values of y (price) are estimated by the values of x, according to the essential theoretical assumptions of the primary linear modeling method known as OLS (attributes). The predicted model must have the smallest possible sum of squares of estimated parameter errors (Deilami et al. 2016; Li et al. 2017). The fundamental issue with standard statistical analysis techniques, such as the OLS methodology, is that they typically seek to define common correlations between the variables being studied across diverse contexts (Cao et al. 2019). Through Eq. 2, the global regression model can be demonstrated:

$$Y = \beta _{0} + \sum\limits_{{j = 1}}^{p} {\beta _{j} } x_{j} + \varepsilon$$
(2)

where Y is the dependent variable, β0 is the model’s intercept, Xj corresponds to the jth explanatory variable of the model (j = 1 to p), and ε is the random error.

Inverse distance weighting (IDW)

Inverse distance weight (IDW), a popular interpolation technique, considers that each input point has a local influence that decreases as the distance increases. The points physically closer to the processing cell are given more weight than those farther away. The output value of each location can be calculated for an analysis using IDW using either a predetermined number of points or all points inside a predetermined radius. This method’s application is predicated on the idea that a variable’s influence reduces as it is moved away from the spot where it was sampled (Gong et al. 2014).

The IDW technique is a moving average interpolator typically used with highly variable data. It is feasible to go back to the data collection location and record a new value for some data types that are statistically distinct from the original reading but falls within the region’s overall trend. The interpolated surface is less than the maximum local value and more than the local minimum value, as determined by a moving average estimation method (Rocha et al. 2018). Through the use of Eq. 3, the inverse distance weighting algorithm is determined:

$$Z_{0} = \frac{{\sum\nolimits_{{i = 1}}^{N} {z_{i} } d_{i}^{{ - n}} }}{{\sum\nolimits_{{i = 1}}^{N} {d_{i}^{{ - n}} } }}$$
(3)

where \({{Z}}_{0}\) is the variable estimation value, \({{z}}_{i}\) is the sample value at point \({i}\), \({d}_{\text{i} \text{i}\text{s} }\) the distance of the sample point to the estimated point, and \(n\) is the coefficient that determines the weight based on the distance (Childs 2004).

Spatial autocorrelation (Global Moran’s I)

The qualities and locations of the spatial features are addressed in the assessment of spatial autocorrelation, which considers the correlation of a variable concerning its spatial location (Goodchild 1986). A typical test statistic for spatial autocorrelation is Moran’s I. When the values are distributed randomly in space, solid spatial autocorrelation occurs even though there should not be any correlation between the values. The correlation between the same values and variables in several locations is indicated by spatial autocorrelation (Global Moran’s I analysis) (Lee 2011).

Moran’s I value will range between 1 and 1. A larger positive Moran’s I suggest that values in nearby places tend to cluster, whereas a lower negative Moran’s I suggests that high and low values are interspersed. There is no geographic autocorrelation when Moran’s I is close to zero, indicating that the data are dispersed randomly (Overmars et al. 2003; Getis 2007). Equation 4 calculates it for n observations on a variable at locations I and j:

$$I = \frac{N}{W}\frac{{\sum _{i} \sum _{j} wij(x_{i} - \mathop x\limits^{ - } )(x_{j} - \mathop x\limits^{ - } )}}{{\sum _{i} (x_{i} - \mathop x\limits^{ - } )^{2} }}$$
(4)

where N is the numeral of spatial one indicator by i and j; x is the variable of the connector; x is the mean of x; wij is the spatial weights matrix, and W is the sum of all.

Results

Twenty-eight confirmed cases of COVID-19 pandemic were announced on February 24, 2020, in four Provinces of Iran (Tehran, Isfahan, Markazi, and Alborz), and the confirmed cases for Qom and Mazandaran were 56.25% and 32.58% of total cases, respectively. The number of confirmed cases, recovered, and death increased from February 24, 2020, to October 2021. After Tehran, the highest number of confirmed cases infected with the COVID-19 pandemic are in Mazandaran and Qom provinces. The trend of the COVID-19 pandemic for these two Provinces (confirmed cases, recovered, and deaths) is presented in Figs. 4 and 5. The rate of confirmed cases for Qom province between February 24, 2020, and late October 2021 was 44.25%. While the rate of deaths in this province was 4.34%, the maximum spatial distribution of death cases was shown in the northwestern parts of this province.

Fig. 4
figure 4

Average of three indicators of the COVID-19 pandemic in Qom province

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Fig. 5
figure 5

Average three indicators of the COVID-19 pandemic in Mazandaran province

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Spatiotemporal outbreak of COVID-19 pandemic in Qom province, the GWR model

Due to pilgrimage and tourism trips to Qom province, the first case was confirmed. After February 24, 2020, the spread of the COVID-19 pandemic increased and reached more than 1000 confirmed cases in a day. Investigations from the GWR model showed that the spatial distribution of COVID − 19 is spreading in surrounding provinces increasingly via Qom, Tehran, Mazandaran, and Markazi Provinces. Consequently, the percentage of confirmed cases in Qom province is 44.25%. Most of the affected population was distributed in the southern parts of Qom province, including Nofel Loshato, Qom, and Salafchegan. Due to pilgrimage and tourism trips to Qom province, the death rate reached 4.08%. By the GWR model, most of the death cases were distributed in the northwestern and southern parts of Jafarabad, Khalajastan, and Loshato. From February 24, 2020, to late October 2021, the rate of recovered cases was 61.07%, and based on the GWR model, most of these cases are scattered in the central parts of Qom province. According to the OLS model, this province’s death cases are mainly dispersed in the southwest and southern regions, the southeast, and small portions of the northwest and northeast. The OLS model’s findings indicate that most recovered cases are dispersed throughout this province’s northern and northwestern regions and southern cities such as Nofel Loshato, Salafchegan, and Jafarabad. Observance of health protocols, quarantine, and the closing of pilgrimage and tourism centers by the country’s Health and Medical Education Organization can be the main reason for increased recovered cases. The spatiotemporal distribution of (confirmed cases, recovered, and deaths) in Qom province utilizing GWR and OLS models are presented in Fig. 6. Using the GWR model as a visual technique can reveal interesting patterns in geographic data. The spatial distribution of confirmed cases, deaths, and recovered patients in Qom province (explanatory variable) shows a strong relationship between the indicators in some provinces. The coefficient of determination (\({R}^{2}\)), which expresses how accurate and good the model is, is one of the important parameters. This parameter is closer to 1 than other important parameters. It means that the explanatory variable can explain the changes well. This investigation exposed feasible functionalities of the GWR model in modeling the spatiotemporal distribution of the COVID-19 pandemic; according to this modeling technic, the spatial scattering of the indicators is well estimated in Qom province. Table 3 presents the results obtained from the GWR model.

Fig. 6
figure 6

Spatiotemporal distribution of COVID-19 pandemic utilizing GWR (a, b, c) and OLS (d, e, f) model

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Table 3 The GWR model for indicators (confirmed cases, recovered, and death) in Qom province
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In Qom province, the rate of confirmed cases and deaths are inversely related to elevation; with the increase in altitude, a considerable reduction of these two indicators can be seen. However, the rate of recovered cases in the elevated area of this province increased significantly. Qom city, which has the lowest elevation across the Qom province (726 m), had an upward trend of deaths and confirmed cases in the whole province, while the cities of Nofel, Loshato, Salafchegan, Khalajistan, and Jafarabad, with a maximum elevation of 3200 m, exposed the lowest dispersion rate across the province. The results of the GWR model show that between February 24, 2020, and October 20, 2021, a Moran’s I coefficient of 0.008821, a Z-Score of 2.230280, an expectation index value of − 0.001136, and a P value of 0.025729 were obtained. The pattern of spatial distribution (confirmed cases, recovered and death) is based on clustered spatial autocorrelation of (Moran’s I), in Qom province and implies the high quantity of confirmed cases, deaths, and recovered, corresponding to the GWR model, confirmed cases, recovered, and deaths are dispersed in the southern, northwestern, and central parts of the province. However, the result of the spatial distribution of the COVID-19 pandemic obtained by employing the OLS model proved the (Moran’s I) with a coefficient of 0.014834, an expectation index of 0.000871, Z-score of 3.675040 and a P value of 0.000238. Accordingly, its spatial distribution pattern is dispersed in clusters throughout the Qom province. The northern and northwestern regions of Qom are where these three COVID-19 pandemic indicators are dispersed. Spatial distribution (confirmed cases, recovered, and deaths) based on spatial autocorrelation model utilizing GWR and OLS models are presented in Fig. 7.

Fig. 7
figure 7

Spatial distribution of (confirmed cases, deaths, and recovered) cases obtained using a GWR and b OLS model

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Spatiotemporal outbreak of COVID-19 pandemic in Mazandaran province, the OLS model

Mazandaran province is considered another province in Iran struggling with the COVID-19 pandemic and experiencing a rapid outbreak. Being the destination for the tourists of neighboring provinces is the main reason to intensify the COVID-19 pandemic outburst in this province. Figure 7 illustrates the spatiotemporal dispersion of COVID-19 pandemics in Mazandaran province applying GWR and OLS models from February 24, 2020, to October 2021.

GWR model showed that the spatial disperse of the COVID-19 pandemic from the provinces of Tehran, Qom, Gilan, Markazi, Mazandaran, and Isfahan to the adjacent regions initiated a rapid outbreak on February 24, 2020. Further spatial spread of the COVID-19 pandemic was revealed in northern, central, and northwestern regions, and the lowest incidence of the dissemination is visible in the eastern and southeastern regions of the country.

According to the outputs of the GWR model distribution of confirmed cases in Mazandaran province on February 24, 2020, was observed regularly in Ramsar, Nowshera, the southern parts of Sari, and parts of northern Babol cities. The GWR model revealed the impact of tourist trips on the geographical dispersion of confirmed cases and the increased number of deaths in Mazandaran province. The death cases were spatially distributed mainly in the south and northern parts of Mazandaran province, including cities (Ramsar, Tonekabon, Kelardasht, Chalous, Noor, and Amol). The number of deaths in this province for February 24, 2020, to October 2021 reached 61.2%. As a result of the national COVID-19 pandemic headquarters policies, for instance, the implementation of screening, increasing the capacity of hospitals, providing accurate information about the spatial distribution of COVID-19 pandemic in Mazandaran province, and offering assistance to reduce the number of death cases, and increased recovered cases to 57.34% in north, south, and northeast parts of Mazandaran.

The rate of the spatial distribution of (confirmed cases, recovered and deaths) cases obtained by the OLS model from February 24, 2020, to October 21, 2021, is highly different from the results achieved by employing the GWR model. The result acquired utilizing the OLS model exposed confirmed cases further distributed in the central parts of Mazandaran. This dispersion caused a high number of death cases in the central parts of this province. The OLS model output indicated that, from February 24, 2020, to October 21, 2021, the cases were habitually scattered in the central parts and a small portion of the southern parts of the province. Using sanitizer and masks is considered the main factor of increment in the spatial distribution of recovered cases and potentially reduced the number of death cases in these parts of the province. Based on the OLS model, the spatial distribution of the COVID-19 pandemic needs to be better estimated. It shows that the OLS model cannot explain the COVID-19 pandemic spatial distribution epidemic in Mazandaran province. The \({R}^{2}\) rate for confirmed cases recovered and death is 0.72%. The outputs of the GWR model for the spatial distribution of the COVID-19 pandemic in Mazandaran are presented in Table 4 (Fig. 8). 

Fig. 8
figure 8

Spatiotemporal distribution of COVID-19 pandemic utilizing GWR (a, b, c) and OLS (d, e, f) model

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Table 4 Results obtained from the GWR model for indicators (confirmed cases, deaths, and recovered) in Mazandaran province
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In Table 4, residual of squares, the difference between the observed value and predicted value of the Y were acquired using the geographically weighted regression model. Relative performance measurement indicates the gamut to which the use of a statistical model causes loss of information. The threshold is the square root of the sum of the residual squares calculated for the residues. Standard deviation and low values are preferred. Coefficient of determination, how independent variables explain the viability of dependent variables. The adjusted coefficient of determination presents the measurement of the model’s predictive accuracy in Table 4.

In this paper, the digital elevation model (DEM) is used to determine the effects of elevation on the spatial distribution of the COVID-19 pandemic within the specified study area. In Mazandaran Province, Chalous, Savadkooh, Ramsar, Sari, and Neka have a maximum altitude of 5599 m, and the density of the two indicators (confirmed cases and deaths) were low. The rate of recovered cases was more significant than in the cities with lower elevations. The results show that from February 24, 2020, to late October 2021, the spatiotemporal autocorrelation of the COVID-19 pandemic based on spatial autocorrelation, with a (Moran’s I) coefficient of 0.482419, an expected index value of − 0.001653, a Z-score of 106.107828, and the P value was 0%. According t this pattern, the spatial distribution of indicators (confirmed cases, deaths, and recovered) achieved by employing GWR in Mazandaran province are random. Based on the GWR model, these dispersions are primarily dispersed in this province’s eastern and southeastern parts. While the spatial autocorrelation attained using the OLS model exposed a (Moran’s I) coefficient equal to 0.215666, an expected index value of −  0.001770, a value of Z-score equal to 14.314292 and a P value equal to 0%. Corresponding to this model, the spatial dispersion of the patterns is a cluster-based distribution, which is observed primarily in the focus and southern parts of this province. The spatial distribution of (confirmed, death, and recovered) cases of the COVID-19 pandemic according to spatial autocorrelation patterns utilizing GWR and OLS is demonstrated in Fig. 9.

Fig. 9
figure 9

Spatial distribution of (confirmed, deaths, and recovered) cases obtained using a GWR and b OLS model

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Discussion

Overall, our research results show the exponential growth of mortality in the central regions of Qom and Mazandaran and the quick dispersion of this virus compared to other regions. Other studies have also been performed about two widespread diseases and COVID-19, and the bulk showed an affirmative relationship between patients with COVID-19 and other diseases, such as blood pressure, diabetes, and cardiovascular diseases (Guan et al. 2020; Li et al. 2020). An analysis of COVID-19 and the number of deaths using modeling tools was shown in prior research to involve a wide range of socioeconomic and environmental parameters (Smith and Mennis 2020). In addition, Giuliani et al. (2020) also modeled the spatiotemporal dynamics of outbreaks and mortality due to COVID-19 at the provincial level in Italy. The local pandemic was more diverse than it was in Italy. Although it had a solid northward bias, it was slowly making its way into the southern provinces. The spatial distribution of the COVID-19 pandemic with the GWR model revealed the highest rate of deaths in the northwestern and southern parts of Jafarabad and Khalajistan cities and the city of Nofel Loshato during February 24, 2020, to late October 2021. During these 8 months, Qom province’s recovery rate reached 61.6%. Most of these cases were observed in the central parts of this province based on the GWR model (Fig. 3). The results are similar to the results of research conducted by (Xu et al. 2022) to evaluate influencing factors of self-reported COVID-19 dispersion using GWR and OLS models in Wuhan, China. Xu et al. (2022) stated the feasible functionalities of OLS and GWR models in the spatiotemporal modeling of pandemic disease. However, the OLS model exposed a different spatial distribution of the COVID-19 pandemic. In addition, the results of research conducted in order to study the propagation of the virus, Abolfazl et al. (2020) used GWR and multi-geographical weighted regression (MGWR) to predict the prevalence of (COVID-19) geographically as well as its variability across the United States. Compared to the MGWR model, findings of this study showed that GWR performed relatively well in the spatial analysis of COVID-19 prevalence. According to the OLS model, confirmed cases in Qom province are generally scattered in Khalajistan, the southeast of Nofel Loshato, and parts of the south of Salafchegan cities. Considering the results of the OLS model, confirmed cases are dispersed in central and southern parts of Mazandaran province. As a result of the spatial dispersion, the central regions exposed the most significant number of death cases. As a result, this condition led to the National COVID-19 pandemic Headquarters policies, such as implementing the screening plan and increasing the capacities of the hospitals.

Regarding the outputs of the GWR model, after implementing these policies, the rate of deaths and confirmed cases were mitigated and recovered evidence increased significantly by 57.34% in the north, south, and northeast regions of Mazandaran province. Peak et al. (2020) demonstrated the impacts of quarantine on the rate of COVID-19 dispersion and deaths.

Conclusion

The prevalence of the COVID-19 pandemic has come to be a clinical threat all over the world. According to the results of this research, the models (GWR, OLS, and Moran’s I) used in this study exposed adequate capabilities to investigate the spatiotemporal variation of pandemic disease and quantify the influences of explanatory factors. According to the outputs of GWR, the spatial distribution of the COVID-19 pandemic in Qom province is very well estimated. It shows that the GWR model could explain the pandemic of COVID-19 spatial distribution in Qom province confirmed cases, recovered, and death rate \({R}^{2}\)= 70.41%. Moreover, outputs of the GWR model for Mazandaran province revealed that the confirmed cases in this province are generally witnessed in Ramsar, Nowshahr, and the southern parts of Sari, the northern region of Babol influenced by tourists’ trips and transportation. Based on the GWR model, the highest spatial distribution of deaths, with a percentage of 2.61%, is observed in the northwestern and southern parts (Ramsar, Tonekabon, Kelardasht, Chalous, Noor, and Amol) in Mazandaran province.

Moreover, the outputs of the OLS model exhibited that the death cases in Qom province mainly depressed in the southwestern and southern parts and part of the southeast and a small region of the northwest and northeast, and the recovered cases are observed in northern, northwestern, and eastern areas. Based on the OLS model, the spatial distribution of the COVID-19 pandemic is not well estimated compared to GWR. It shows that the OLS model has not been able to explain the COVID-19 pandemic spatial distribution epidemic in Mazandaran province. According to the outcomes of this model, the \({R}^{2}\) for confirmed cases recovered and death is 0.72%. The findings of the GWR model demonstrate that the COVID-19 pandemic’s spatial-temporal autocorrelation was based on spatial autocorrelation, with a Moran’s I coefficient of 0.482419, an expected index value of − 0.001653, a Z-score of 106.107828, and a P value of 0%.

While the spatial autocorrelation attained using the OLS model in Mazandaran province exposed a (Moran’s I) coefficient equal to 0.215666, an expected index value of − 0.001770, a value of Z-score equal to 14.314292 and a P value equal to 0%.

The results of this paper in Mazandaran and Qom Provinces indicated that the indicators of confirmed cases and deaths are inversely related to the altitude, and the rate of recovered cases has a direct relationship with the elevation.

Based on Moran’s autocorrelation pattern, the results of the GWR model confirmed that a coefficient of 0.008821 for (Moran’s I), 2.230280 for Z-Score, the value of the expectation index being − 0.001136 and the P value equal to 0.025729% are acquired, while the result of the spatial distribution of the COVID-19 epidemic obtained using the OLS model showed a coefficient (Moran’s I) of 0.014834, an expectation index of 0.000871, a Z-score of 3.675040 and a P value of 0.000% for Qom province. Wearing masks and using sanitizers are considered the most critical factors in reducing deaths. A significant increase in recovered cases decreases the number of deaths and increases the rate of recovered cases in Mazandaran.