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Modern Geomatics Technologies and Applications

Where is the deviation of an attribute for feature from its mean ( − ), is the spatial weight between features and ,

,

is equal to the total number of features, and is the aggregate of all the spatial weights.
0

2.2.2 Getis-Ord Gi*: Regions with the highest rates of incidence were identified as hot spot areas. Developed by Getis and Ord
[17, 18], hot spot analysis could be beneficial in terms of studying the evidence of identifiable spatial patterns [19].
This technique, implemented in ArcGIS software, identifies statistically significant spatial clusters of high values (hot spots)
and low values (cold spots). In Getis-Ord Gi*, the significance and intensity of clustering is evaluated based on a confidence
level and on output z-scores. For positive z-scores, higher z-scores reveal more intense clusters (hot spots). However, for
negative z-scores, smaller z-score values represent more intensity of clustering of low values (cold spots) [20].

2.2.3 Anselin Local Moran’s I: In order to obtain more information about high and low-risk zones, Anselin Local Moran’s I
was applied. Given a set of weighted features, this technique identifies statistically significant hot spots, cold spots, and spatial
outliers.

2.3 Spatial statistical models
2.3.1. Ordinary Least Squares (OLS): This global linear modeling method can be employed to examine the global relationships
between the set of independent and dependent variables. Considering the assumption of spatial stationary, this method
investigates the relationship between the set of explanatory and dependent variables [21, 22]. The formula of ordinary least
squares is characterized by: [23]

= + + (3)
0

Where denotes the COVID-19 incidence rate (dependent variable) at the th location (province). is the estimated

0
intercept, representing the value of when is 0, signifies the vector of selected explanatory variables, indicates the

vector of regression coefficients, and is a random error term.

2.3.2. Geographically weighted regression (GWR): Local GWR model was introduced to relax the assumption of spatial
stationary and allowing the parameters to vary over space. Unlike global regression models, GWR detects spatial variation
within relationships in a model and makes useful information to examine and explain spatial non-stationarity. Therefore,
considering spatial context by GWR, this method predicts local regression parameters separately for each location [24]. The
GWR equation is as follows: [25]

= + ∑ + , = 1,2,3, … , . (4)
0

=1

Where illustrates the COVID-19 incidence rate value at the th province, represents the local predicted intercept,

0
specifies the th regression parameter for the th province, denotes the values of th explanatory variables, and signifies a

random error term.

3. Results and discussion
3.1 Distribution of COVID-19 incidence rates
Qom, as the epicenter of the disease, had the highest incidence rate among other provinces. After Qom, provinces
such as Tehran, Alborz, Qazvin, Markazi, Zanjan, and Lorestan were the most infected provinces with highest incidence rates
among others in Iran until October 21, 2020 (Fig. 1). It is worth mentioning that most of which are located around Qom.
At the time of the study, southern and eastern provinces of Iran were detected as the most COVID-19 infected regions
compared to central, northern, and western provinces. Razavi Khorasan, Sistan and Baluchistan, and Kerman were top three
provinces in terms of lower prevalence of the disease across Iran. Higher urban population of central provinces of Iran could be
an influential factor related to the higher levels of incidence rates in these areas.

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