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Article

Spatial Modeling of COVID-19 Prevalence Using Adaptive Neuro-Fuzzy Inference System

by
Mohammad Tabasi
1,
Ali Asghar Alesheikh
1,
Mohsen Kalantari
2,
Elnaz Babaie
1 and
Abolfazl Mollalo
3,*
1
Department of GIS, Faculty of Geodesy and Geomatics Engineering, K. N. Toosi University of Technology, Tehran 19967-15433, Iran
2
School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW 2052, Australia
3
Department of Public Health and Prevention Science, School of Health Sciences, Baldwin Wallace University, Berea, OH 44017, USA
*
Author to whom correspondence should be addressed.
ISPRS Int. J. Geo-Inf. 2022, 11(10), 499; https://doi.org/10.3390/ijgi11100499
Submission received: 22 July 2022 / Revised: 15 September 2022 / Accepted: 21 September 2022 / Published: 24 September 2022
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Abstract

:
This study is dedicated to modeling the spatial variation in COVID-19 prevalence using the adaptive neuro-fuzzy inference system (ANFIS) when dealing with nonlinear relationships, especially useful for small areas or small sample size problems. We compiled a broad range of socio-demographic, environmental, and climatic factors along with potentially related urban land uses to predict COVID-19 prevalence in rural districts of the Golestan province northeast of Iran with a very high-case fatality ratio (9.06%) during the first year of the pandemic (2020–2021). We also compared the ANFIS and principal component analysis (PCA)-ANFIS methods for modeling COVID-19 prevalence in a geographical information system framework. Our results showed that combined with the PCA, the ANFIS accuracy significantly increased. The PCA-ANFIS model showed a superior performance (R2 (determination coefficient) = 0.615, MAE (mean absolute error) = 0.104, MSE (mean square error) = 0.020, and RMSE (root mean square error) = 0.139) than the ANFIS model (R2 = 0.543, MAE = 0.137, MSE = 0.034, and RMSE = 0.185). The sensitivity analysis of the ANFIS model indicated that migration rate, employment rate, the number of days with rainfall, and residential apartment units were the most contributing factors in predicting COVID-19 prevalence in the Golestan province. Our findings indicated the ability of the ANFIS model in dealing with nonlinear parameters, particularly for small sample sizes. Identifying the main factors in the spread of COVID-19 may provide useful insights for health policymakers to effectively mitigate the high prevalence of the disease.

1. Introduction

Coronavirus disease 2019 (COVID-19), caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) [1], has adversely affected the daily lives of humans worldwide and has caused an unprecedented socio-economic burden. The rapid diffusion of the infection has resulted in high disease prevalence and mortality in over 200 countries in less than a few months after the outbreak [2]. In mid-February 2020, the World Health Organization (WHO) announced Iran as the second epicenter of virus transmission worldwide [1]. As of 1 July 2022, Iran has reported a case fatality ratio (CFR) of 1.95%, significantly higher than the CFR worldwide (1.15%) [3]. Although preventive public health measures, such as vaccination and early testing, are necessary to cope with the disease [2] in a timely fashion, they seem insufficient to control the outbreak, especially in developing or underdeveloped countries.
With the onset of the pandemic, several attempts have been carried out for early diagnosis and forecasting of COVID-19 [4,5,6,7,8]. Although these studies have performed well in diagnosing and forecasting COVID-19, they did not account for the spatial component of the disease and potential factors affecting the spatial distribution of COVID-19. Recent studies have indicated that socio-economic [9], demographic [10], climatic [11], and environmental [12] variables can potentially influence spatial variations in COVID-19. Therefore, investigating the impacts of these variables on the spread of COVID-19 may provide guidelines for health policymakers to have a better understanding of disease-prone regions, monitor the spread, and efficiently allocate medical resources.
The geographical information system (GIS) has been leveraged frequently to examine the spatial dynamics of infectious diseases [13,14,15]. To date, many GIS-related studies on COVID-19 have been conducted from different perspectives, including spatial and temporal analysis [16], spatial modeling using environmental determinants [12,17], data mining [18], and predictive models using intelligent systems [19]. For instance [10], applied geographically weighted regression (GWR) and multiscale GWR methods in a GIS framework to explore the COVID-19 distribution in the United States. This study indicated that income inequality, black females (%), nurse practitioners (%), and household income were the most significant factors affecting COVID-19 incidence. In another GIS-based study [12], predicted the cumulative incidence of the disease throughout the continental United States by a multilayer perceptron (MLP) neural network. Their findings indicated that median household income, pancreatic cancer, leukemia, age-adjusted mortality rates of ischemic heart disease, and total precipitation are the main drivers of the spread of COVID-19.
While the spatial analysis of COVID-19 distribution has been frequently conducted in many countries, including China [16], Italy [20], Brazil [21], the United States [10,12], and India [22], relatively little attention has been paid to the spatial dynamics of the disease in Iran using machine learning (ML) algorithms and GIS techniques. For instance [23], presented risk maps of COVID-19 in Iran at the provincial level using an adaptive neuro-fuzzy inference system (ANFIS), GWR, and multiscale GWR. This study showed that older adults and population density were the most critical indicators of COVID-19 prevalence. Another study conducted by [9] modeled the COVID-19 distribution by three ML approaches, including random forest (RF), logistic regression, and ANFIS according to eight land uses (bakeries, automated teller machines (ATMs), public transport stations, supermarkets, banks, pharmacies, hospitals, and fuel stations) in Tehran, Iran. They showed that the distribution of the disease was more concentrated in pharmacies and public transport stations.
ANFIS, a robust ML approach, maintains the benefits of artificial neural networks (ANN) and fuzzy inference systems (FIS) [24]. In addition to the power of the ANFIS model in exploring complex problems, principal component analysis (PCA) can reduce the complexity of the dataset by reducing a large number of factors to a new set of fewer parameters [25,26]. PCA can be combined with ML approaches, such as the ANFIS, to reduce the convergence time and enhance its predictive performance [15,27].
Although there have been numerous studies for spatial modeling of COVID-19 using ML approaches worldwide, little attention has been paid to the ANFIS or PCA-ANFIS, mainly when dealing with small sample sizes and small areas through a fuzzy perspective. Regarding the high flexibility and versatility of the ANFIS and the ability of the PCA to increase the model’s predictive performance, the main contribution of this study is the combined use of PCA and ANFIS methods to model COVID-19 prevalence. This study aims to compare the performance of ANFIS and PCA-ANFIS models in modeling the spatial distribution of COVID-19 prevalence in the Golestan province, where its CFR was approximately 2.5 times more than the CFR in Iran (9.06% vs. 3.68%) [28]. The findings of this study may provide valuable insights for health managers to identify factors affecting COVID-19 prevalence, which may lead to developing targeted interventions in response to COVID-19 transmission.

2. Materials and Methods

2.1. Study Area

Golestan province geographically lies between longitudes 53°57′ to 56°22′ E of the Greenwich meridian and latitudes 36°30′ to 38°08′ N of the equator, located on the southeastern shores of the Caspian Sea and south of the Republic of Turkmenistan (Figure 1). The province has a total area of 20,367 square kilometers and a population of over 1.87 million. The province consists of 14 counties divided into 60 rural districts (i.e., the unit of analysis in this study) [29].

2.2. Data Collection and Preparation

The disease data and potentially relevant factors (n = 32) were collected based on previous studies [9,10,11,12]. The prepared dataset includes COVID-19 prevalence per 100,000 population (as the dependent variable) and socio-demographic, environmental, land use, and climatic data as independent variables. Detailed information about the variables is provided in Table 1. ArcGIS 10.2 (ESRI, Redlands, CA, USA) and Microsoft Excel 2016 were used to prepare the dataset at the rural district scale. Continuous raster grids of the climatic data were generated using the inverse distance weighting interpolation method [30]. The zonal statistic function was applied to calculate average values of the digital elevation model (DEM), normalized difference vegetation index (NDVI), and climatic variables at the rural district level. We used the min-max normalization approach [31] for dependent and independent variables to increase the computational performance of models based on Equation (1):
X n = X i − X m i n X m a x − X m i n ,
where Xi, Xmin, Xmax, and Xn are the initial, minimum, maximum, and normalized values, respectively.

2.3. Statistical Analysis

Initially, the linear regression (LR) method was used to select independent and main variables as inputs for modeling. This method also was used as the baseline to investigate the effects of independent variables on the dependent variable. Tests of tolerance and variance inflation factor (VIF) were applied to examine the multicollinearity of all variables [34]. To conduct the PCA, factor analysis in dimension reduction was employed [35]. In this regard, Kaiser-Meyer-Olkin (KMO) and Bartlett’s tests were used to assess the suitability and adequacy of the data for use in the PCA [15]. All statistical analyses were conducted in the SPSS software version 23.

2.4. ANFIS

The fuzzy theory is an approach to making decisions when dealing with ambiguous and inaccurate data with no explicit criteria and accurate boundaries [36,37]. Although this method is popular among researchers in numerous fields, it does not generate high accuracies in unforeseen circumstances [27]. Due to the learning abilities of the ANN to optimize the fuzzy methods, ANFIS was developed [38]. ANFIS, a combination of the ANN and Takagi-Sugeno fuzzy system, benefits from both the learning ability of ANN and the computational ability of fuzzy methods to solve the optimization issue of nonlinear functions [36]. Neuro-fuzzy models were found beneficial compared to classical models of ANNs in some studies [27,39,40,41]. ANFIS is less dependent on the knowledge of experts, can capture nonlinear structures, is adaptable, and can learn quickly [27].
The ANFIS generates a mapping between inputs and outputs by applying fuzzy if-then rules [24]. Figure 2 illustrates the main architecture of the ANFIS with five layers and two inputs x and y (i.e., variables) in the input layer (Layer 0). More information about the structure of ANFIS is presented in [24].

2.5. PCA

It is evident that smaller datasets are easier to visualize and explore; hence, they are faster to be processed. The PCA was first presented by Pearson to reduce the dimensions of a dataset, containing many correlated variables [35,42,43]. Therefore, it preserves the diversity in the dataset to the maximum extent [44] and reduces complexity in the dataset while controlling data loss [26]. In this method, by maximizing the correlation between the variables, the variables are transformed into principal components (PCs). The PCs are the eigenvectors of a covariance matrix and are mutually uncorrelated [35,42]. To apply the PCA-ANFIS model, we decomposed the input variables into PCs and then used them for training the ANFIS model [27]. More information about PCA is presented in [35,42,43].

2.6. Model Development and Evaluation

To implement the ANFIS model, the potentially selected variables (resulted from the LR analysis) and the COVID-19 prevalence were set as independent (inputs) and dependent variables, respectively. The ANFIS model was implemented using the ANFIS toolbox in MATLAB R2015a. In the ANFIS model, three methods of Fuzzy C-means (FCM) clustering, subtractive clustering, and grid partitioning were used to cluster the input data and to facilitate the training phase. However, as FCM clustering usually has shown a better performance than subtractive clustering and grid partitioning [14,45], this method was used in this study. The Gaussian and linear membership functions were employed in the ANFIS model. The parameters of the maximum epoch and error goal were set to thirty and zero, respectively.
We randomly divided the dataset into three categories: training data (52%, thirty-one rural districts), validation data (13%, eight rural districts), and test data (35%, twenty-one rural districts). The training data were considered to calibrate the model, and the validation data were used to avoid overfitting in the training process. The test data were considered to evaluate the ability of the model to predict the target variable. To estimate the model accuracy, four evaluation metrics were used in the model development and evaluation stages: determination coefficient (R2), mean square error (MSE), mean absolute error (MAE), and root mean square error (RMSE) [14,15]. To deal with model uncertainty (i.e., overestimation and underestimation), the training, validation, and test data were set in four different modes. In each mode, we ran the model 5 times. Then, we calculated the average of the results.
In the PCA-ANFIS model, we applied the PCA to extract the PCs. Then, the PCs were considered as inputs for the ANFIS model. To compare the performance of the ANFIS and PCA-ANFIS models, we used the same training, validation, and test data for the above-mentioned models.
Finally, sensitivity analysis was performed to explore the contribution of selected variables in predicting COVID-19 prevalence. In this regard, each factor was removed from the ANFIS model separately for the test data, and the impact of that factor on the model’s accuracy was assessed by the evaluation indicator of R2.

3. Results

Among 32 potential variables, only 17 independent variables were selected as the final input candidates, including average household size, percentage of people over 65 years, migration rate, employment rate, literacy rate, residential apartment units, educational facilities, cultural and sports facilities, religious facilities, municipal services, health facilities, NDVI, maximum wind speed, number of days with rainfall, mean dew point temperature, mean temperature, and mean soil temperature.

3.1. Statistical Analysis

The results of the LR model are presented in Table 2. The linear correlation between the desired and predicted dependent variable was R = 0.697. The R2 = 0.486 shows that 48.6% of total variations in COVID-19 prevalence can be predicted by the selected variables. The value of the Durbin–Watson test was close to two, indicating the independence of the error assumption [14].
Table 3 shows the results of the collinearity of the input factors. The values of tolerance and VIF statistics (tolerance > = 0.1 and 1 < VIF < = 10) imply that multicollinearity is not a major concern. Thus, they can be used in the ANFIS model [15].
The value of the KMO test was 0.719, which indicates the data are sufficient to apply the PCA. In addition, the value of Bartlett’s test (approx. Chi-Square = 709.571) indicates that the data are appropriate for the factor analysis [35].
Among seventeen components, only five components (with eigenvalues > 1) were selected as PCs (Table 4). To optimize the structure of the PCs and equalize their relative importance, we rotated them using the Varma rotation [35,46]. After rotation, the eigenvalues of the PCs were updated and included in the section of rotation sums of the squared loadings. Based on Table 4, the most important PCs in explaining the cumulative variance of the PCs (76.976%) were the PC1 (variance = 29.867%), followed by PC2 (variance = 14.329%), PC3 (variance = 12.341%), PC4 (variance = 11.458%), and PC5 (variance = 8.980%).
According to Table 5, the varimax rotation with Kaiser Normalization was used to obtain the loading values of each variable for each PC [47], and only the largest absolute value was selected. The variables associated with that value were considered as the candidate variables for the related PCs [35]. The PC1 has a strong positive loading with the percentage of people over 65 years (0.769), residential apartment units (0.739), educational facilities (0.673), cultural and sports facilities (0.813), religious facilities (0.821), health facilities (0.807), NDVI (0.632), and mean dew point temperature (0.580). The PC2 has a negative loading with employment rate (−0.492) and the number of days with rainfall −0.931), while it has a strong positive loading with mean soil temperature (0.910). The PC3 has a strong positive loading with the average household size (0.893) and municipal services (0.676). The PC4 has a strong negative loading with maximum wind speed (−0.839), whereas it has a strong positive loading with the mean temperature (0.835). The PC5 is associated with migration (0.711) and literacy rates (0.799).

3.2. Model Evaluation

According to Table 6, the PCA-ANFIS model could explain larger variations in COVID-19 prevalence (mean R2 = 0.615) than the ANFIS model (mean R2 = 0.543) on the test data.

3.3. Sensitivity Analysis

The largest reduction in the R2 occurred when the migration rate (15.16%), the employment rate (13.62%), the number of days with rainfall (13.61%), and residential apartment units (11.05%) were excluded from the ANFIS model. Therefore, these factors are considered the most contributing variables in predicting the geographical distribution of COVID-19 prevalence. Figure 3 depicts the importance of each variable on COVID-19 prevalence.

4. Discussion

In this study, we assumed that the heterogeneous spatial distribution of COVID-19 prevalence could be explained by socio-demographic, environmental, climatic, and urban land uses factors. We compiled a broad range (n = 32) of these factors to predict COVID-19 prevalence at the rural district level. However, due to the relatively small sample size, traditional modeling techniques could result in overfitting. To address this problem, we used the hybrid neural network and fuzzy logic called ANFIS in a GIS framework. The ANFIS has a robust predictive capability in modeling complex and nonlinear relationships [38]. We further improved the model’s performance [15,27] using PCA. The results of this study will enable policymakers to predict the spatial distribution of COVID-19 and make decisions on designing preventive policies to control future epidemics. In addition, identifying the most contributing factors in COVID-19 prevalence provides valuable insights into the disease transmission, thereby helping more targeted interventions to weaken the spread of the disease.
Among 32 variables, only 17 variables were selected as the inputs for modeling after variable selection. The baseline LR model showed that the selected variables could explain 48.6% of the total variations in COVID-19 prevalence. We improved the performance of the model by at least 13% when using the ANFIS (R2 = 0.543) and PCA-ANFIS (R2 = 0.615) models. This might be due to the ability of ANFIS in capturing nonlinear and linear relationships [14]. The previous literature has implied that nonlinear models had superior performance compared to linear models. For example, [12] indicated that an MLP neural network with one hidden layer (as a nonlinear model) could predict COVID-19 incidence better than an LR model. Reference [11] showed that a combination of the virus optimization algorithm (VOA) with the ANFIS model improves the performance of the ANFIS model in predicting the infection rate of COVID-19. They also indicated that both ANFIS (R2 = 0.691) and ANFIS-VOA models (R2 = 0.834) performed better than LR (R2 = 0.392). Another study stated that RF and ANFIS, as nonlinear models, had higher accuracy in predicting the spatial variation in COVID-19 cases than the logistic regression model (i.e., a generalized linear model) [9]. In line with our results, previous studies also have indicated that the PCA can improve the performance of ML approaches [15,25,26,27,35].
The sensitivity analysis of the ANFIS model showed that four variables of migration rate, employment rate, number of rainfall days, and residential apartment units were among the most contributing factors in predicting COVID-19 prevalence in the Golestan province. The results are consistent with previous studies. For instance, [48,49,50] proposed that the high risk of the spread of COVID-19 was associated with areas with a higher migrant population. Areas with high rates of migrant population can catalyze disease transmission. With the increase in population movements in these areas, the number of people entering and leaving those areas increases. In turn, migrant populations have to travel a greater distance between their residence and workplace, which increases the chance of their contact with other people. It makes the migrant population more likely to contract the virus and causes long-distance transmission of COVID-19. On the other hand, areas with higher populations and higher socio-economic conditions usually attract more migrant people [51]. In this study, according to our census data [29], the rural districts with high migration rates usually had high populations, which can facilitate the COVID-19 transmission in those areas. This suggests the importance of formulating lockdown measures in the early stages of the pandemic to prevent large-scale disease transmission.
Moreover, the previous literature has suggested that a higher employment rate can increase the likelihood of COVID-19 exposure [52,53], particularly when using public transportation to commute to and from the workplace. The proximity of employed people in workplaces, such as offices, can provide a suitable environment for virus transmission. In addition, employed people are usually more exposed to touching infected work surfaces, including keyboards, public toilets, doors, and window handles, as the virus can survive for up to 72 h on high-touch surfaces [54].
Reference [55] assessed the impact of climate factors on COVID-19 transmission. They showed that precipitation, low temperature, dew/frost point, and wind speed escalate the disease incidence. Climate factors, such as low humidity and temperature, may allow the virus to retain its viability longer and subsequently prolong its infectivity [55]. On the other hand, cold and dry weather conditions may also disrupt the human immune response, thereby increasing the risk of disease [55]. In terms of health policy implications, health authorities can adjust their intervention based on different weather conditions. Contrary to the results of this study, some previous research indicated that climatic variables (e.g., temperature and humidity) were not effective in COVID-19 occurrence [10,12,23]. The differences in findings may be attributed to different geographic areas, various methods, and different spatial scales of analysis.
In our study area, the residential apartment units were more concentrated in densely populated urban areas; thus, they were more likely to be exposed to the virus. In agreement with our results, [56] concluded that residential areas are among the most significant urban land uses in the spread of COVID-19. This implies that health authorities should allocate more health resources to the residents of these populated areas to control COVID-19 transmission. To the best of our knowledge, this research is the first attempt to use a comprehensive set of urban land uses for modeling the spatial variations in COVID-19 prevalence, particularly using the ANFIS and PCA-ANFIS. Previous studies have recommended using land use variables in future works [9,11,12].
This study has some limitations that may impede the reliable prediction of the disease distribution. First, although our findings align with some previous studies, interpreting the results at the individual level may not be reliable due to ecological fallacy. Thus, the conclusions can only be drawn at the rural district scale. The lack of some main socio-economic variables (e.g., poverty, race, and insurance status) at the rural district level is another limitation. Moreover, errors and irregularity in the data collection phase can compromise the model’s accuracy. For instance, some cases may be misdiagnosed, or the asymptomatic patients not being reported may lead to unreliable estimations of disease prevalence. Examining data uncertainty should be addressed in future works.

5. Conclusions

Despite the low number of training samples, both the ANFIS and PCA-ANFIS models predicted COVID-19 prevalence in the Golestan province with decent accuracy. Regarding public health implications, the results showed how migration rate, employment rate, and the number of rainfall days could predict COVID-19 prevalence. Moreover, high contributions of residential apartment land use in predicting COVID-19 distribution imply that health authorities should allocate more medical resources to the residents of areas with a higher density of apartment units. To improve the predictability of the ANFIS model, other optimization algorithms, such as equilibrium optimizer algorithm [57], crow search algorithm [58], and Harris Hawks Optimizer [59], can be used in future works. With the increase in the amount of training data, deep learning models can be used, which can lead to higher accuracy of the model. However, the low number of training samples in this study impedes us from using the deeper networks. For future works, by considering a longer time period (if available) or finer spatial scales (which was not possible in this study), we can increase the amount of data and, in turn, adjust the deep learning models [6]. Further studies, such as agent-based models [60,61,62], can be helpful to better understand the complex spatial dynamics of COVID-19 in communities. Nonetheless, this study can be served as a helpful guideline for health policymakers to determine potential risk factors pertaining to COVID-19, particularly for areas with small sample sizes.

Author Contributions

Conceptualization, Mohammad Tabasi, Elnaz Babaie, and Abolfazl Mollalo; methodology, Mohammad Tabasi and Elnaz Babaie; software, Elnaz Babaie; validation, Mohammad Tabasi, Elnaz Babaie, and Abolfazl Mollalo; formal analysis, Mohammad Tabasi and Elnaz Babaie; investigation, Mohammad Tabasi, Elnaz Babaie, and Abolfazl Mollalo; resources, Mohammad Tabasi and Elnaz Babaie; data curation, Mohammad Tabasi; writing—original draft preparation, Mohammad Tabasi; writing—review and editing, all authors; visualization, Mohammad Tabasi and Elnaz Babaie; supervision, Ali Asghar Alesheikh and Mohsen Kalantari; project administration, Ali Asghar Alesheikh. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data underlying this article will be shared on reasonable request to the corresponding author.

Acknowledgments

The authors gratefully acknowledge the support of the staff of the CDC of the Golestan province for sharing the COVID-19 dataset at the rural district level.

Conflicts of Interest

The authors declare no conflict of interest.

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Ijgi 11 00499 g001 550
Figure 1. Location of Golestan province and its 60 rural districts.
Figure 1. Location of Golestan province and its 60 rural districts.
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Figure 2. The primary architecture of the ANFIS [24].
Figure 2. The primary architecture of the ANFIS [24].
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Figure 3. The contribution of input variables in predicting the spatial distribution of COVID-19 prevalence using the ANFIS model.
Figure 3. The contribution of input variables in predicting the spatial distribution of COVID-19 prevalence using the ANFIS model.
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Table
Table 1. Summary of the dataset used in this study.
Table 1. Summary of the dataset used in this study.
ThemeVariableDescriptionSource
(a) Disease data(a1) COVID-19 prevalence per 100,000 people(a1) (The ratio of COVID-19 cases in a rural district during the study period to the population living in that rural district during that period of time) * 100,000(a1) Center for Disease Control and Prevention (CDC) of Golestan province, from 2020 to 2021 [28]
(b) Socio-demographic(b1) Percent of male (b1–7) Statistical Center of Iran, 2016 (the last year of the census in Iran) [29]
(b2) Percent of female
(b3) Average household size(b3) The ratio of household population to the number of occupied households
(b4) Percentage of people over 65 years
(b5) Employment rate(b5) The ratio of employed people to people aged 10+
(b6) Migration rate(b6) Number of immigrants minus the number of emigrants of an area divided by the total population of that area
(b7) Literacy rate(b7) The ratio of literate people aged 6+ to all people aged 6+
(c) Urban land use(c1) Residential units < 100 m2(c1) Percentage of residential units with an area of less than 100 m2(c1–10) Deputy of Statistics and Information of Golestan Province, from 2020 to 2021 [29]
(c2) Residential apartment units(c2) The ratio of residential apartment units to total residential units
(c3) Educational facilities(c3) The total number of educational centers, including kindergartens, primary schools, middle schools, secondary schools, special schools, colleges, and universities
(c4) Cultural and sports facilities(c4) The total number of cultural and sports centers, including parks and green spaces, public libraries, sports fields, and sports halls
(c5) Religious facilities(c5) The total number of religious places, including mosques, shrines, seminaries, and other religious centers
(c6) Government offices(c6) The total number of government offices, including employment offices, banks, registry offices, municipal offices, welfare centers, post offices, courthouses, and other administrative land uses
(c7) Municipal services(c7) The total number of facilities pertaining to municipal services, such as water supplies, water purification systems, sewage disposal systems, and electricity and gas supplies
(c8) Health facilities(c8) The total number of medical centers, including hospitals, clinics, pharmacies, nursing homes, medical laboratories, healthcare centers, maternity centers, and other specialized care centers
(c9) Commercial facilities(c9) The total number of commercial centers such as passages, grocery stores, retail stores, bakeries, supermarkets, hotels, and restaurants
(c10) Communication and transportation facilities(c10) The total number of communication and transportation facilities such as airports, railway stations, highways, public transportation facilities, post offices, telecommunication offices, and information and communication technology centers
(d) Environmental(d1) NDVI(d1) Normalized difference vegetation index (90-m spatial resolution)(d1) United States Geological Survey (USGS), from 2020 to 2021 [32]
(d2) DEM(d2) Digital elevation model (90-m spatial resolution)(d2) United States Geological Survey (USGS), from 2020 to 2021 [32]
(e) Climatic(e1) Precipitation(e1) Total rainfall; Number of days with rainfall(e1–6) Meteorological Organization of Iran, from 2020 to 2021 [33]
(e2) Humidity(e2) Average relative humidity
(e3) Temperature(e3) Minimum temperature; Mean temperature; Maximum temperature; Mean dew point temperature*; Mean soil temperature
(e4) Evaporation(e4) Maximum evaporation; Total evaporation
(e5) Wind speed(e5) Maximum wind speed; Mean wind speed
(e6) Sea pressure(e6) Mean sea-level pressure
e1: Total amount of rainfall recorded during a month at the site, mm; number of days with rainfall during a month at the site. e2: Percentage measure of the amount of moisture in the air compared to the maximum amount of moisture the air can hold at the same temperature and pressure. * The dew point is the temperature at which water vapor can condense, assuming constant air pressure and water content, °C. e4: Evaporation is the amount of water evaporated from a unit surface area per unit of time, mm. e6: The mean sea-level pressure (MSLP) is the atmospheric pressure at the mean sea level (PMSL), Pa.
Table
Table 2. The results of the LR model.
Table 2. The results of the LR model.
ModelRR SquareAdjusted R
Square		Change StatisticsDurbin–Watson
R Square ChangeFdf1df2Sig. F Change
LR0.6970.4860.2780.4862.33817420.0132.234
Table
Table 3. Multicollinearity analysis of input variables in the LR model.
Table 3. Multicollinearity analysis of input variables in the LR model.
Input VariableCollinearity Statistics
ToleranceVIF
Average household size0.2603.850
Percentage of people over 65 years0.2014.964
Migration rate0.6181.618
Employment rate0.6491.541
Literacy rate0.3752.667
Residential apartment units0.4582.185
Educational facilities0.1616.197
Cultural and sports facilities0.2404.163
Religious facilities0.2793.589
Municipal services0.1616.217
Health facilities0.1069.390
NDVI0.3103.225
Maximum wind speed0.1985.054
Number of days with rainfall0.1516.637
Mean dew point temperature0.2853.511
Mean temperature0.3163.167
Mean soil temperature0.1496.701
Table
Table 4. Selecting the PCs according to the total variances.
Table 4. Selecting the PCs according to the total variances.
ComponentInitial EigenvaluesExtraction Sums of Squared LoadingsRotation Sums of Squared Loadings
Total% of VarianceCumulative %Total% of VarianceCumulative %Total% of VarianceCumulative %
15.86134.47434.4745.86134.47434.4745.07729.86729.867
22.47314.54549.0192.47314.54549.0192.43614.32944.197
32.22713.10262.1212.22713.10262.1212.09812.34156.538
41.3638.02070.1411.3638.02070.1411.94811.45867.996
51.1626.83576.9761.1626.83576.9761.5278.98076.976
Table
Table 5. The loading of each variable on each PC using the rotated component matrix (rotation converged in 10 iterations). The bold values are associated with the candidate variables for the related PCs.
Table 5. The loading of each variable on each PC using the rotated component matrix (rotation converged in 10 iterations). The bold values are associated with the candidate variables for the related PCs.
VariablePC
12345
Average household size0.039−0.0790.893−0.1960.042
Percentage of people over 65 years0.7690.191−0.1120.221−0.350
Migration rate0.260−0.128−0.340−0.0950.711
Employment rate−0.355−0.4920.117−0.1490.155
Literacy rate0.0470.1110.3320.0930.799
Residential apartment units0.739−0.130−0.041−0.0990.164
Educational facilities0.6730.2000.5310.1070.169
Cultural and sports facilities0.8130.1030.083−0.0010.271
Religious facilities0.8210.0880.1530.0770.021
Municipal services0.635−0.0430.6760.092−0.048
Health facilities0.8070.0650.4060.2140.180
NDVI0.632−0.367−0.2330.326−0.148
Maximum wind speed−0.3870.1790.104−0.8390.113
Number of days with rainfall0.044−0.931−0.0760.106−0.099
Mean dew point temperature0.5800.2400.1900.4150.139
Mean temperature−0.0820.352−0.0530.8350.079
Mean soil temperature0.0630.910−0.0470.221−0.027
Table
Table 6. Comparison of predicted COVID-19 prevalence using the ANFIS and PCA-ANFIS models.
Table 6. Comparison of predicted COVID-19 prevalence using the ANFIS and PCA-ANFIS models.
Statistical CriteriaModel Evaluation (Test Data)
ANFISPCA-ANFIS
R2(Mean: 0.543, SD: 0.045)(Mean: 0.615, SD: 0.060)
MAE(Mean: 0.137, SD: 0.020)(Mean: 0.104, SD: 0.010)
MSE(Mean: 0.034, SD: 0.007)(Mean: 0.020, SD: 0.004)
RMSE(Mean: 0.185, SD: 0.020)(Mean: 0.139, SD: 0.016)
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Tabasi, M.; Alesheikh, A.A.; Kalantari, M.; Babaie, E.; Mollalo, A. Spatial Modeling of COVID-19 Prevalence Using Adaptive Neuro-Fuzzy Inference System. ISPRS Int. J. Geo-Inf. 2022, 11, 499. https://doi.org/10.3390/ijgi11100499

AMA Style

Tabasi M, Alesheikh AA, Kalantari M, Babaie E, Mollalo A. Spatial Modeling of COVID-19 Prevalence Using Adaptive Neuro-Fuzzy Inference System. ISPRS International Journal of Geo-Information. 2022; 11(10):499. https://doi.org/10.3390/ijgi11100499

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Tabasi, Mohammad, Ali Asghar Alesheikh, Mohsen Kalantari, Elnaz Babaie, and Abolfazl Mollalo. 2022. "Spatial Modeling of COVID-19 Prevalence Using Adaptive Neuro-Fuzzy Inference System" ISPRS International Journal of Geo-Information 11, no. 10: 499. https://doi.org/10.3390/ijgi11100499

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