Prioritizing and Analyzing the Role of Climate and Urban Parameters in the Confirmed Cases of COVID-19 Based on Artificial Intelligence Applications

Nowadays, an infectious disease outbreak is considered one of the most destructive effects in the sustainable development process. The outbreak of new coronavirus (COVID-19) as an infectious disease showed that it has undesirable social, environmental, and economic impacts, and leads to serious challenges and threats. Additionally, investigating the prioritization parameters is of vital importance to reducing the negative impacts of this global crisis. Hence, the main aim of this study is to prioritize and analyze the role of certain environmental parameters. For this purpose, four cities in Italy were selected as a case study and some notable climate parameters—such as daily average temperature, relative humidity, wind speed—and an urban parameter, population density, were considered as input data set, with confirmed cases of COVID-19 being the output dataset. In this paper, two artificial intelligence techniques, including an artificial neural network (ANN) based on particle swarm optimization (PSO) algorithm and differential evolution (DE) algorithm, were used for prioritizing climate and urban parameters. The analysis is based on the feature selection process and then the obtained results from the proposed models compared to select the best one. Finally, the difference in cost function was about 0.0001 between the performances of the two models, hence, the two methods were not different in cost function, however, ANN-PSO was found to be better, because it reached to the desired precision level in lesser iterations than ANN-DE. In addition, the priority of two variables, urban parameter, and relative humidity, were the highest to predict the confirmed cases of COVID-19.


Introduction
Sustainable development is an approach planned to improve human life and considers the development process while simultaneously analyzing related impacts [1][2][3]. Its critical role is becoming more and more important every day. After great efforts, in 2015, United Nations member states

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The analysis factors are the population density of each region, average daily temperature, relative humidity, wind speed, and the positive cases in the following days; • Since the incubation period of the virus is about 14 days, the sum of previous positive cases up to 14 days previously has been considered; • The analysis period is from 14 February 2020 to 24 March 2020.
In addition, it must be noticed that there are some delays between the exact dates when patients got infected by the COVID-19, and the dates when confirmed cases were registered in the media as follows: • The incubation period of COVID-19 varies from about 2 to 14 days [33]; • The lab tests of COVID-19 were on patients with symptoms [34]; • The symptoms of COVID-19 occur after 3 to 5 days [35]; • The results of the laboratory tests took one day to be ready [36,37]; • The daily announcement of new confirmed cases of COVID-19 usually refers to one day before [38].
Therefore, to find an appropriate correlation between weather data and confirmed cases, the climate factors have been shifted backward from one to nine days with respect to observations, and by the MLR method, the best correlation for each region has been selected. The results are presented in Appendix A, and have been used as a database in the artificial intelligence method.
It is evident that using daily positive cases-and especially data from one day before-could not be correct, due to the incubation period of COVID-19 (2 to 14 days), the symptoms of COVID-19 (which occur after 3 to 5 days), and finally, the fact that the lab tests of COVID-19 were on patients with symptoms. Therefore, the new positive case in date X will depend on the accumulative positive cases up to 14 days ago (Date X- 14). This variable cannot reach a plateau since it represents the accumulation of 14 days, not the period from start to end, as presented in Appendix B.

Artificial Neural Network (ANN)
The human brain, as a complex natural system, is unique in its kind. Some of the processes in this natural system are so complex that their processing is also complex for many super systems [39][40][41][42][43][44]. Analytical processes are very complex, because of the high speed and power of information processing by brain cells. Researchers were enabled to design advanced methods for solving various problems of real world inspired by the function of the human brain. Hence, artificial intelligence (AI) is considered one of the most successful achievements of computer science, simulating the behavior of the human brain in data analysis [45][46][47][48][49][50][51]. One of the AI branches is the artificial neural network (ANN). This information processing system, by a simulating strategy like communication between brain neurons, has become a tool for analyzing complex and real systems. In recent years, ANN models have been developed to overcome the difficulties presented by health issues [52][53][54]. Many types of computational models have been introduced as general neural networks. The multilayer perceptron (MLP) model is one of the most efficient ones, and has been used in a variety of activities. The MLP is a supervised artificial neural network with at least three layers, including the input layer, hidden layer, and output layer. The basic form of an artificial neural network includes a set of connected units or nodes (artificial neurons), and connections (weights). The connections can transmit a signal from one neuron to another, as shown in Figure 1. Depending on a particular problem, the number of neurons and the hidden layer can be changed to find the best prediction model [55][56][57][58][59][60]. The performance indicators of the algorithm evaluate the difference between the predicted values and the last layer (output). The process of training and evaluating the results in this algorithm continues until a desirable convergence is reached, and then it stops.

Particle Swarm Optimization (PSO) Algorithm
In recent years, the use of artificial intelligence by many researchers to solve complex and uncertain problems has become widespread [62][63][64][65][66][67][68][69][70][71], and there have been especially successful applications in the health problems [72][73][74][75][76]. One of these advanced techniques is the particle swarm optimization (PSO) algorithm, first introduced by Kennedy and Eberhart [77][78][79]. The algorithm was designed to simulate the swarm behavior of particles and to inspire the movement of birds and flocks. The PSO algorithm has been used successfully for modeling in engineering and academic applications. In this algorithm, each particle in the particle set is considered as a potential solution that the process of this algorithm begins with the generation of a random particle set. Then, the process continues by moving the set of particles to search for an optimal answer in the search space. In addition, if there is a D-dimensional set, including N particles, each i particle in this set is indicated with an Xi vector that includes vectors of position and velocity. In fact, the PSO algorithm differs from other algorithms in having a velocity vector. The new velocity vector and the new position vector of each particle are updated based upon Equations (1) and (2) in each moment. They depend on the particle's best position (Pbest) and the global best position (Gbest) [80].  Figure 2 shows the update of the velocity and position vectors of a particle in the set [81,82].

Particle Swarm Optimization (PSO) Algorithm
In recent years, the use of artificial intelligence by many researchers to solve complex and uncertain problems has become widespread [62][63][64][65][66][67][68][69][70][71], and there have been especially successful applications in the health problems [72][73][74][75][76]. One of these advanced techniques is the particle swarm optimization (PSO) algorithm, first introduced by Kennedy and Eberhart [77][78][79]. The algorithm was designed to simulate the swarm behavior of particles and to inspire the movement of birds and flocks. The PSO algorithm has been used successfully for modeling in engineering and academic applications. In this algorithm, each particle in the particle set is considered as a potential solution that the process of this algorithm begins with the generation of a random particle set. Then, the process continues by moving the set of particles to search for an optimal answer in the search space. In addition, if there is a D-dimensional set, including N particles, each i particle in this set is indicated with an X i vector that includes vectors of position and velocity. In fact, the PSO algorithm differs from other algorithms in having a velocity vector. The new velocity vector and the new position vector of each particle are updated based upon Equations (1) and (2) in each moment. They depend on the particle's best position (Pbest) and the global best position (Gbest) [80].
where X k i and V k i are the current position and velocity of the particle i, respectively, and V (k+1) i and X (k+1) i its new position and velocity. The parameter w is called the inertia weight, and varies between 0.4 and 0.9. The r 1 and r 2 are two random numbers within [0, 1]. The constants C 1 and C 2 , called the individual learning factor and social learning factor, are positive and must satisfy Equation (3). Figure 2 shows the update of the velocity and position vectors of a particle in the set [81,82]. Eventually, all particles converge to the optimal point after a thorough search. Figure 3 presents the flowchart of the PSO algorithm.

Differential Evolution (DE) Algorithm
The differential evolution (DE) is an evolutionary computation that is suitable for dealing with complex problems in the real world. The DE algorithm is a population-based algorithm that was proposed by Price and Storn for solving the continuous value problems [84][85][86][87]. Then, in the following years, the method developed and used for solving binary and discrete problems. The DE algorithm has been widely applied as an optimization algorithm to solve complex problems in various engineering sectors. The DE algorithm and some Meta heuristic algorithms like genetic algorithms have similar operators, including crossover, mutation, and selection. However, there are Eventually, all particles converge to the optimal point after a thorough search. Figure 3 presents the flowchart of the PSO algorithm. Eventually, all particles converge to the optimal point after a thorough search. Figure 3 presents the flowchart of the PSO algorithm.

Differential Evolution (DE) Algorithm
The differential evolution (DE) is an evolutionary computation that is suitable for dealing with complex problems in the real world. The DE algorithm is a population-based algorithm that was proposed by Price and Storn for solving the continuous value problems [84][85][86][87]. Then, in the following years, the method developed and used for solving binary and discrete problems. The DE algorithm has been widely applied as an optimization algorithm to solve complex problems in various engineering sectors. The DE algorithm and some Meta heuristic algorithms like genetic algorithms have similar operators, including crossover, mutation, and selection. However, there are

Differential Evolution (DE) Algorithm
The differential evolution (DE) is an evolutionary computation that is suitable for dealing with complex problems in the real world. The DE algorithm is a population-based algorithm that was proposed by Price and Storn for solving the continuous value problems [84][85][86][87]. Then, in the following years, the method developed and used for solving binary and discrete problems. The DE algorithm has been widely applied as an optimization algorithm to solve complex problems in various engineering sectors. The DE algorithm and some Meta heuristic algorithms like genetic algorithms have similar operators, including crossover, mutation, and selection. However, there are some differences among them, like the lack of local search in genetic algorithm, while the DE algorithm supports local search. In addition, the DE relies on mutation operation while the genetic algorithm relies on a crossover. Like other evolutionary algorithms, the DE starts by randomly generating the initial population. Then, after initialization, the search space is expanded by the mutation. The V g i is the mutant solution vector of X g i which is calculated based on Equation (4) [88].
where F k is the scaling factor varying in the range [0, 1] and determines the length of the mutation step. X g r1 , X g r2 and X g r3 are solution vectors that are randomly selected, with the condition expressed by Equation (5) [89].
where "i" is the index of the current solution. The trial vector (U g ij ) is produced by mixing the mutated vector and the parent vector in a crossover operation based on Equation (6) [90].
where Rand j is a randomly chosen real number in the interval between 0 and 1. The CR is a crossover constant. If the Rand j is less than or equal to CR, the trial vector (U g ij ) is inherited from the mutant solution vector, otherwise, the CR is considered equal to X g ij . The flowchart of the DE algorithm is shown in Figure 4.

Subsection
In this research, the case studies are the four regions in Italy with the largest numbers of confirmed cases of COVID-19, namely Lombardy (Milan), Piedmont (Turin), Veneto (Venice), and Emilia-Romagna (Bolonia), whose general data are presented in Table 1. The locations of the case studies are shown in Figure 5.

Subsection
In this research, the case studies are the four regions in Italy with the largest numbers of confirmed cases of COVID-19, namely Lombardy (Milan), Piedmont (Turin), Veneto (Venice), and Emilia-Romagna (Bolonia), whose general data are presented in Table 1. The locations of the case studies are shown in Figure 5.

PSO Modelling
The main goal of PSO is to train the artificial neural network for determining the feature selection of confirmed cases of COVID-19, and the reduction of them under the highest relationship between several independent variables and the dependent variable. For this purpose, three notable climate parameters, namely daily average temperature, relative humidity, and wind speed, and one urban parameter (population density × positive cases up to 14 days before), were considered as input data set, and confirmed cases of COVID-19 were considered as the output dataset. It is worth mentioning that the 4 input parameters are evaluated and reduced to 2. Firstly, before modeling, the control parameters of an algorithm should be selected. There are no specific rules, and most of them are considered based on the experts' opinions and previous studies [61,82]. Hence, a number of different modeling are done to determine an appropriate value for control factors, for instance, the size of a hidden layer of ANN was selected for 10, 20, and 30, the maximum iteration value was considered as 15, 20, 25, 30, 40, and 50 and the swarm sizes as 5, 10, 20, 30, and 40. Secondly, after the initial analysis and trial and error, the best developed model was constructed with a structure shown in Table 2. Finally, the developed model was implemented for determining the best answer with 2 parameters. The obtained result of the best cost in each iteration is shown in Figure 6 for 2 parameters,

PSO Modelling
The main goal of PSO is to train the artificial neural network for determining the feature selection of confirmed cases of COVID-19, and the reduction of them under the highest relationship between several independent variables and the dependent variable. For this purpose, three notable climate parameters, namely daily average temperature, relative humidity, and wind speed, and one urban parameter (population density × positive cases up to 14 days before), were considered as input data set, and confirmed cases of COVID-19 were considered as the output dataset. It is worth mentioning that the 4 input parameters are evaluated and reduced to 2. Firstly, before modeling, the control parameters of an algorithm should be selected. There are no specific rules, and most of them are considered based on the experts' opinions and previous studies [61,82]. Hence, a number of different modeling are done to determine an appropriate value for control factors, for instance, the size of a hidden layer of ANN was selected for 10, 20, and 30, the maximum iteration value was considered as 15,20,25,30,40, and 50 and the swarm sizes as 5, 10, 20, 30, and 40. Secondly, after the initial analysis and trial and error, the best developed model was constructed with a structure shown in Table 2. Finally, the developed model was implemented for determining the best answer with 2 parameters. The obtained result of the best cost in each iteration is shown in Figure 6 for 2 parameters, respectively. In fact, the best cost in each iteration shows the performance function of the algorithm depends on the values of error in each iteration of modelling. It should be noted that we consider the mean squared error (MSE) for evaluation of the performance, and 70% of data set were considered for training, and the rest were considered for validation (15%) and testing (15%) [99].   According to Figure 6, it is evident that after the sixth iteration with 0.00133, the best cost was reached, and the model achieves a worthy convergence, and it was fixed to the end of the iteration. In addition, the model reduced the number of parameters from 4 to 2 that, in fact, reveal that the urban parameter and relative humidity were the priority of the model.

DE Modelling
As mentioned earlier, the DE algorithm is used for training the artificial neural network to apply the feature selection with the four climate parameters, namely daily average temperature, relative humidity, and wind speed, and one urban parameter (population density × positive cases up to 14 days before) considered as the input data set, and the confirmed cases to COVID-19 considered as an output dataset. At first, the control parameters of DE algorithm are determined to find the optimum weights and biases of ANN model that can converge faster and accurately. For this purpose, similar to PSO model, the crossover probability coefficient was selected as 0.2, and other parameters were determined by trial and error method from previous studies and experts' opinions [87,88]. In addition, the datasets for modeling were randomly divided into several subsets, including 70% for training and the rest for validation (15%) and testing (15%) [99]. Hence, population sizes of algorithm of 5, 10, 20, 30, and 40 were selected, and the maximum iteration was used with a range of values equal to 15, 20, 25, 30, 40, and 50. The values of 10, 20, and 30 were chosen for the size of the hidden According to Figure 6, it is evident that after the sixth iteration with 0.00133, the best cost was reached, and the model achieves a worthy convergence, and it was fixed to the end of the iteration. In addition, the model reduced the number of parameters from 4 to 2 that, in fact, reveal that the urban parameter and relative humidity were the priority of the model.

DE Modelling
As mentioned earlier, the DE algorithm is used for training the artificial neural network to apply the feature selection with the four climate parameters, namely daily average temperature, relative humidity, and wind speed, and one urban parameter (population density × positive cases up to 14 days before) considered as the input data set, and the confirmed cases to COVID-19 considered as an output dataset. At first, the control parameters of DE algorithm are determined to find the optimum weights and biases of ANN model that can converge faster and accurately. For this purpose, similar to PSO model, the crossover probability coefficient was selected as 0.2, and other parameters were determined by trial and error method from previous studies and experts' opinions [87,88]. In addition, the datasets for modeling were randomly divided into several subsets, including 70% for training and the rest for validation (15%) and testing (15%) [99]. Hence, population sizes of algorithm of 5, 10, 20, 30, and 40 were selected, and the maximum iteration was used with a range of values equal to 15, 20, 25, 30, 40, and 50. The values of 10, 20, and 30 were chosen for the size of the hidden layers of ANN. After the initial evaluation, the optimized model selected with the values of 5, 15, and 30 for the hidden layer, population size, and the maximum number of iterations, respectively. The process of optimization based on iterations is presented in Figure 7, which shows that the process reached the desired precision level of best cost with the value of 0.0014 from the 8th iteration, and it was fixed from the 8th to the 30th iteration. The developed model by DE algorithm determined the urban parameter and relative humidity as priorities of prediction in this research. More discussions regarding the comparison of algorithms' performances and the priorities of the parameters in the forecast will be given in the following section.

Discussion
In this research, two machine learning techniques of artificial intelligence, namely ANN based on the PSO algorithm and DE algorithm, were used for prioritizing climate and an urban parameter based on the feature selection process. Both developed models based on PSO and DE algorithms selected the urban parameters and relative humidity in the feature selection process, and the reduction of number of parameters. In fact, at first, these models calculated and achieved the best relationships between the output and all inputs based on the values of best cost, then the models considered the features as a binary choice, and finally they could find out that the best values of best cost with these two features are very close to the values of the best cost of all features. The developed model by the PSO algorithm achieved a suitable convergence with good accuracy in the sixth iteration, while the developed model by DE algorithm reached an appropriate convergence in the eighth iteration. Consequently, it is clearly seen that, although there is no salient difference between the performances of the two models, the model developed by PSO algorithm has a better performance in this specific problem, based on the best cost value and the rate of convergence.
Our results are in good agreement with those of Chan et al. [32] about the important role of humidity in another type of coronavirus, SARS, and of Pirouz et al. [28], that identified relative humidity as the higher-impact weather parameter.
For further evaluation, the obtained results were validated by multivariate linear regression (MLR) technique and partial least squares regression (PLSR). For this, since for all four case studies, the correlations can be based on the two variables of humidity and urban parameter, the simplified final MLR and PLSR models are as follows: • Prediction of MLR y = 169.96 + 0.000284 X 1 + 0.59 X 2, R2 = 0.76 The developed model by DE algorithm determined the urban parameter and relative humidity as priorities of prediction in this research. More discussions regarding the comparison of algorithms' performances and the priorities of the parameters in the forecast will be given in the following section.

Discussion
In this research, two machine learning techniques of artificial intelligence, namely ANN based on the PSO algorithm and DE algorithm, were used for prioritizing climate and an urban parameter based on the feature selection process. Both developed models based on PSO and DE algorithms selected the urban parameters and relative humidity in the feature selection process, and the reduction of number of parameters. In fact, at first, these models calculated and achieved the best relationships between the output and all inputs based on the values of best cost, then the models considered the features as a binary choice, and finally they could find out that the best values of best cost with these two features are very close to the values of the best cost of all features. The developed model by the PSO algorithm achieved a suitable convergence with good accuracy in the sixth iteration, while the developed model by DE algorithm reached an appropriate convergence in the eighth iteration. Consequently, it is clearly seen that, although there is no salient difference between the performances of the two models, the model developed by PSO algorithm has a better performance in this specific problem, based on the best cost value and the rate of convergence.
Our results are in good agreement with those of Chan et al. [32] about the important role of humidity in another type of coronavirus, SARS, and of Pirouz et al. [28], that identified relative humidity as the higher-impact weather parameter.
For further evaluation, the obtained results were validated by multivariate linear regression (MLR) technique and partial least squares regression (PLSR). For this, since for all four case studies, the correlations can be based on the two variables of humidity and urban parameter, the simplified final MLR and PLSR models are as follows: • Prediction of MLR y = 169.96 + 0.000284 X 1 + 0.59 X 2, R2 = 0.76 • Prediction of PLSR y = 193.26 + 0.00028 X 1 + 0.257 X 2, where X1 is the urban parameter, and X2 is the relative humidity. Therefore, the analysis shows that the prediction of confirmed cases of COVID-19 could be made by using two factors of relative humidity and urban parameter (population density X positive cases up to 14 days before). The trend of confirmed cases in four regions is shown in Figure 8, and the daily relative humidity in Figure 9. According to Figure 8, it is evident that the number of infections in all regions were equal at the beginning, but in Lombardy with the highest density increased more. Analysis of relative humidity exhibits that the fluctuations of humidity percentage was the highest in Lombardy, and then in Piedmont, as well as the number of confirmed cases that in both case studies show daily fluctuations.   In addition, the analysis determined that even in one climate type, as the climate type of all four regions is humid subtropical, there might be other essential variables such as population density that affect the final results. In addition, the differences in the fluctuation of relative humidity in one type of climate as an influential parameter in the number of confirmed cases of COVID-19 show that for other types of climates, the selection of different case studies is a necessity.
Finally, it is worth mentioning that the results of this research are derived explicitly for the studied regions in the north of Italy with a humid subtropical climate, and they should not be used directly in other countries. For possible future work referring to other countries, it is recommended to see the effectiveness of the other parameters, such as different climate conditions and urban parameters. In addition, the outdoor humidity could affect the indoor humidity, which might be another important parameter for future analysis. In addition, it might be worth studying whether the use of other machine learning methods may improve our results.  In addition, the analysis determined that even in one climate type, as the climate type of all four regions is humid subtropical, there might be other essential variables such as population density that affect the final results. In addition, the differences in the fluctuation of relative humidity in one type

Conclusions
With regard to the immense importance of sustainable development to improve the conditions of today's and future generations, evaluating its challenges and obstacles has considerable effects on government decisions. Hence, in this research, the pandemic novel coronavirus infection (COVID-19) as a new challenge of sustainable development was investigated, using two machine learning techniques. For this purpose, we evaluated several notable climate parameters and an urban parameter, in order to find a relationship between them and the confirmed cases of COVID-19. For this, two artificial intelligence techniques, including ANN based on the PSO algorithm and DE algorithm, were used to predict the confirmed cases of COVID-19 with highly acceptable degrees of accuracy and robustness, in order to prioritize and reduce input parameters. The obtained results indicated that both developed models by PSO and DE algorithms were able to select the urban parameter and relative humidity from other effective parameters. In addition, although the two developed models had the high capability in predictive process with best costs equal to 0.0013 and 0.0014 for the PSO and DE algorithms, respectively, the developed model by PSO algorithm was a more efficient approach, compared to the other predictive method. Finally, the results were tested by a MLR and PSLR, which described the correlation between the urban parameter and relative humidity and the confirmed cases of COVID-19, with R 2 equal to 0.76 for both regression models. For future studies, it is recommended to focus on other algorithms, other parameters for proper feature selections, and other types of climate.

Appendix A
As, the graphs show, neither X4 nor X4new reached a plateau. Thus, the mentioned method for X4, using the shifted sum of 14 days previously that is in line with the COVID-19 incubation period, might be more exact than using daily confirmed cases.  Table A5.