General assessments of the air pollution-COVID-19 nexus

Coccia [Reference Coccia62] collected data on 55 Italian cities which are provincial capitals and suggested that the diffusion of COVID-19 in cities with high levels of air pollution generated higher numbers of COVID-19 related infected individuals and deaths. More specifically, results reveal that the number of infected people is significantly higher in cities where the limits of PM₁₀ or ozone are exceeded over 100 days per year and the average wind speed and temperature level are lower. In Magazzino et al. [Reference Magazzino, Mele and Morelli63], the authors used ANNs experiments in an ML framework on Brazilian series. They showed that more intensive use of renewable energy could generate a positive GDP acceleration, which in turn, could offset the harmful pollution-COVID-19 association. Using a slightly different approach, Magazzino et al. [Reference Magazzino, Mele and Sarkodie39] inspected the case of New York state using city-level daily data and two ML experiments. PM_2.5 and NO₂ were found to be the most significant pollutant agents responsible for facilitating COVID-19 attributed death rates. Going one step further, Mele et al. [Reference Mele38] estimated that the threshold values of NO₂ connected to COVID-19 range between 15.8 μg/m³ for Lyon, 21.08 μg/m³ for Marseille and 22.9 μg/m³ for Paris. Finally, these results are in line with those of Travaglio et al. [Reference Travaglio36] for England; Bashir et al. [Reference Bashir34] for California and a set of Italian examinations: Zoran et al. [Reference Zoran64] for the city of Milan; Setti et al. [Reference Setti35] for eight Italian regions; Conticini et al. [Reference Conticini, Frediani and Caro65] for northern Italy; Fattorini and Regoli [Reference Fattorini and Regoli66] for 71 Italian provinces; and Frontera et al. [Reference Frontera67] for the major Italian regions. On a more global scale, this corroborates the findings of Razzaq et al. [Reference Razzaq68] for the top 10 affected states of the U.S., but also Vasquez-Apestegui et al. [Reference Vasquez-Apestegui69] for 24 districts of Lima (Perù). Finally, Sarkodie and Owusu [Reference Sarkodie and Owusu70] demonstrated that high temperature and high relative humidity reduce COVID-19 cases, deaths and improve recovery using series covering 20 countries. Reciprocally, low temperature, wind speed, dew/frost point, precipitation and surface pressure prolong the activation and infectivity of the virus. At the city level, Sasidharan et al. [Reference Sasidharan71] designed a preliminary assessment on the linkage between short-term NO₂ concentration and COVID-19 cases and fatality rates for the case of London (UK). Based on data up to March 31^st 2020, the COVID-19 fatality rate was found positively correlated with short-term NO₂ pics. Nonetheless, Saez et al. [Reference Saez, Tobias and Barceló41] contrast with these studies as they showed that, although some mechanisms may explain this air pollution-COVID-19 dynamic, the spatial spread in Catalonia (Spain) might be more attributed to population interactions rather than a chronic immune sensitivity to this virus. Finally, the latest evidence on this channel can be found in Konstantinoudis et al. [Reference Konstantinoudis72] for England; Liu et al. [Reference Liu73] for California; Coccia [Reference Coccia74] for Italian regions; Coccia [Reference Coccia75] for a global sample of 160 countries.

With a slightly different approach, Haque and Rahman [Reference Haque and Rahman76] relied on linear regression models and concluded that high temperature and humidity are coupled with a significant reduce COVID-19 transmission reduction in Bangladesh. Such evidence is in line with those of Mele and Magazzino [Reference Mele and Magazzino40] who drew similar conclusions for India. Following this view, Rosario et al. [Reference Rosario77] highlighted that there is a substantial negative correlation between solar radiation and COVID-19 incidence in the State of Rio de Janeiro (Brazil), whereas negative inferences are indicated when looking at temperature and wind speed. A review on the association among meteorological factors, air pollution and COVID-19 can also be found in Magazzino et al. or Srivastava [Reference Srivastava78]. Table 1 summarises the main information of this novel literature.

Table 1. Previous air pollution-COVID-19 assessments, excluding the Chinese case

Source: our elaborations.

Notes: ‘Yes’ means that the existence of a significant association between air pollution levels and COVID-19 cases/mortality was established. ‘No’ indicates that no significant relationship was supported among indicators.

Studies On the air pollution-COVID-19 nexus in China

A few assessments have tackled the single case of China and associated findings suggested that metropolitan cities in China contribute significantly to higher mortality rates in China as many develop respiratory-related issues from exposure to polluted air. For instance, Shen et al. [Reference Shen79] argued that critical atmospheric pollution events were frequently observed during the strictest lockdown in Hubei. Zhang et al. [Reference Zhang80] applied a mathematical model with multiple datasets to estimate the transmissibility of the COVID-19 virus and the severity of the illness associated with the infection and how both were affected by unprecedented control measures. The analyses show that before 19^th January 2020, 3.5% of infected people were detected; this percentage increased to 36.6% thereafter.

Xu et al. [Reference Xu81] collected data on three cities in the Hubei province and supported that during February 2020, when the epidemic prevention and control actions were taken, the average concentrations of atmospheric PM_2.5, PM₁₀, SO₂, CO and NO₂ in the three cities were 46.1 μg m^–3, 50.8 μg m^–3, 2.56 ppb, 0.60 ppm and 6.70 ppb and were 30.1%, 40.5%, 33.4%, 27.9% and 61.4% lower than the levels in February 2017–2019, respectively. Going one step further, Yongjian compiled data on 120 Chinese cities ranging from 23^rd January to 29^th February 2020. A Generalised Additive Model (GAM) is applied on a framework and associated findings claimed evidence of a positive and significant association between PM_2.5, PM₁₀, NO₂ and O₃ concentrations with COVID-19 confirmed cases in this country, which is in line with Yao et al. [Reference Yao82, Reference Yao83] for the city of Wuhan (China). Finally, Gupta et al. [Reference Gupta84] collected data on nine cities in Asia (including three in China) and provided evidence supporting the existence of a correlating relationship between PM_2.5 and PM₁₀ and COVID-19-related deaths. A neighbouring conclusion can be found in Xie and Zhu [Reference Xie and Zhu85] who indicated that temperature has a positive linear relationship with the number of COVID-19 cases with a threshold of 3 °C in 122 cities from China. Nonetheless, no evidence supporting that case counts of COVID-19 could decline when the weather becomes warmer was provided. Table 2 outlines the main information of this Chinese-related literature.

Table 2. Previous air pollution-COVID-19 assessments in China

Source: our elaborations.

Notes: ‘Yes’ means that the existence of a significant association between air pollution levels and COVID-19 cases/mortality was established. ‘No’ indicates that no significant relationship was supported among indicators.

Lastly, Kucharski et al. [Reference Kucharski86] provided specific analysis of the city of Wuhan but excluded pollution series from their framework. Instead, they fitted a stochastic transmission dynamic model to four datasets and underlined that in locations with similar transmission potential to Wuhan in early January 2020, the likelihood that the infection spreads within the population reached 50% if at least four independent COVID-19 cases are introduced within the total sample. In Sarkodie and Owusu [Reference Sarkodie and Owusu87], the authors revealed that the effect of confirmed cases on the novel coronavirus attributable deaths is heterogeneous across the 31 Provinces/States in China. More specifically, an increase in confirmed cases by 1% increases coronavirus attributable deaths by ~0.10%–~1.71% (95% CI). All in all, further neighbouring COVID-19-related investigations can be found in Balsalobre-Lorente et al. [Reference Balsalobre-Lorente88] who examined the effects of economic and social isolation as dimensions of globalisation and brought fresh evidence on the effect of the isolation phenomenon due to the COVID-19 outbreak on the Chinese economic performance. In the same vein, Alola et al. [Reference Alola, Alola and Sarkodie89] employed the empirical Markov switching regression approach to identify the first causal channels among the US financial stress situation resulting from the effects of COVID-19 daily deaths, COVID-19 daily recovery and the global economic policy uncertainty.

Data Collection and empirical strategy

To assess the relationship among COVID-19 deaths, air pollution and economic growth in China (Hubei area), we collected daily data at a city level for the period from 20 January to 31 July 2020.

The study here focuses on a case study of the Chinese province of Hubei, the first area in the world to experience a rapid increase in confirmed cases of COVID-19 and related deaths. Sources of data are the Chinese Center for Disease Control and Prevention (http://www.chinacdc.cn/) for numbers of infected people and deaths; the Hubei Environmental Protection Agency (http://sthjt.hubei.gov.cn/) for levels of air pollution; and the institutional website of the three main cities of Hubei province for per capita economic growth series (en.yichang.gov.cn; en.xiangyang.gov.cn; en.whuan.gov.cn).

To generate a daily time-series relating to the variable of economic growth, we used the monthly and standardised data for the number of days. This procedure is suitable for an ML process. In fact, the machine interprets the data not as a time series, but as an aggregate of data. Each variable was transformed into logarithms (ln), first differences (d), squared (s) and logarithmic differences (d.ln). Thus, we have a dataset with 8100 observations. The large number of observations justify the choice of an experiment in DL.

ML studies have been an exponential growth in the last years, receiving interest from industry, academia and popular culture. These are driven by breakthroughs in ANNs, a set of techniques and algorithms that enable computers to discover complicated patterns in large datasets. Feeding the breakthroughs is the increased access to data (‘big data’), user-friendly software frameworks and an explosion of the available computing power, enabling the use of NN that is deeper than ever before [Reference Lundervold and Lundervold90].

Recently, due to the optimisation of algorithms, the improved computational hardware and access to a large amount of imaging data, DL has demonstrated indisputable superiority over the classic ML framework. DL is a class of ML algorithms that uses ANN architectures that bear resemblance to the structure of human cognitive functions. It is a type of representation learning in which the algorithm learns a composition of features that reflect a hierarchy of structures in the data [Reference Chartrand91].

Following Gardner and Dorling [Reference Gardner and Dorling92], Magazzino et al. [Reference Magazzino, Mele and Schneider93–Reference Magazzino95] and Mele and Magazzino [Reference Mele and Magazzino96] we performed a DL experiment. NNs work in parallel and are, therefore, able to process a lot of data simultaneously and autonomously.

On the contrary, in standard or econometric statistical processes, each data is treated individually and/or in time series. Even though each neuron is relatively slow, parallelism partly explains the faster speed of the brain in performing tasks that require the simultaneous processing of a large number of data. In essence, it is a sophisticated statistical system with excellent noise immunity; if some units of the system were to malfunction, the network as a whole would have reduced performance but would hardly encounter a system crash. To do so, we used Oryx, a software that emerged as a power tool able to identify and analyse causal linkages in a multivariate setting. Adequate applications on neighbouring topics can be found in Didelez et al. [Reference Didelez, Kreiner and Keiding97], Sparks et al. [Reference Sparks98] and Gärdenfors and Lombard [Reference Gärdenfors and Lombard99].

The features of an ANNs model are the following:

1. (a) the development of the ‘neuron system’ is distributed over many elements. In other words, many neurons do the same thing;

2. (b) an address identifies each data of the algorithm used (a number), which is used to retrieve the knowledge necessary to perform a certain task;

3. (c) ANNs, unlike standard econometric models and their software, do not have to be programmed to perform a task. ANNs learn independently, based on experience or with the help of an external instructor.

The use of ANNs, as a subset of the ML tools, follows a precise implementation scheme for building the network and obtaining results. In Figure 1 we synthesised the process.

Fig. 1. The ANNs process.

Source: our elaborations in YeD.

Mathematical process on NNs

In what follows is described the theoretical process of the NNs experiments.

(1)$${\rm input}\;\to x\in R^D$$

(2)$${\rm output}\;\to y\in R^J$$

(3)$${\rm output\;vector\;in}\ n{\rm \;levels}\to \;\sigma ^l\in R^{Ml}\;\,{\rm with\ each\ layer}\,1, \;2 \ldots , \;L$$

(4)$${\rm weight\;matrix}\;\to \;W^l\epsilon R^{Ml\otimes Ml-1}\,{\rm with}\,M_0 = D; \;\;M_L = K$$

(5)$${\rm bias\;vector}\to u^l\in R^{Ml}$$

(6)$$\gamma = ( W^l\epsilon\, R^{Ml\otimes Ml-1}) + u^l\in R^{Ml}$$

(7)$$\delta ({\cdot} ) \colon R\to R$$

Our NN can be written as:

(8)$$f( {x, \;\gamma } ) = \sigma ^l$$

(9)$$\sigma ^l = \delta ( {\;a^l} ) = \delta ( {W^l\sigma^{l-1} + u^l} ) \,{\rm where}\,a^l = W^l\sigma ^{l-1} + u^l$$

(10)$$u^0 = x$$

The activation functions can be linear or nonlinear, with L = n. In the first case:

(11)$$f( {x, \;\;( W^l\epsilon\; R^{Ml\otimes Ml-1}} ) + u^l\in R^{Ml} = \sigma ^n = \delta ( {W^n\sigma^1} ) = \delta ( {W^n\delta ( {W^1x} ) } ) $$

If δ is a linear function → δ(u ^l) = k _lu ^l where $f( {x, \;\gamma } ) = k_n( {W^nkx + \vartheta_1} ) + \vartheta _n = \hat{W}x + \hat{u}$

If we choose, in an arbitrary way, to use a non-linear activation function, we have:

(12)$$\delta ( x ) = \displaystyle{1 \over {1 + {\rm exp}( {-x} ) }}$$

(13)$${\delta }^{\prime} = \delta ( x ) ( {1-u( x ) } ) $$

(14)$${\rm tanhtan}h{\rm \;}( x ) = \displaystyle{{e^x-\;e^{{-}x}} \over {e^x + e^{ + x}}}$$

(15)$${\rm tan}h^{\prime}( x ) = 1-{\rm tan}h^2( x ) $$

Thus, with rectified linear unit, we have:

(16)$${\rm Relu}( x ) = \{ x\;{\rm for}\;x > 0\;0\;{\rm for}\;x < = 0\;$$

In our NN, MSE will be:

(17)$${\rm MSE}( \tau ) = \displaystyle{1 \over {2N}}\mathop \sum \limits_{n = 1}^N {\rm \Vert }f( {x_n, \;\;\tau } ) -t_n{\rm \Vert }_2^2 $$

In (17):

(18)$${\rm \Vert }f( {x_n, \;\;\tau } ) -t_n{\rm \Vert }_2^2 = ( l_{2, n}) ^2\to {\rm \Vert }V{\rm \Vert }_2^2 = \mathop \sum \limits_{k = 1\;or\;n}^n V_k^2 $$

Now, the Log-Likelihood (LL) will be:

(19)$$LL[ {x_n} ] = \displaystyle{1 \over N}\mathop \sum \limits_{n = 1\;or\;n = n}^N {\rm log}P\;( {x_n} ) $$

Therefore, after uploading the dataset in Oryx, we adapted the data series to an ML process through logarithmic and differential transformations. In fact, the higher the volume of data, the greater the capacity of analysis of the automatic intelligence system. The values are then normalised through the training selection procedure, which also begins a first test phase. In this phase, we evaluate the presence of omitted variables or outliers, which might cause false values of the NN. Subsequently, starting from the results obtained with the first test, we choose the suitable number of hidden neurons that are an integral part of the network. The next step is to launch the algorithm to create the NN. The result obtained is carefully analysed and we verify the precision and generalisation of the obtained network.

Then, we can proceed with the generation of a multivariate NN by targeting the number of deaths caused by COVID-19. We try to verify if the process of economic growth – connected to the pollution levels – represents a random acceleration of deaths from COVID-19. The following inputs are used: economic growth (GDP_p, lnGDP_p, dGDP_p, sGDP_p and d.lnGDP_p); pollution (PM2.5, lnPM2.5, dPM2.5, sPM2.5, d.lnPM2.5, PM10, lnPM10, dPM10, sPM10, d.lnPM10, CO2, lnCO2, dCO2, sCO2, d.lnCO2). The target are COVID-19 deaths (Deaths, lnDeaths, dDeaths, sDeaths, d.lnDeaths).

Once the NN has been built and the levels of inputs vs. targets calculated, we test the result through a model of relationships between variables via the Adaptive moment estimation (Adam) optimisation algorithm. In this way, two different estimation models are tested.