Given the analysis of many different factors, this section is structured into different parts to facilitate reading and comprehension.
Variables for COVID-19 rates and detected temporality
During the time this analysis was carried out, PCR tests for detecting positive cases of COVID-19 were only used for those people who presented symptoms compatible with the disease. According to a later prevalence study, SARS-CoV-2 in Spain (ENE-COVID) , “One in three infections seems to be asymptomatic, while a substantial number of symptomatic cases remained untested”. Thus, the confirmation of cases during the study period analyzed was carried out in large part among those who presented symptoms with a certain level of severity. This would explain the high percentage of admissions (47.1 percent of all detected cases) and of deaths in Madrid in relation to the incidence of the disease (11.9%) and in relation to data from other European and Spanish cities , which was almost triple that established by the WHO, which indicated a percentage of around 4% for deaths and diagnoses .
This severity of diagnosed cases would also explain the existence of the association in lag 0 between the incidence and rates of hospital admission and even ICU admission. That is to say, these were people who were diagnosed with the disease and were admitted due to its severity to the hospital and even the ICU on the same day of diagnosis. The lags found between the incidence rate and hospital admissions in lags 6, 7 and 10 (at short and medium term) are also compatible with the time that took place between the occurrence of symptoms and worsening of symptoms and arrival at the hospital [20, 21]. On the other hand, the lag times found between incidence, admission in the ICU and death were similar to those expected in the evolution of COVID-19 in Spain .
The relationship with air pollution variables
The time evolution of the concentrations of the pollutants analyzed, PM10 and NO2, clearly showed a trend of decline, which could be explained by the restrictions on mobility that took place in Madrid after the declaration of the state of alarm on March 14. The decline observed in the concentrations of the pollutants in the last week of the study, compared to the first, were 34.5% for PM10 and 66.8% for NO2, which shows the marked anthropic origin of the NO2 in Madrid and the important natural origin component (including processes of resuspension) of PM10 concentrations . “Peaks” in PM10 can be observed in Fig. 2, related to the advection of particulate matter of Saharan origin during these dates . The declines in the concentrations of PM10 and NO2 are similar to those found in other cities in Spain during the confinement [27, 28].
Table 3 shows the existence of an association between average daily concentrations of PM10 and NO2 and the COVID-19 incidence rate, the rate of hospital admissions and ICU admissions. There is even an association with p-value below 0.05 detected between PM10 and the death rate.
There are two biological mechanisms that could explain the existence of these associations . On one hand, is clear that air pollution affects human health . On the other hand, Pothirat et al.  investigated the association between daily average seasonal air pollutants and daily mortality of hospitalized patients and community dwellers, as well as emergency and hospitalization visits for serious respiratory, cardiovascular, and cerebrovascular diseases. It was found that air pollutants were associated with higher mortality of the hospitalized patients and community dwellers, with varying effects on severe acute respiratory, cardiovascular, and cerebrovascular diseases. In relation to the age of the individuals who are affected by outdoor air pollution—with particular attention to the respiratory system—those of elderly ages are one of the most sensitive groups [32,33,34]. That is to say that air pollution worsens the same type of pathology in the same vulnerable age groups impacted more severely by SARS-Cov2 .
The other mechanism is based on the fact that air pollution weakens the immune system in the short term. There is growing evidence that pollution can induce oxidative stress, resulting in the production of free radicals, which in turn, may damage the respiratory system, reducing the resistance to viral and bacterial infections . Air pollutants could influence the immune system and affect its ability to limit the spread of infectious agents like the Respiratory Syncytial Virus (RSV) [36, 37]. On the other hand, Zhao et al.  has established that short-term exposure to PM2.5 could act on the balance of inflammatory M1 and anti-inflammatory M2 macrophage polarizations, a fact that might be involved in air pollution-induced immune disorders and diseases.
Furthermore, in the case of PM concentrations, there is another possible mechanism related to the transmission of the virus. According to a study carried out in Lombardia , traces of RNA of SARS-CoV-2 were found in samples of PM measured both in industrial and urban settings in Bergamo. The authors suggest that the aerosol particles that contain the virus of between 0,1 and 1 µm can travel further when they group together with pollutant particles of up to 10 µm (PM10), given that the resulting particle is larger and less dense a respiratory droplet, which could increase the time it remains in the atmosphere. However, other research also carried out in Italy suggests the opposite in terms of the possible transmission of the virus via material particles . Other studies carried out in Spain on days with an increase in PM from Saharan dust support this last hypothesis .
The lags in which associations were established with the different disease indicators in our analysis, both for PM10 and for NO2, are compatible with both the needed incubation times of the virus (of between 2 and 12 days ) and the different processes of worsening of the disease . In all cases a logical offset was observed in the lags from the time of case detection to death in the case of PM10. The association with p-value below 0.05 observed in the short term (lags 0 and 5) for NO2 with the incidence rate, hospital admission rate and ICU admission rate, is noteworthy. We understand that such a short-term association cannot be justified by the damage of NO2 to the immunological system in the short-term and supporting infection mechanisms, as has been reported, but rather by the worsening of prior respiratory and cardiovascular pathologies. The concentrations of NO2 in Madrid are related to both an increase in mortality due to circulatory causes [41, 42] and respiratory causes [41, 42], as well as to hospital admissions , especially for people over age 75 .
The two-variable models that include PM10 and NO2 together with the dependent variables related to COVID-19 analyzed show more robust associations for NO2 than for PM10 in all cases. Prior studies carried out in Madrid related to the impact of both PM10  and to NO2  on all-cause daily mortality, show greater RR for NO2 RR: 1.012 (95% CI 1.010, 1.014) compared to PM10 RR: 1.009 (95% CI 1.006, 1011). While these RR slightly overlap, this greater risks of NO2 could account for the fact that NO2 shows a more robust association in the two-variable models that combine both primary pollutants with a high collinearity (in the period analyzed the correlation between both pollutants is 0.519 with p < 0.0001) (Table 2).
The results of the models of COVID-19 rates concerning the association of the average daily concentrations between 0 and 14 days prior (shown in Table 4) show behavior that is similar to what was described earlier for daily values. It should be noted that the short-term association of NO2 disappeared, which is in accordance with the hypothesis of the acute effect of exacerbation of circulatory and respiratory symptoms described for the daily values. Furthermore, in general, the lags in which associations were established for NO2 and for PM10 were more long-term, which is compatible with less acute effects. It should be noted that in this case an association did appear between PM10, NO2 and mortality due to COVID-19.
The association of the meteorological variables (temperature and absolute humidity)
Maximum daily temperature (Tmax) showed more robust behavior compared to the variables related to COVID-19 rates in the modeling process than average and minimum daily temperatures, thus it was selected as the variable for the analysis. There was a greater number of associations with p-values below 0.05 and greater statistical significance. The finding that Tmax was more closely related to COVID-19 rates than Tmin may be counter-intuitive. One explanation could be that Tmin is usually recorded around 7 a.m., a time when very little human activity occurs outdoors, while Tmax is usually recorded at around 4 p.m. .
The increasing trend in maximum daily temperature and the increasing trend in absolute daily humidity (AH) shown in Fig. 2b, c is coherent with climate conditions that are usually present in Madrid during the period analyzed .
The results shown in Table 3 indicate the existence of an association with p-value below 0.05 for both Tmax and AH. The relationship was negative for all of the all indicators analyzed, except for mortality, for which there was no detected association. That is to say, low and humid temperatures are related to higher incidence rates. In vitro studies have shown that SARS-CoV is inactivated at both higher temperatures and humidities , the results founded are in line.
On the other hand, the serological study of the prevalence of SARS-CoV-2 in Spain (ENE-COVID)  indicates that a lower prevalence of COVID-19 in Spain was produced in coastal regions that, during the time of the study and in general, are characterized by higher temperatures and humidity than the interior areas of the Peninsula .
Seasonal respiratory viruses are transmitted through aerosols, large respiratory droplets, or by direct contact with fomites . Lower temperatures could also be an important factor that favors the diffusion of the SARS-CoV-2 in temperate regions [13, 46]; in the same way, relatively low humidity could also contribute to greater transmission of the new virus . Other studies show results that are similar to what we found in our analysis, in terms of humidity and the incidence of COVID-19 transmission [49,50,51,52].
On the other hand, the results of our study show that higher temperatures correlates with lower incidence and severity of the disease. This may be compatible with a protective association of the temperature. Similar results have been found in other studies carried out in different parts of the world, including China [6, 53], the United States  and Spain , even though the evidence of the role of temperature on the incidence of the virus is still unclear . The results of some studies are contradictory to what we describe here , and still other studies carried out in different parts of the U.S. are inconclusive.
Extreme temperatures can also affect morbidity and mortality due to different causes [56, 57]. However, the temperatures registered during the study period are far from cold spells or heat wave temperatures  for the city of Madrid. Thus the expected association of temperature would be to facilitate or make more difficult the transmission of the virus. This result agrees with the lags in which the associations were found, shown in Table 3 for daily values and in Table 4 for 14-day averages. It can be observed that in neither of the two cases are there short-term lags (lag 0), but there are lags in the values similar to the incubation period of the virus  and with the worsening of the disease .
The association of AH is predominant in the two-variable models compared to Tmax, both for daily values as well as 2-week averages. This result agrees with what was found in a study of eight U.S. cities  which concluded, “Humidity was observed as the best predictor for the coronavirus outbreak followed by temperature“.
Results of the all variables models (pollution and meteorology)
In general, the behavior of the models with all variables was similar to that of the two-variable models (Table 4), both in terms of daily values and of average values, with a predominant association with concentrations of NO2 over PM10 and of AH over Tmax.
The higher RR values obtained for the 14-day average values as compared to daily values (Table 5), especially for NO2, show that it is not the higher daily levels of pollution that most correlated the incidence and severity of the disease; rather it is the average values. This supports that the preventive public health measures related to pollution and COVID-19 must be structural and aimed at decreasing the pollution in the city, as opposed to conjectural measures to avoid episodic situations.
The RR of these environmental factors are small (in terms of relative risk) and, by themselves, cannot explain the behavior of the incidence and severity of COVID-19, which is explained by social distancing and public health measures not considered in our analysis, this assumption is similar to the findings founded in the First report of the WMO COVID-19 Task team . Only RR related to AH are relevant, but the low mean values corresponding to AH (as can been observed in Table 1), makes its contribution to the COVID-19 variables not so high.
Strengths and limitations of this study
One of the principal strengths of this study is the longitude of the series used. Although the series was of 212 days, or 4 months, it is longer than the majority of studies carried out to date. The duration of the series allowed for carrying out generalized linear models with control variables such as trend, seasonality and the autoregressive component. In addition, it also allows for models with all the variables that include both meteorological and pollution-related variables, which is a significant improvement compared to the many investigations carried out to date in this field, that have used two variables correlations corresponding to series of 30 days.
Another strength of this study is the robust nature of the findings, first between the lags in which associations were established, which are coherent with biological mechanisms that link the different variables analyzed and the incidence and severity of the disease with the period of incubation and the course of the disease. This analysis was possible thanks to the daily data on COVID-19 variables as opposed to accumulated data or data averaged over time.
In addition, not only was a single association found between an indicator and the disease, rather there were four indicators with coherent results between them. This robustness extends as well to the relationship between the two variables and models with all variables and to the results obtained for the daily as well as averaged series. On the other hand, not only daily values are used but also averages of 0–14 days, which eliminates the weekly seasonality that exists in the dependent and independent variables. The longitude of the series is also, paradoxically, a weakness. Only a 4-month period was considered, without accounting for the complete annual variation.
About the study design, the analysis is a descriptive observational study. Specifically, it is a population-based ecological study. Generally, in epidemiological studies it constitutes a level of basic evidence. This type of study does not allow a causal relationship; but it constitutes useful exploratory approach . Another limitation of the study consist in the lock-down period, this period was completely anomalous in terms of the decrease in air pollutants levels. This determines people exposure, which was different from usual situation. For example, in the analysis conducted, the impact of ozone concentrations on health was not included, due to previous analysis performed in Madrid city  have concluded that the threshold for ozone values from which effects on health are detected is over 60 µg/m3 (daily average). This value was not reached any day in the study period.
On the other hand, the conditions under which the data were obtained correspond to a period in which the declaration of cases only occurred when people already presented important symptoms of the disease.
The study conducted by the authors corresponds to an ecological time series design, with all the epidemiological limitations inherent in this type of study, especially the ecological fallacy. Both of the aforementioned points show the need for prudence in extrapolating the results to other situations in time other than those corresponding to the time this study was carried out. Nevertheless, this study could be evaluated with other methodologies that could complement the analysis carried out, a methodology such as propensity score matching , even a cohort study could help to improve the quality of observed findings. However, due to the immediacy of the COVID-19, there has not been enough time to carry out a follow-up study to guarantee better scientific evidence. On the other hand, the time series analysis methodology used has been previously implemented in Spain, for example, studying the relationship between COVID-19 and environmental variables such as traffic noise  and analyzing the effect of particulate matter from Sahara dust in the incidence of COVID-19 . In addition, there are other examples using time series design to analyze the association between COVID-19 and air pollution carried out in Italy , France , United Kingdom , China , and Latin America . Finally, ecological studies are a very efficient tool for making decisions in public health at the short-term  and very useful in the context of the current pandemic to identify environmental risks factors. Later studies will carry out a more in-depth and joint analysis of the impact of climate variability, air pollution and other factors that are extrinsic to the transmission of COVID-19.