Environmental drivers of influenza A and B: causal analysis and forecasting

Abstract

Background

Influenza is a globally important acute respiratory infectious disease, with types A and B being the most prevalent in humans. Both circulate annually but differ in timing, duration, and severity of epidemics. Understanding the environmental factors that influence influenza A and B provides new insights into effective prevention and management.

Method

Weekly influenza surveillance data in Korea (2016–2023) were analyzed to quantify the causal influence of environmental factors, include meteorological factor: temperature, rainfall, wind speed, humidity, sunshine; air pollution factor: SO₂, CO, O₃, NO₂, PM(Particulate Matter)10, and PM2.5 on influenza A, B, and ALL (all influenza cases) using four causal inference methods: granger causality (GC), convergent cross mapping (CCM), partial cross mapping (PCM), and general model-based causal inference (GOBI) methods. Based on important factors identified by these methods, we constructed a seq2seq prediction model aligning environmental factors as causes and influenza as the outcome. To evaluate factor importance, we applied the causal importance score (CIS), which integrates prediction errors (MAE, RMSE, and R²) between models with all variables and those restricted to important factors.

Result

GC was effective for type A, CCM for type B, and GOBI for influenza ALL. NO₂, O₃, and SO₂ consistently identified as important across all types, while CO, PM10, and PM2.5 were significant for types A and B only. Temperature showed distinct causal patterns: influenza A was associated with short-term warming during cold seasons, whereas influenza B was related to low temperatures from late winter to early spring. Average relative humidity was significant across all types, and wind speed exhibited a negative causal effect. In delayed causality, influenza A showed persistent strong causal effects from CO and NO₂, influenza B from SO₂, and influenza ALL from wind speed, SO₂, and NO₂.

Conclusions

This study highlights that applying multiple causal inference methods can provide a more comprehensive view of influenza transmission dynamics, as each method uncovers different types of causal signals. Common pollutants such as NO₂, O₃, and SO₂ consistently act as dominant environmental drivers, whereas temperature and humidity shape subtype-specific seasonal behaviors. By integrating causal analysis with predictive validation, our findings bridge mechanistic understanding and practical forecasting, providing a data-driven foundation for improved influenza prevention strategies.

Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1186/s12889-026-28134-1.

Background

Influenza viruses (A, B, and C) primarily infect the respiratory tract, causing systemic symptoms such as fever, muscle pain, headache, and fatigue, as well as respiratory symptoms such as cough, sore throat, and sputum. They are generally transmitted through droplets [1–3]. Of the three types, types A and B mainly cause infection in humans, and type A has posed a significant public health burden through the 1918 H1N1, 1957 H2N2, and 2009 novel influenza pandemics [4–6]. Unlike measles, smallpox, and polio viruses, influenza viruses undergo continuous antigenic mutations and possess animal hosts that can lead to the emergence of new unpredictable subtypes. Therefore, it is important to identify the factors that affect the survival and transmission of the virus and develop effective prevention and control strategies [7–11].

[12–16]It has been widely reported that various environmental factors are involved in the transmission of influenza. Low temperatures enhance viral viability and influence human immune responses and behavior, facilitating transmission [17–20]. Rainfall can have an indirect effect by increasing the frequency of contact. Heavy rainfall has been identified as a factor triggering the movement of microbial particles within a short period [21–23]. A decrease in relative humidity provides conditions that enhance the stability and persistence of respiratory droplets and aerosols, thereby facilitating viral transmission [24, 25], and increased wind speed can reduce the risk of infection over a certain distance through the transport and dilution of droplets and aerosols [26]. Furthermore, day length and solar irradiance are closely linked to other meteorological variables such as temperature and humidity and are also considered background factors related to virus inactivation by ultraviolet light and human health indicators [27, 28]. Some studies have suggested that air pollutants may increase susceptibility to influenza infection by impairing the protective function of the respiratory mucosa [25].

In Korea, a correlation between these environmental factors and influenza outbreaks has been suggested using regression analysis [29, 30]. However, these studies primarily focused on correlation assessments, which are inherently distinct from causal inference [31, 32]. Numerous studies have investigated the relationships between environmental factors and influenza epidemics. A study analyzing laboratory-confirmed influenza case time series and environmental data by country using empirical dynamic modeling based on convergent cross mapping (CCM) identified absolute humidity as a key environmental factor for influenza and reported that it exhibited a U-shaped effect depending on the temperature level, with influenza increasing in temperate zones as the temperature increased and in tropical zones as the temperature increased [33]. In the United States, analyses of medical claims-based influenza data that integrated environmental, sociodemographic, mobility, and viral mutation variables using Granger causality, regression, and matching approaches revealed that seasonal epidemics are not driven by a single factor but by the simultaneous interplay of multiple factors [34]. Another study that applied a CCM-based state-space reconstruction technique to both a simulated epidemic time series and empirical influenza-like illness (ILI) data demonstrated that seasonality and synchronization effects can generate spurious causal signals unrelated to actual transmission dynamics, thereby warning of the limitations of using CCM in isolation for infectious disease causal inference [35]. Nevertheless, these studies did not account for the heterogeneous epidemic patterns of the influenza virus subtypes, limiting their ability to disentangle the causal pathways between influenza types A and B, which often peak at different times. Furthermore, most studies employed a single causal inference methodology, precluding the cross-validation of findings across approaches.

This study conducted causal inference regarding environmental factors explaining the heterogeneous epidemic patterns of different influenza types. Influenza types were classified into A, B, and all based on the virus, and environmental factors were categorized into temperature, rainfall, wind speed, humidity, sunshine, and air pollution (SO₂, CO, O₃, NO₂, PM10, and PM2.5). For causal inference, GC, CCM, PCM, and GOBI were utilized as representative methods, and the results of causal inference for each virus type were quantified using importance scores (CIS) to verify their validity through analysis. Additionally, four complementary causal inference methods were applied in parallel using different information to cross-verify direct and indirect causal effects and their time lags.

Methods

Data collection

The study area was the entire Republic of Korea. The study period spanned from week 36 of 2016 to week 35 of 2023. The primary data used were the influenza surveillance data provided by the Korea Disease Control and Prevention Agency. Thirty-six medical institutions nationwide participated in this study, covering all age groups. In this study, the number of influenza patients was defined as the number of laboratory-detected cases [36]. The environmental factors were classified into two categories, and each is further subdivided. Meteorological data were collected from publicly available data of the Korea Meteorological Administration. These data comprised daily data on 12 factors (temperature, rainfall, wind speed, humidity, sunshine, etc.) from 105 observation points nationwide [37]. Air pollutant data were released daily by AirKorea, and 6 factors (SO₂, CO, O₃, NO₂, PM10, and PM2.5) measured at 642 observation points nationwide were used [38].

Study design

This study aimed to comprehensively investigate the causal effects of 6 environmental factors-temperature, rainfall, wind speed, relative humidity, sunshine, and air pollution-on the occurrence of influenza (types A, B, and ALL) in Korea. To this end, we applied GC [34, 39, 40], which detects linear causal relationships between time series; CCM [33, 35, 41], which identifies nonlinear causality in complex dynamical systems; PCM [42], which extracts direct causality by removing disturbances in indirect paths; and GOBI [43], which alleviates synchronicity and indirect effect problems and distinguishes positive and negative causal directions. In GC, the F-statistic based on the difference in predictive power was used; in CCM and PCM, the cross and partial map coefficients obtained from state-space reconstruction were employed; and in GOBI, a model-based discriminant index was used to evaluate the strength and direction of causality [33–35, 39–43]. Based on the identified causal relationships, we developed a sequence-to-sequence (seq2seq) prediction model that incorporated only important factors selected by each method as independent variables. We further introduced CIS, integrating the differences in the mean absolute error (MAE), root mean square error (RMSE), and R² relative to the baseline model using all variables. By simultaneously quantifying the representativeness and parsimony of the selected important factors and expressing their predictive contributions, we simultaneously validated the causal claims and predictability (Fig. 1). CIS is defined to decrease as the predictive performance approaches that of the baseline model with fewer variables.

Fig. 1.

Study design. Weekly influenza and environmental data were collected and preprocessed. Causal strengths were quantified using multiple causal inference methods, and important factors were extracted based on method-specific thresholds. The importance of these factors was then evaluated using the Causal Importance Score

Causal inferences

In this study, four causal inference methods were used to extract the important factors. The characteristics, advantages, and disadvantages of each method are presented in Table 1 and the detailed mathematical formulations are provided in Additional file 1 (Supplement S1).

Table 1.

Comparison of four causal inference methods (GC, CCM, PCM, and GOBI)

	Characteristics	Advantages	Disadvantages	Reference
GC	Tests whether past values of one time series help predict another; based on linear vector-autoregressive (VAR) models	Simple, widely used, computationally efficient; good for detecting linear causal relationships	Assumes linearity; needs sufficient time-series length	[34, 39, 40]
CCM	Uses state-space reconstruction (Takens’ embedding) to identify causality in nonlinear dynamical systems	Capable of detecting nonlinear causality; suitable for complex systems	Computationally intensive; requires long and clean time-series; sensitive to noise; embedding dimension, delay are critical	[33, 35, 41]
PCM	Extension of CCM that controls for indirect effects by conditioning on third variables	Can identify direct causal relationships while excluding indirect influences	Even more data-intensive; requires parameter tuning; interpretation can be complex	[42]
GOBI	Uses general differential equations to infer causality and direction based on time series data	Can infer causality without strict model assumptions; flexible to various systems	May require careful model fitting; is sensitive to data quality and model misspecification	[43]

The algorithm for each methodology is shown in Fig. 2. The criteria for extracting the important factors in each methodology are different. The notations used for GC, CCM, PCM, and GOBI are summarized as follows: denotes the value of the causal variable  Y at time  t, and represents the value of the response variable  X at time  t. The detailed methodology description is included in the supplementary material.

Fig. 2.

Algorithm of causal inference. (A) GC; (B) CCM; (C) PCM; (D) GOBI

To check the stability of the time-series data, GC first performs the KPSS test (the p-value must be greater than 0.05 and the test statistic must be less than the critical value) and then performs the ADF test to further check the stability of the data. If the data were stable, the optimal lag time was calculated. We obtain 17 using the Bayesian information criterion (BIC). If the GC test is performed and , it is concluded that variable  Y affects variable  X. Here, variables with p-values less than 0.05 are selected as important factors (Fig. 2A).

CCM first determines the optimal embedding delay time and embedding dimensions. The optimal delay was calculated using mutual information. The calculation results were as follows: ; for influenza A; ; for influenza B; and ; for influenza ALL The  E and  tau represent the embedding dimension and time delay, respectively. Using this, we perform cross mapping and check whether the correlation predictive power index between variables is greater than 0 and the CCM results converge. If the CCM results converge, we infer that  Y is the cause of  X. Variables with a p-value less than 0.05 and a correlation coefficient value greater than 0.3 are selected as important factors (Fig. 2B).

PCM first calculates the causality using cross mapping in the same manner as CCM. If the predictive power index of the correlation between variables is greater than 0, it is inferred that  Y is the cause of  X. Then, the indirect causes are eliminated, and only the direct causes are selected. Variables with a p-value less than 0.05 and a correlation coefficient value greater than 0.3 are selected as important factors (Fig. 2C).

GOBI first used data with a window size of 52 and an overlap ratio of 90%. The thresholds of (consistency score) and (regulation threshold) are set to 0.1 and 0.05, respectively. If and are greater than the threshold and TRS (total regulation scores) can be calculated, it is inferred that  Y is the cause of  X. Variables with an absolute value of TRS greater than 0.3 are selected as important factors (Fig. 2D).

Causal importance score

The validity of the selection of important factors was evaluated based on predictive performance. We constructed seq2seq prediction models that used only the environmental factors selected by each causal inference method (GC, CCM, PCM, and GOBI) as independent variables and compared their performance with the baseline model using all variables using MAE, RMSE, and R². In light of several validation results reported in previous studies, particularly those employing spider map-based sensitivity analyses to quantify the contribution of factor groups, we introduced CIS to summarize both the performance difference and number of variables into a single index [44]. CIS is smaller when the performance of the model approaches the baseline with fewer variables, thereby quantifying both the representativeness and simplicity of the selected factors. For each method  j, the model was trained along the causal direction from environmental factors to influenza cases; the smaller the increase in error compared to the baseline and the smaller the number of variables used, the lower the CIS.

Let be the observed targets and be the predictions over a test horizon of length  L. The performance was assessed using MAE, RMSE, and R² and each was converted to a single metric score as follows:

1

2

3

4

Here, . represents the MAE, RMSE, and R² of the model that uses the important factors selected by method  j as independent variables. represents the MAE, RMSE, and R² of the model that uses the all-variables model. is the number of important factors selected by method  j. The absolute difference rewards closeness to the all-variable model, while penalizes larger factor sets (log denotes the natural logarithm). Finally, we define △ as the equiangular triangle whose three radii are the three metric scores (for MAE, RMSE, and ), and CIS as the area of △.

5

By construction, a smaller indicates that method  j extracts the most concise and important factors that can maintain the predictive performance of all variable models.

Results

Influenza and environment trends

Figure 3 illustrates the hypothetical causal relationships between the environmental factors, air pollution, and influenza transmission we considered as directed acyclic graphs. All factors are influenced by time-series properties and exhibit similar trends. Since this seasonality affects both environmental conditions and influenza transmission [18, 45], it can act as a confounding factor; however, this was not explicitly corrected for in this study (Fig. 3A). The detailed relationships between meteorological factor and influenza, and between air pollution and influenza, are shown in Fig. 3B and C [18, 20, 25, 29, 46, 47]. The relationship between meteorological factor and air pollution is shown in Fig. 3D [48].The relationships between each factor are direct and indirect. Through experiments to determine causality, GC, CCM, and GOBI were analyzed by assuming only direct factors, while PCM was analyzed by assuming both direct and indirect causation simultaneously.

Fig. 3.

Directed acyclic graphs (DAGs) illustrating hypothesized causal relationships between environmental factor and influenza transmission. (A) Environmental factors exert direct and indirect influence through meteorological factors and air pollution, and seasonality acts as a confounding variable affecting both environmental factors and influenza. (B) Meteorological factors (solar radiation, temperature, humidity, rainfall, wind speed) influence influenza directly and indirectly through interactions. (C) Air pollutants (SO₂, NO₂, O₃, and CO) influence influenza directly or indirectly through PM, and PM acts as a direct mediating variable. (D) Meteorological factors influence air pollution concentrations and form an indirect causal pathway to influenza

The influenza A virus infects both humans and animals. Because it has a very strong transmission power and rapidly mutates, the epidemic pattern changes every year [49]. Owing to these characteristics, the relationship between influenza A and environmental factors can exhibit significant variability during specific periods and conditions. In contrast, influenza B primarily spreads from person to person. Although its transmissibility is somewhat lower than that of influenza A, it can cause severe disease in children and the elderly [50]. In addition, the influenza B virus mutates relatively slowly [51]. These differences may lead to different response patterns when analyzing the causal relationships between environmental factors and influenza types. Therefore, by analyzing influenza A and B separately, we can more accurately assess the impact of environmental factors on each type and interpret independent causal relationships.

Figure 4 shows trends in influenza cases from 2016 to 2023, divided into influenza A, influenza B, and influenza ALL (sum of influenza A and B). As shown in Fig. 4A, influenza cases generally increased sharply during winter, with influenza A cases rising markedly in 2018 and 2019. Although influenza B is less prevalent than influenza A, its epidemic period is longer.

Fig. 4.

Weekly trends and seasonal detection pattern heatmaps for influenza A, B, and ALL. (A) Weekly influenza case counts from week 36 of 2016 to week 35 of 2023; (B-D) Heatmaps of weekly case counts by influenza subtype and by season; darker colors denote higher case frequencies in each week. The dashed line shows the change in year from week 52 to week 1; (B) influenza A; (C) influenza B; and (D) influenza ALL

The highest weekly case counts were recorded in week 3 of 2018 (199 cases, influenza ALL), week 51 of 2018 (159 cases, influenza A), and week 15 of 2019 (121 cases, influenza B). Influenza A was predominant in winter (December-February), whereas influenza B was prevalent mainly from late winter to spring (March-April). In some years, these two types were prevalent concurrently or with temporal lags (Fig. 4B-D).

Notably, strong winter epidemics of influenza A were observed in December 2016, 2018, and 2022, whereas a prominent spring epidemic of influenza B occurred in April 2019. Since 2020, the effects of the COVID-19 pandemic, including associated quarantine policies, have led to a marked reduction in reported influenza outbreaks during the 2020–2022 season; however, epidemic activity appears to have resumed in the 2022–2023 season.

Environmental factor data were analyzed by preprocessing the daily data from 2016 to 2023 into weekly data with the same time axis as the influenza data, and an overview of this data is in Table 2.

Table 2.

Overview of environmental factors in Korea from 2016 to 2023

Group name	Unit	Factor	Mean	Variance
Temperature	℃	Average temperature	13.4448	83.5796
		Minimum temperature	8.7250	93.8048
		Maximum temperature	18.9129	78.7931
Rainfall	mm	1 h maximum rainfall	1.2182	3.8267
		Daily rainfall	3.7437	27.6693
Wind speed	m/s	Maximum instantaneous wind speed	7.9778	1.6562
		Maximum wind speed	4.6967	0.4927
		Average wind speed	1.9453	0.1475
Humidity	%	Minimum relative humidity	44.9992	163.1889
		Average relative humidity	69.1706	108.1258
Sunshine	hr MJ/m2	Day length	6.2932	3.3718
		Total Solar Radiation	6.6761	5.5519
Air pollution	ppm	SO2	0.0033	0.0000
		CO	0.4427	0.0094
		O3	0.0299	0.0001
		NO2	0.0179	0.0000
		PM10	38.9063	245.4069
		PM2.5	21.1526	74.3556

Groupings, measurement units for weekly aggregated data and descriptive statistics (mean and variance)

As shown in Fig. 5A, all temperature indicators exhibited distinct annual seasonal patterns, with the lowest values occurring in February. This was consistent with the mid-latitude climatic characteristics of South Korea. While the annual temperature pattern remained consistent overall, sharp temperature increases and decreases were observed in 2017–2018 and 2020–2021.

Fig. 5.

Weekly trends of environmental factors in Korea from 2016 to 2023. (A) Temperature (average, maximum, minimum); (B) Rainfall (daily and 1-h maximum); (C) Wind speed (average, maximum, maximum instantaneous); (D) Relative humidity (average and minimum); (E) Sunshine (day length and total solar radiation); (F) SO₂, O₃, and NO₂; and (G) CO, PM10 and PM2.5

Both rainfall indicators exhibited heavy-tailed distributions, with low rainfall for most of the year and extremely high values from June to August (Fig. 5B). Although the rainfall frequency and intensity vary by year, they are concentrated in summer, with record-breaking rainfall events identified in August 2018, July 2020, and July 2023.

The average wind speed remained constant at the level of variance 0.1475 m/s; however, the maximum instantaneous wind speed fluctuated rapidly during the same period (Table 2; Fig. 5C).

Figure 5D shows that both related humidity factors exhibited extreme fluctuations, with high levels (70%-90%) in summer and low levels (20%-50%) in winter. In particular, the minimum relative humidity exhibited a sharp decline in winter, and the overall variance was high (Table 2).

In Fig. 5E, the two factors related to sunshine are day length and total solar radiation. Day length is the time for which sunlight shines on the Earth’s surface during a certain period, and total solar radiation is the total amount of solar radiation energy that reaches the Earth’s surface during a certain period. These two factors were highly correlated, with maximum and minimum values in summer and winter, respectively.

The factors affecting air pollution were SO₂, CO, O₃, NO₂, PM10, and Pm2.5concentrations. O₃ is affected by solar radiation, temperature, and atmospheric precursor (NO_x and VOCs) concentrations; its concentration increases in summer and decreases in winter. NO₂ increases in winter owing to traffic and heating, and its concentration decreases during summer. The seasonality of NO₂ showed a pattern opposite to that of O₃. SO₂ remained at very low concentrations throughout the year; however, a slight increase was observed in winter and early spring (Fig. 5F). CO, PM10, and PM2.5 also exhibited distinct seasonality. Overall, CO concentrations show a long-term decreasing trend, but short-term high concentrations occurred during some periods, such as 2017–2018 (Fig. 5G). PM10 repeatedly exhibited sharp increases and extremely high concentration peaks in spring (Fig. 5G). PM2.5 remained at relatively lower levels overall but showed several brief surges in concentration during specific periods. (Fig. 5G).

Causal strength

Figure 6 presents the causal relationships between influenza A cases and 18 environmental factors analyzed using the four causal inference methods: GC, CCM, PCM, and GOBI. In Fig. 5A, each cell represents the strength of the causal relationships between a method and an environmental factor; the GC results are expressed as F-statistics normalized to the range 0–1, while the CCM, PCM, and GOBI results are given as correlation coefficients or TRS values.

Fig. 6.

Causal influences between environmental factors and influenza A. (A) Heatmap of causal relationships. GC values are normalized F-statistics scaled; CCM, PCM, and GOBI values are correlation or TRS values. Non-significant relationships (p-value 0.05) are shown without color; (B-E) Important environmental factors selected by each causal inference method. Highlighted bars indicate important factors, and black dots represent statistically non-significant factors (p-value 0.05); (B) (GC) Important factors were selected based on the criterion p-value < 0.05; (C-D) (CCM, PCM) Important factors were selected based on the criteria |correlation| > 0.3 and p < 0.05; (E) (GOBI) Important factors were selected based on the criterion |TRS value| > 0.3

The GC test revealed that minimum temperature (F-statistic 55, score: 1.00) and NO₂ (0.96) serve as the most dominant causal drivers. In contrast, total solar radiation (0.11), average wind speed (0.14), and O₃ (0.14) exhibited relatively weak causal linkages (Fig. 6B). CCM analysis identified maximum temperature (0.64), average temperature (0.63), and CO (0.63) as exhibiting robust coupling and causal linkage. Conversely, meteorological factors such as daily rainfall and day length (both 0.21) demonstrated minimal causal influence (Fig. 6C). In the PCM framework, O₃ (0.67) emerged as the primary influential factor, followed by CO (0.63) and total solar radiation (0.60), indicating significant direct causality when accounting for confounding variables (Fig. 6D). GOBI analysis highlighted a strong negative causality associated with wind speed metrics, including maximum (-0.86), maximum instantaneous (-0.80), and average wind speed (-0.77). Furthermore, PM2.5 (-0.66) and SO₂ (-0.61) exerted negative causal effects, while temperature-related factors and minimum relative humidity (0.59) were positively correlated with the target variable (Fig. 6E).

Overall, except for PCM, all three methods selected all temperature factors as important (causality 0.5). This suggests that temperature may not act as a primary direct causal driver but instead influences influenza A. Given that influenza A typically peaks in winter, these findings imply that relative warming during cold periods may be associated with an increased risk of influenza A infection. The results were consistent with the observed data, as shown in Additional file 2 (Sup. Fig. S1A). In the winter periods, the weeks with higher temperatures than the preceding week are highlighted in yellow. These periods coincide with increases in influenza A cases and repeated outbreaks across multiple epidemic waves. In GOBI, wind speed factors showed strong negative causality, indicating that reduced wind speeds may elevate infection risk by prolonging the residence time of the influenza A virus particles in shared spaces. Among the air pollutants, SO₂, CO, O₃, NO₂, and PM2.5 showed high causality, with CO and O₃ exerting the strongest direct effects in PCM.

Figure 7 summarizes the causal relationships between influenza B detections and the 18 environmental factors using the four methods.

Fig. 7.

Causal influences between environmental factors and influenza B. (A) Heatmap of causal relationships. GC values are normalized F-statistics scaled; CCM, PCM, and GOBI values are correlation or TRS values. Non-significant relationships (p-value 0.05) are shown without color; (B-E) Important environmental factors selected by each causal inference method. Highlighted bars indicate important factors, and black dots represent statistically non-significant factors (p-value 0.05); (B) (GC) Important factors were selected based on the criterion p-value < 0.05; (C-D) (CCM, PCM) Important factors were selected based on the criteria |correlation| > 0.3 and p < 0.05; (E) (GOBI) Important factors were selected based on the criterion |TRS value| > 0.3

In the GC analysis (Fig. 7B), the causal landscape for Influenza B is primarily characterized by atmospheric pollutants rather than thermal conditions. The high causal scores of PM2.5 (1.00), CO (0.81), and NO₂ (0.63), alongside the peak F-statistic observed for PM2.5 ( 77), underscore the criticality of air quality in Influenza B transmission. Notably, the causal influence of temperature factors remained marginal (range: 0.10–0.18), suggesting that Influenza B may be less sensitive to ambient temperature fluctuations compared to influenza A. CCM identified SO₂ (0.57) and temperature factors (ranging from 0.47 to 0.48) as having relatively high causality. Rainfall and wind speed factors showed moderate causal strength, generally falling within the 0.20–0.30 range (Fig. 7C). PCM identified limited direct causal effects. No variables met the predefined significance criteria (|correlation| > 0.3 and p < 0.05), suggesting that the direct, independent influence of individual factors on Influenza B may be constrained by other variables (Fig. 7D). GOBI analysis revealed a complex directional dependency. While most factors exhibited negative causal effects, CO (0.74), NO₂ (0.70), and PM2.5 (0.40) showed significant positive causality. Furthermore, O₃, day length, and total solar radiation were identified as factors with negative causal relationships, indicating that the association between Influenza B and environmental drivers is highly factor-specific (Fig. 7E).

Overall, temperature factors showed relatively higher magnitudes in both CCM and GOBI, with comparable absolute values; given GOBI’s explicit modeling of causal direction, this suggests that temperature may exert a negative directional effect on influenza B. Because influenza B typically peaks in spring, factors such as diurnal temperature variation and behavioral responses (e.g., clothing adjustments to falling outdoor temperatures) may play a more prominent role. The results, which were consistent with the observed data, are presented in Additional file 2 (Sup. Fig. S1B). In spring, the weeks with lower temperatures than the preceding week are highlighted in blue, and these periods coincide with marked increases in influenza B cases. Similar to influenza A, CO and NO₂ also showed strong causality.

Figure 8 reports the causal analysis results for influenza ALL detection and 18 environmental variables.

Fig. 8.

Causal influences between environmental factors and influenza ALL. (A) Heatmap of causal relationships. GC values are normalized F-statistics scaled; CCM, PCM, and GOBI values are correlation or TRS values. Non-significant relationships (p-value 0.05) are shown without color; (B-E) Important environmental factors selected by each causal inference method. Highlighted bars indicate important factors, and black dots represent statistically non-significant factors (p-value 0.05); (B) (GC) Important factors were selected based on the criterion p-value < 0.05; (C-D) (CCM, PCM) Important factors were selected based on the criteria |correlation| < 0.3 and p < 0.05; (E) (GOBI) Important factors were selected based on the criterion |TRS value| < 0.3

According to the GC, minimum temperature emerged as the primary determinant (F-statistic62, score: 1.00), with NO₂ (0.84), CO (0.82), and PM2.5(0.73) also functioning as dominant causal drivers. Conversely, factors such as average wind speed and O₃ (both 0.08) maintained only marginal causal strength (Fig. 8B). The CCM framework robust coupling CO (0.54), total solar radiation (0.52), O₃ (0.52). While SO₂ (0.51) and NO₂ (0.50) also exhibited significant causal strength, meteorological variables specifically maximum instantaneous wind speed (0.11) and daily rainfall (0.12) exerted negligible influence (Fig. 8C). Through the PCM approach, CO (0.63) was confirmed as the most influential factor, followed by total solar radiation (0.53) and O₃ (0.52). These results underscore a strong direct causality that persists even when controlling for indirect causality (Fig. 8D). Finally, GOBI analysis provided a contrasting perspective by highlighting powerful negative causalities associated with wind speed metrics, particularly maximum and average wind speeds (both − 0.71). While SO₂ (-0.56) also showed a negative relationship, NO₂ (0.56) stood out as the most prominent positive driver within this model (Fig. 8E).

Overall, the air pollutants NO₂, CO, SO₂, and O₃ showed high causality, while wind speed factors demonstrated strong negative causality, underscoring methodological differences across approaches. Many factors showed similar patterns to influenza A, but with slightly lower magnitudes. This may be because influenza A predominates in influenza ALL. In particular, whereas temperature factors were relatively strong for influenza A and B, their causal effects were diminished for influenza ALL, consistent with the two types peaking in different seasons, thereby attenuating overall seasonality when aggregated.

Causal evaluation using CIS

To validate the causal significance of these factors, Table 3 summarizes the predictive performance of the models that used only the important environmental factors selected by GC, CCM, PCM, and GOBI for each influenza type (A, B, and ALL). The “Whole A,” “Whole B,” and “Whole ALL” models used all 18 variables as baselines. The score indicates the performance gap between each subset model and its corresponding baseline; lower scores indicate a smaller loss (i.e., accuracy closer to the baseline with greater parsimony).

Table 3.

Prediction performance comparison using important factors selected by four causal inference methods

	# Feature	MAE	MAE-Score	RMSE	RMSE-Score	R 2	R2-Score
Whole A	18	5.7439	0.0000	12.4496	0.0000	0.8006	0.0000
GC A	17	5.7395	0.0125	12.4598	0.0289	0.8005	0.0003
CCM A	13	5.8033	0.1524	12.7532	0.7787	0.7911	0.0244
PCM A	5	5.8199	0.1223	12.8421	0.6317	0.7886	0.0193
GOBI A	15	5.7787	0.0942	12.6825	0.6307	0.7931	0.0203
Whole B	18	1.8063	0.0000	4.3504	0.0000	0.9488	0.0000
GC B	13	1.9188	0.2886	4.7758	1.0911	0.9375	0.0290
CCM B	13	1.8739	0.1734	4.4576	0.2750	0.9462	0.0067
PCM B	-	-	-	-	-	-	-
GOBI B	11	1.9197	0.2719	4.7488	0.9553	0.9391	0.0233
Whole All	18	8.2111	0.0000	16.5182	0.0000	0.8099	0.0000
GC All	17	8.2446	0.0949	16.6231	0.2972	0.8073	0.0074
CCM All	10	8.2977	0.1994	16.6809	0.3746	0.8061	0.0087
PCM All	7	8.1238	0.1699	16.2801	0.4633	0.8154	0.0107
GOBI All	11	8.1938	0.0415	16.4077	0.2650	0.8124	0.0060

Whole: prediction using all 18 environmental factors; MAE-Score, RMSE-Score, and R²-Score represent the difference in prediction accuracy between important factor models and all variables model, with values closer to 0 indicating performance similar to the all-variables model; - indicates NAN value

For influenza A, the GC-based prediction (GC A) closely matched the all-variable model, with MAE, RMSE, and R² scores of 0.0125, 0.0289, and 0.0003, respectively. In terms of parsimony, CCM A (13 factors) and PCM A (5 factors) reduced the input size by 28% and 72%, relative to the Whole model (18 factors).

For influenza B, the CCM B model most closely matched the all-variable baseline (MAE score: 0.1734; RMSE score: 0.2750; R² scores: 0.0067). For PCM B, no important factors (NaN) were selected; therefore, no results were reported. GC B exhibits the weakest performance among the four.

For influenza ALL, the GC-based model (GC all) achieved an R² scores of 0.0074, which was comparable to that of the all-variable model. In contrast, the CCM and PCM models showed larger deviation from the baseline. The GOBI model performed the best overall for these metrics (MAE score: 0.0415; RMSE score: 0.2650; R² score: 0.0060).

To visualize the balance between performance preservation and variability minimization, and summarize it in the CIS defined above, we constructed a triangular radar chart and compared the areas between the methods (Fig. 9). The area of the triangular region is calculated in Additional file 1 (Supplement S2).

Fig. 9.

CIS based on four causal inference methods for each influenza type. The three vertices represent the MAE, RMSE, and R² scores, respectively. Models plotted closer to the center (0) indicate higher predictive accuracy and fewer selected variables, reflecting greater overall efficiency. (A) Influenza A; (B) influenza B; and (C) influenza ALL

Overall, the important factors selected by GC yielded the highest predictive accuracy for influenza A, whereas CCM performed best for influenza B. For influenza ALL, GOBI achieved the strongest performance. These findings indicate that efficient and parsimonious forecasting models can be constructed using only important causally selected factors, thereby obviating the need for all-variable models (Table 4).

Table 4.

CIS values based of four causal inference methods for each influenza type

	GC	CCM	PCM	GOBI
Influenza A	0.0019 (0.07%)	1.2990 (45.28%)	0.8359 (29.13%)	0.7324 (25.52%)
Influenza B	1.2990 (53.27%)	0.1505 (6.17%)	-	0.9889 (40.56%)
Influenza ALL	0.4653 (16.23%)	0.9904 (34.54%)	1.1708 (40.83%)	0.2407 (8.40%)

- indicates NAN value

Bold indicates the best performance

Accordingly, subsequent analyses used the following subsets for each outcome: GC (Influenza A), CCM (Influenza B), and GOBI (Influenza ALL).

Among the air pollution factors (SO₂, CO, O₃, NO₂, PM10, and PM2.5), NO₂, O₃, and SO₂ were consistently selected as important across influenza A, B, and ALL, whereas CO, PM10, and PM2.5 were not selected for influenza ALL (Fig. 10). This pattern suggests that NO₂, O₃, and SO₂ exert broad type-invariant influences on transmission, whereas CO, PM10, and PM2.5 contribute less to the ALL trend, although they are relevant for specific types.

Fig. 10.

Venn diagram of type-specific important environmental factors (best method per type). For each influenza type (A, B, and ALL), the diagram displays the set selected by the best-performing method under CIS (A = GC, B = CCM, and ALL = GOBI). Overlaps indicate factors shared across types; non-overlapping regions indicate type-specific factors

Temperature factors (average, maximum, and minimum) were selected only for types A and B, indicating that temperature variations are more tightly coupled to type-specific epidemics and that their effects are attenuated in influenza ALL by cross-type compensation. For relative humidity, the average was important across all types, whereas the minimum was excluded from influenza ALL. This implies that overall humidity conditions affect all types, while dry conditions may more directly facilitate the transmission of influenza A and B. Regarding wind speed, the average wind speed and maximum instantaneous wind speed were important for influenza A and ALL, and the maximum wind speed was important for all three types. This indicates that wind speed dynamics matter for influenza A and ALL, whereas influenza B appears to be less sensitive. Both rainfall metrics (daily total and 1-h maximum) were important for influenza A and ALL, whereas day length was important only for influenza ALL. Temperature was repeatedly selected as an important factor in subtype-specific analyses, highlighting its type of specificity. Conversely, rainfall and day length were significant for influenza ALL.

Taken together, these findings underscore the importance of considering type specificity along with aggregation effects when selecting predictors for real-world forecasting, thereby enabling parsimonious models to retain their predictive skill.

Delay causal effect

Based on the GC analysis, the causal influence of environmental factors on Influenza A exhibited distinct temporal trajectories depending on their physical characteristics (Fig. 11A).

Fig. 11.

Delay causal effects of environmental factors are shown for lags 0–2 weeks. Higher values indicate stronger causal evidence from predictors to influenza cases, while black markers denote non-significant associations. (A) GC F-statistics for influenza A; (B) CCM cross map skill () for influenza B; and (C) GOBI TRS values for influenza ALL

Temperature factors showed their maximum causal influence at Delay 0, followed by a rapid and consistent decay as the time lag increased. Specifically, minimum temperature, which recorded the highest initial F-statistic (54.60), declined by 33.1% at a one-week delay and maintained a 31.2% cumulative reduction by two weeks. Maximum temperature exhibited the most pronounced decay, dropping by 41.5% cumulatively (from 31.36 to 18.36), while average temperature followed a similar downward trend with a 4.9% cumulative decrease. These results indicate that the causal impact of thermal conditions is primarily contemporaneous and diminishes sharply within a two-week window.

In contrast, air pollutants, rainfall, and humidity factors demonstrated relative persistence or delayed amplification, in contrast to the rapid decay of temperature effects. Among the air quality constituents, NO₂ maintained a robust and top-ranked causal influence through Delay 2 (from 52.56 to 45.95; cumulative − 12.6%). Notably, CO exhibited a distinct delayed-response pattern, peaking at Delay 1 (+ 11.7%) before stabilizing at Delay 2 (41.18). PM showed remarkable stability, with PM10 remaining nearly constant (cumulative change: -4.1%) and PM2.5 showing a gradual adjustment (-15.7%). Although NO₂, PM2.5, and SO₂ showed moderate initial declines, their causal values remained substantial at Delay 2, reinforcing the notion that air pollutants exert a more enduring and consistent influence on Influenza A transmission than temperature. Rainfall factors followed this persistent trend; 1-hour maximum rainfall remained nearly stationary (cumulative − 3.0%), while daily rainfall showed a gradual downward trajectory (-14.9%). Furthermore, minimum relative humidity emerged as a significant delayed driver, with its causal influence increasing by 58.5% (from 18.23 to 28.88) within the first week. Detailed statistics are provided in Additional file 3 (Sup. Tab. S1).

In summary, while temperature effects decay rapidly, the sustained or amplified impacts of air pollutants, rainfall, and humidity suggest their prolonged roles in the dynamics of Influenza A transmission.

Figure 11B shows the results of the CCM causal analysis for influenza B. All temperature factors demonstrated a consistent pattern of strong contemporaneous causality followed by a precipitous decline as the time lag increased. Specifically, maximum temperature exhibited the highest initial causal strength at Delay 0 (0.48) but dropped significantly by 28.4% at the two-week delay (0.33) after a modest 5.0% decrease at Delay 1. Average and minimum temperatures followed a similar two-stage decay; while their reductions at one-week delay were marginal (3.8% and 3.5%, respectively), they declined sharply by 32.8% and 35.8% between Delay 1 and Delay 2, resulting in cumulative reductions of 35.3% and 38.0%. These findings suggest that while temperature factors are potent immediate drivers of Influenza B, their causal connectivity diminishes rapidly within a two-week window.

In contrast to the temperature factors, air pollution factors exhibited higher persistence or more complex, non-monotonic trajectories. SO₂ recorded the most robust overall causal effect at Delay 0 (0.57), ranking as the most influential factor among all factors. It decreased by 6.9% after a one-week delay and by a further 2.5% at two-week delay, indicating relatively strong persistence (cumulative decrease of 9.3%). In contrast, NO₂ and CO were more vulnerable to delay, with cumulative decreases of 27.6% and 24.8% over two-week delay, respectively. Furthermore, O₃, PM10, and PM2.5 displayed dynamic patterns; O₃ exhibited a non-monotonic trend by briefly increasing at Delay 1 before declining at Delay 2, while PM10 and PM2.5 followed a U-shaped recovery, rebounding by 5.5% and 0.88% at the two-week delay after an initial 13.4% and 16.5% decline. Detailed statistics are provided in Additional file 3 (Sup. Tab. S2).

Collectively, these results highlight that while temperature exerts short-term dominance, SO₂ stands out for its high causal magnitude and temporal persistence, distinguishing it from more delay-sensitive pollutants.

Figure 10C, the GOBI analysis for Influenza ALL show three main patterns: stability, rapid weakening, and delayed strengthening.

Wind speed factors showed the most stable and strongest negative effect. Both maximum and average wind speeds recorded the largest effects at delay 0 weeks (-0.7083) and remained at similar levels at one-week delay (-0.6809 and − 0.6596) and two-week delay (-0.6957 and − 0.6957), with cumulative changes of only − 1.8%, indicating remarkable stability. Maximum instantaneous wind speed also remained stable, shifting slightly from − 0.6667 to -0.6383 and then to -0.6522, corresponding to a cumulative reduction of 2.2% over two-week delay, thereby exhibiting strong persistence.

In contrast, the effects of rainfall and Sunshine factors faded very quickly. The impact of 1-hour maximum rainfall dropped by 93.5% (from − 0.3333 to -0.0217) within two weeks, and daily rainfall decreased by 58.3%. Similarly, the effects of day length and solar radiation decreased by 80.1% and 54.6%, showing that these factors only have a short-term influence. At the same time, NO₂ was very sensitive to time, with its effect dropping sharply by 72.9% by the second week.

Humidity and SO₂ showed unique changes over time. Average relative humidity became a stronger positive driver, increasing its influence by 53.8% (from 0.3958 to 0.6087) over two weeks. SO₂ became 23.7% stronger at Delay 2 compared to its initial effect. Detailed statistics are provided in Additional file 3 (Sup. Tab. S3).

In summary, while wind speed keeps a steady and strong negative effect, the influence of rainfall and sunshine disappears quickly. Meanwhile, humidity and SO₂ show their strongest roles after a time delay, highlighting the complex timing of environmental impacts on Influenza ALL.

Discussion

This study conducted causal inference between weekly influenza data from Korea and environmental factors. Influenza data was classified into A, B, and all based on virus type, while environmental factors were categorized into temperature, rainfall, wind speed, humidity, sunshine, and air pollution (SO₂, CO, O₃, NO₂, PM10, and PM2.5). GC, CCM, PCM, and GOBI were used to inference for causal relationship, and the performance and practicality of the CIS were evaluated.

In the GC, the largest number of environmental factors were identified as important factors compared to other methods. Notably, factors such as maximum instantaneous wind speed and minimum relative humidity, which were not consistently selected in other methodologies, were included. This suggests that GC likely over-detected variables in natural systems with strong nonlinearity, as it utilizes a linear-based VAR. CCM effectively selected total solar radiation and temperature factors that are kinetically closely linked to influenza outbreaks. It accurately reflects the inherent nonlinear link between meteorological systems and virus spread. PCM demonstrated the most conservative variable selection, a result of focusing on identifying direct causality. The analysis revealed factors SO₂ and NO₂ were important factors exerting a direct causal influence on influenza outbreaks. Finally, GOBI evaluates whether variables interact consistently according to established directional principles. Identifying the rainfall factors in influenza B or selecting day length in influenza A can be understood as capturing physical regulatory mechanisms operating with a certain directionality within the system.

This study cross-validates four causal inference methods to identify important consensus-based factors. By analyzing influenza A and B separately, we minimized the inherent bias in analyses that relied solely on aggregated data. We introduced CIS, which consolidates predictive performance into a single metric. CIS is designed to assign lower values to a small number of important factors that achieve a predictive power close to that of the model using all factors. The practicality of the extracted important factors was verified from the perspective of predictive applications. CIS enables a fair comparison between methods by quantifying the balance between predictive power and parsimony. Previous studies relied on correlation-based methods and integrated data, resulting in a loss of heterogeneity across types and a lack of systematic validation of predictive utility. This study addresses these limitations by selecting the important factors based on causal inference and employing a type-specific decomposition design.

The prediction validation results showed that GC was the most suitable method for extracting important factors for influenza A, CCM for influenza B, and GOBI for influenza ALL. This demonstrates that the characteristics of each causal inference method align well with the propagation dynamics of each type. GC, with its linear structure and robustness to short delays, effectively captured the seasonal variation in influenza (A) CCM, which is nonlinear and sensitive to state-dependent signals, demonstrated superior performance for influenza (B) GOBI, with its advantage of distinguishing between positive and negative nonlinearities, excelled particularly in influenza ALL, where different signals were mixed. In addition, the direct effects of CO and O₃ were prominent in PCM, clearly demonstrating that PCM was more sensitive to the direct pathway. This suggests that appropriately selecting a different causal inference method for each virus type is crucial, and that using CIS scores in this process is useful for establishing preventive measures based on environmental factors.

For each influenza type, minimum temperature, NO₂, CO, daily rainfall, 1 h maximum rainfall, PM2.5, average temperature, maximum temperature, maximum wind speed, PM10, maximum instantaneous wind speed, average relative humidity, SO₂, minimum relative humidity, O₃, average wind speed and total solar radiation were selected as important factors in A; SO₂, maximum temperature, average temperature, minimum temperature, average relative humidity, CO, NO₂, minimum relative humidity, O₃, PM2.5, maximum wind speed, total solar radiation and PM10 were selected as important factors in B; and maximum wind speed, average wind speed, maximum instantaneous wind speed, NO₂, SO₂, total solar radiation, O₃, day length, average relative humidity, 1 h maximum rainfall and daily rainfall were selected as important factors in ALL. In the analysis of lagged causal effects, influenza A showed consistent strong causal effects of CO and NO₂; influenza B showed consistent strong causal effects of SO₂; and influenza ALL showed consistent strong causal effects of wind speed (maximum instantaneous, maximum, and average), SO₂, and NO₂. The causal effect of average relative humidity nearly doubled with increasing delay in influenza ALL.

The overall results show notable causal relationships in NO₂, O₃, SO₂, wind speed, and temperature. NO₂, O₃, and SO₂ were identified as important factors common to all influenza types. This finding is consistent with research demonstrating that environmental pollutants increase host susceptibility through airway inflammation, oxidative stress, and impaired mucociliary function [46]. Indeed, a one-hour exposure to 0.1 ppm NO₂ was shown to weaken the nasal epithelial barrier and induce inflammatory responses [52]. An increase in inflammatory cells in the airways was also observed in a low-concentration O₃ exposure study conducted on healthy adults [53]. Furthermore, oxidative stimuli such as O₃, NO₂, and SO₂ induce oxidative stress, inhibit ciliary formation and beating frequency, reduce airway surface fluid, and ultimately impair pulmonary function [54]. These studies support the possibility that NO₂, O₃, and SO₂ collectively contribute to influenza transmission by weakening the primary barriers of host defense and impairing viral clearance.

In the GOBI analysis, wind speed exhibited a consistent negative causal effect. This is consistent with aerodynamic evidence that outdoor wind rapidly disperses cough droplets, thereby reducing the average concentration in the respiratory tract of exposed individuals [26]. A similar trend has been observed in epidemiological studies. In Wuxi, China (2014–2019), a 1 m/s increase in weekly average wind speed was associated with a 33.8% reduction in risk [47]. In Chongqing, China (2012–2019), an increased risk was observed when average wind speeds fell below 1.55 m/s, with the effect persisting for up to four weeks [55].

The causal effect of temperature was heterogeneous across the subtypes. In our analysis, excluding PCM, which identified only direct causation, the other causal inference methods indicated that influenza A was associated with an increased risk of short-term warming in the cold seasons, whereas influenza B exhibited a clear signal at low temperatures from late winter to early spring. This is consistent with previous studies showing that rapid temperature fluctuations under cold-dry conditions in temperate zones promote transmission [18, 20]. Furthermore, Japanese data have reported that a sharp drop following a relatively warm preceding week amplified this risk [19]. In contrast, in influenza ALL, differences in subtype phases led to offsetting effects when aggregated, making the overall direction unclear. This suggests that separating causal relationships across influenza types may be beneficial for practical prevention.

This study has several limitations. First, owing to the use of weekly collective data, it was difficult to isolate and control for individual-level confounding factors, such as individual behavior, vaccination, and viral mutations. Second, regional heterogeneity between environmental factors (e.g., “urban and rural” and “coastal and inland”) is not considered, requiring a model that includes spatial structure. Third, a dynamic model that captures temporal variations in causal effects, such as seasonality and policy changes, was not applied. Future research will expand the scope of the analysis by incorporating additional information such as vaccination information and movement patterns. We will quantify the time-varying effects by applying spatiotemporal models that reflect regional differences and seasonal variations. Furthermore, external validation will be conducted using data from other regions and periods, and policy effects will be evaluated in advance using hypothetical scenarios such as air pollution reduction and ventilation improvements.

Nevertheless, our study demonstrates that even without using all factors in alerts and predictions, we can achieve a performance close to that of the baseline model using only the important factors. This simplified the model and facilitated its practical applications in the field. In environmental management, policies to reduce NO₂, O₃, and SO₂ emissions have the potential to reduce the burden of respiratory infections in the long term. In indoor and outdoor designs, non-pharmaceutical measures include enhancing ventilation, utilizing sunlight, and arranging spaces to accommodate wind. Furthermore, we focus on the different epidemic periods for influenza A and B, noting that A is prevalent during warm winter months and B during cold spring months. This suggests that in order to establish preventive measures for each influenza, it is necessary to focus on temperature changes that are non-specific from the average year and provide warnings and precautions accordingly.

Conclusion

This study analyzes the causal influence of environmental factors on influenza types A and B, aiming to develop and predict influenza control strategies for each type. For causal inference, we used GC, CCM, PCM, and GOBI to extract significant factors for each influenza type, and demonstrated that the CIS index had a significant effect on predictive power even without using all environmental factors. Specifically, we found that environmental pollutants such as NO₂, O₃, and SO₂ were important environmental causal factors for all types. We observed that type A outbreaks occurred during high temperatures in cold winters, while type B outbreaks occurred during low temperatures in warm springs. By integrating causal analysis and predictive validation, our findings link mechanistic understanding with practical predictions, providing a data-driven foundation for improving influenza prevention strategies.

From a public health perspective, policies targeting reductions in NO₂, O₃, and SO₂ emissions have the potential to alleviate the burden of influenza infection. Based on environmental factors, it is possible to predict major epidemics in advance for each influenza type, which has different epidemic patterns depending on the season, and to use it for preventive measures through non-pharmaceutical measures for the surrounding environment. Therefore, integrating causal inference and predictive modeling provides a data-driven foundation for developing adaptive and environmentally informed influenza management strategies.

Abbreviations

GC

Granger causality

CCM

Convergent cross mapping

PCM

Partial cross mapping

GOBI

General model-based causal inference

Seq2seq

Sequence-to-sequence

CIS

Causal importance score

MAE

Mean absolute error

RMSE

Root mean square error

SO₂

Sulfur Dioxide

CO

Carbon Monoxide

O₃

Ozone

NO₂

Nitrogen Dioxide

PM10

Particulate Matter (10 μm)

ILI

Influenza-like illness

VAR

Vector-autoregressive

BIC

Bayesian information criterion

Authors’ contributions

ML curated and analyzed the data, conducted the investigation, developed the methodology, implemented the software, performed visualization, and drafted the original manuscript. SL contributed to the conceptualization, investigation, methodology, software development, visualization, supervision, and validation, and was involved in reviewing and editing the manuscript. SK contributed to the conceptualization, acquired funding, administered the project, and participated in reviewing and editing the manuscript. All authors read and approved the final manuscript.

Funding

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MSIT) (2022R1A5A1033624; RS-2026-25487736); the Global - Learning & Academic research institution for Master’s · Ph.D. students, and Postdocs (LAMP) Program of the National Research Foundation of Korea (NRF) grant funded by the Ministry of Education (No. RS-2023- 00301938) and the 2024 BK21 FOUR Graduate School Innovation Support funded by Pusan National University (PNU-Fellowship program).

Data availability

The dataset supporting the conclusions of this article is included within the article [Additional file 4].

Disclosure

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.