Cycling in Urban and Tourism Areas in the COVID-19 Era: Weather Sensitivity and Sustainable Management Response

Abstract

This study investigates how cycling behaviour in urban and tourism areas of Slovenia responded to the COVID-19 pandemic and its aftermath, with implications for forecasting and sustainable mobility planning. Using high-frequency daily data from January 2020 to August 2024 across Ljubljana (urban) and Rateče (tourism), we model the interdependence between weather conditions, cycling volume, and reported COVID-19 cases. The results reveal contrasting dynamics: in Ljubljana, higher cycling activity correlates with fewer infections, supporting cycling as a low-risk commuting mode, whereas in Rateče, tourism-driven cycling coincides with higher variability in infections. Regression and vector autoregressive (VAR(2)) models highlight the significant roles of precipitation and sunlight in shaping these patterns and enable short-term forecasts of COVID-19 cases up to January 2025. Machine learning methods complemented the VAR model, improving forecasting accuracy and revealing nonlinear interactions. These findings demonstrate the value of integrating behavioural and environmental indicators into public health forecasting and support region-specific strategies for resilient, sustainable mobility during future health or climate disruptions.

1. Introduction

The COVID-19 pandemic triggered unprecedented disruptions in mobility behaviour, urban transport systems, and tourism flows. Lockdowns, social distancing, and heightened health awareness reshaped travel choices, with cycling emerging as a resilient and sustainable alternative to motorised transport. These behavioural shifts also revealed the vulnerability of mobility systems to external shocks and the importance of adaptive, low-emission transport modes for urban and tourist areas. Understanding how health, environment, and mobility interact is therefore essential for developing policies that enhance sustainability, resilience, and public well-being.

In this context, recent research has increasingly examined how meteorological variability, infrastructure, and behavioural adaptation influence cycling activity and sustainable mobility outcomes. The ex ante predicted COVID-19 pandemic transformed daily life in unprecedented ways, disrupting routines and reshaping societal priorities, especially in public health, mobility, and well-being. One area that gained increased attention during this time is active commuting—especially cycling—as a sustainable and health-focused alternative to crowded public transport. Amid growing concerns about virus transmission, more people turned to bicycles for short-distance travel, particularly in urban centres. This behavioural change not only addressed immediate safety issues but also revived longstanding discussions about sustainable mobility, physical health, and urban planning. Since respiratory viruses like COVID-19 are heavily influenced by environmental and behavioural factors, understanding how they interact with daily commuting patterns is crucial for developing predictive models that guide public health strategies and urban policies. On the one hand, tourism is well known for its sustainable development, while mass tourism results in significant pollution. Nevertheless, the double pollution inherent to tourism and bicycling is recognised. Therefore, in this study, greenhushing is omitted [1]. Although commuting trips cannot be fully avoided in adverse weather, weather conditions still influence trip timing, duration, and route choice. Moreover, weather affects the intensity of recreational and tourism cycling, which contributes to overall mobility flows and, in turn, potential exposure patterns that influence epidemiological dynamics.

The motivation for this study stems from the intersection of epidemiology, environmental science, and behavioural geography. By combining high-frequency data on COVID-19 infections, weather variables, and cycling activity, this research aims to capture the complex interactions that govern the transmission of respiratory diseases. In this way, it contributes to the expanding field of data-driven factors, highlighting the challenges and opportunities in forecasting viral trends. While existing research often examines short-term pandemic effects or isolated variables, this study aims to bridge these gaps by applying econometric time-series techniques—namely, regression and vector autoregressive (VAR) models—to estimate the delayed and interactive effects of environmental and behavioural factors on infection rates.

The specific aims of this research are threefold: first, to synthesise the existing empirical literature connecting mobility, weather, and respiratory infections within a forecasting framework; second, to develop and evaluate robust econometric models that examine these relationships using daily data from 2020 to 2024 in Slovenia; and third, to assess the predictive accuracy of these models through both in-sample and out-of-sample forecasting. Note that tourist cycling differs from everyday urban cycling in terms of motivation, distances, and weather sensitivity. Rateče represents a tourism-focused environment with substantial seasonal variation, whereas Ljubljana exemplifies everyday urban commuting, characterised by more stable, year-round patterns. This distinction underpins our empirical analysis.

The link between microbial activity—especially viral infections like COVID-19—and human–environment interactions remains poorly understood within everyday behavioural and climate contexts [2]. Although it was once questioned whether microbiological phenomena could impact socio-environmental factors such as active mobility or urban planning, recent modelling approaches—both mathematical and empirical—are beginning to be used to explore this area. This study contributes to the expanding field of infectious disease prediction by integrating high-frequency environmental and behavioural data to analyse COVID-19 trends regionally. It addresses the need for more comprehensive, time-sensitive models that include human movement, tourism, and weather variations into pathogen monitoring systems [3,4].

There exists a significant research gap in understanding how local climatic variability and cycling activity influence short-term changes in viral transmission [5,6,7,8]. Our dataset records daily interactions among weather conditions, cycling volumes, and reported COVID-19 cases. Incorporating these data into a daily time-series framework enables the testing of hypotheses that extend beyond mere seasonality and long-term trends. Employing base indices and log-differenced (I(1)) series helps to stabilise variances and address non-stationarity, which is essential for VAR and short-term predictions [9,10]. Therefore, we propose the following two hypotheses:

H1. 

Increased COVID-19 infections are statistically significantly associated with bicycle activity in tourism-focused areas, regardless of weather conditions.

In the tourism context (Rateče), this is due to two main factors: recreational and seasonal travel tends to concentrate people, especially during holidays, and additional social activities, such as gatherings at events, increase the likelihood of incidental virus transmission. Additionally, the need for physical distancing during biking contributes to this context.

H2. 

COVID-19 infections are negatively associated with daily bicycle use in urban settings. In the urban context (Ljubljana), cycling represents an active mode of commuting, replacing enclosed public transport and thereby reducing exposure risk. This aligns with the literature suggesting that increased active mobility, especially during restrictive phases of the pandemic, helped to mitigate infection waves by reducing crowding in indoor environments [11].

Both hypotheses use daily COVID-19 infection counts as the dependent variable. In contrast, key independent variables include meteorological data (temperature, precipitation, snow, and sun) and the number of cyclists.

The remainder of this paper is structured as follows: Section 2 reviews the relevant literature on mobility, respiratory disease, and weather effects. Section 3 describes the data sources, variable creation, and methodological approach. Section 4 presents the results from both regression analysis and VAR models to assess the forecasting performance. Section 5 offers a discussion and interpretation of the findings. Finally, Section 6 concludes with implications, limitations, and suggestions for future research. The following sections focus specifically on the behavioural and environmental determinants of cycling and mobility, providing a more targeted contribution to sustainable transport research.

2. Previous Empirical Research

2.1. Study Areas and Context of COVID-19-Related Mobility

This analysis focuses on two contrasting Slovenian locations—Ljubljana and Rateče—that differ in their spatial, demographic, and mobility characteristics. Ljubljana represents an urban commuting environment with established cycling infrastructure and daily travel routines. At the same time, Rateče reflects a tourism-oriented settlement where seasonal weather, visitor flows, and recreational cycling strongly influence mobility behaviour. This geographical and contextual overview provides the foundation for understanding how local conditions shaped the interaction between weather variability, cycling intensity, and COVID-19 dynamics examined in the empirical analysis.

The COVID-19 pandemic has profoundly affected both public health and mobility behaviour, including cycling in urban and tourist destinations. Patients infected with COVID-19 often developed comorbidities and changed their mobility patterns, while detailed medical mechanisms (e.g., microbiota changes, antimicrobial resistance) are only briefly summarised here. Antimicrobial resistance (AMR) causes about 35,000 deaths annually in the European Union (EU) and costs around EUR 1.1 billion; its rise is driven mainly by antibiotic overuse, making consumption data vital for risk assessment [12]. The pandemic disrupted global health systems, leading to increased hospital antibiotic use and multidrug-resistant organism outbreaks. In contrast, outpatient antibiotic use declined in high-income countries due to improved hygiene and reduced mobility [13]. Preventive behaviour was higher among individuals with greater anxiety and perceived susceptibility, especially women, older adults, and those exposed to infection [14].

Conflicts, climate change, and the lifting of COVID-19 restrictions later weakened infection control measures, although improvements in water, sanitation, and hygiene (WASH) remained crucial [15]. Limited migration during lockdowns reduced gastrointestinal infections, such as cholera and dysentery, but these rose again after 2022 with resumed travel [16,17]. The pandemic highlighted bacterial–viral interactions and reinforced the importance of prevention, accurate diagnostics, and antibiotic control programmes [18]. Few hospitalised COVID-19 patients had bacterial co-infections, so antibiotic therapy is now recommended mainly for critically ill or immunocompromised individuals [19]. Excessive antibiotic use has been linked to dysbiosis, an imbalance in the gut microbiota that impairs immunity and contributes to intestinal and systemic disorders [20,21].

Long-term microbiota changes are also associated with long COVID-19, a multisystem condition affecting at least 10% of infections and characterised by fatigue, respiratory, and cognitive symptoms [22,23]. Despite biomedical advances, diagnostic and therapeutic options remain limited [24]. Similar post-viral syndromes (e.g., myalgic encephalomyelitis, postural orthostatic tachycardia syndrome) provide comparative insight [25,26,27,28]. Overall, these findings reveal how public health, infection prevention, and mobility behaviour—including cycling for transport and recreation—are interlinked in the pandemic and post-pandemic eras, influencing resilience and sustainability in both urban and tourism contexts [29,30,31,32,33,34,35].

2.2. Research on Climatic Behaviour and Sustainable Development Goals

The COVID-19 pandemic triggered profound shifts in human mobility, prompting researchers to investigate how transportation choices—particularly active modes, such as bicycling—interact with public health outcomes and broader sustainability goals. Empirical studies have increasingly focused on the dynamic relationships between climate-related behaviours, such as cycling, and pandemic trajectories, offering valuable insights for the Sustainable Development Goals (SDGs), particularly SDG 3 (Good Health and Well-being), SDG 11 (Sustainable Cities and Communities), and SDG 13 (Climate Action) [36].

One central theme in the literature is the resilience and adaptability of urban cycling behaviour during public health crises. Several studies found that while motorised mobility declined sharply during COVID-19 lockdowns, bicycle usage often increased, especially in cities that supported cycling infrastructure. For instance, Kraus and Koch [37] demonstrated that the introduction of pop-up bike lanes across European towns led to a measurable rise in cycling levels—approximately 0.6% for each kilometre of temporary lane added. This behaviour shift helped to maintain urban mobility without reliance on high-contact public transport modes, providing both health and environmental benefits.

These shifts also align with SDG 11, emphasising the need for sustainable and inclusive transport. Empirical research by Buehler and Pucher [38] demonstrated that cities with pre-existing bike-friendly policies (e.g., Amsterdam, Copenhagen, Paris, and Graz) exhibited higher cycling resilience, indicating that proactive, climate-oriented urban planning enhances system stability during crises [39,40,41]. This aligns with the climate behaviour literature, where sustained access to low-emission mobility options correlates with both emission reductions and improved urban livability.

The environmental implications of increased cycling during the pandemic are well-documented. Gössling [42] noted that temporary declines in urban air pollution—resulting from lower car traffic and greater cycling—contributed to short-term climate benefits and potential long-term behavioural shifts. Moreover, a longitudinal study [43] across seven European cities found that replacing just one car trip per week with cycling could reduce an individual’s carbon footprint by approximately 0.5 tons of CO₂ per year. These findings substantiate the direct contribution of behavioural adaptation to climate mitigation, a core tenet of SDG 13. Creutzig et al. [44] demonstrate how COVID-19 led to significant shifts in urban mobility patterns, with implemented policies contributing to reduced greenhouse gas emissions by decreasing dependence on motorised transport. Angin et al. [45] calculated CO₂ emissions from daily motorised vehicle use using the emission formula, providing a baseline essential for shaping effective climate mitigation policies. Expanding on this, Creutzig et al. emphasised that demand-side solutions—such as changes in mobility behaviour—are vital for achieving climate goals while ensuring high levels of societal well-being [46].

From a modelling perspective, efforts to predict COVID-19 dynamics using mobility data have gained momentum [11]. Although much of this work relies on mobile phone tracking or public transit data, some studies have begun integrating bicycle traffic data into epidemiological models. For example, Guo et al. [47] explored bike-sharing demand fluctuations to assess risk exposure and public adaptation in the early pandemic phase. These findings highlight how active mobility data can enrich public health modelling by offering real-time behavioural proxies [48].

Furthermore, the social and psychological underpinnings of cycling adoption during COVID-19 have been a focus of several behavioural studies. Psychological models suggest that individuals were more likely to adopt cycling when it was perceived as safer, healthier, and more socially acceptable amid pandemic restrictions. Research by Teixeira et al. [49] indicated that this shift in modal preference was partly driven by the public’s desire to maintain physical activity while minimising exposure to crowded settings. This observation intersects both SDG 3 and SDG 11.

Despite these promising trends, empirical gaps persist. Most existing studies focus on the initial phases of the pandemic and are primarily based in large, high-income urban areas, providing limited insights into long-term behavioural adaptations [50]. In particular, there is a lack of research exploring how daily weather variability influences cycling volumes over multiple years, especially in middle-income, developed contexts such as Slovenia [51]. The relationship between climatic conditions, active mobility, and trends in respiratory infections has received comparatively little empirical attention, despite its importance for understanding broader patterns in public health resilience [52]. Additionally, while national datasets are available, their utilisation in multi-variable, high-frequency analyses that integrate behavioural, environmental, and epidemiological dimensions remains limited. Addressing these gaps aligns with emerging research priorities that advocate for multiscale modelling frameworks to predict infectious disease dynamics better (Equations (3) and (4)) and support evidence-based urban health planning, particularly concerning long-term pandemic preparedness [53,54,55,56].

Table 1. Key studies on cycling, mobility, weather, and forecasting.

Authors [#]	Method Used	Main Finding (One Sentence)
Gričar, Bojnec, Šugar [1]	Conceptual + empirical synthesis (tourism cycling)	Domestic cycling tourism can generate “double pollution” issues and greenhushing risks that managers must address in sustainable travel policy.
McClymont and Hu [5]	Narrative review (weather–COVID-19)	Weather variability affects COVID-19 transmission through biological and behavioural pathways, warranting its inclusion in forecasting models.
Xu et al. [6]	Retrospective time-series (China, hospital ARIs)	Viral respiratory infections show seasonal associations with meteorological factors, supporting weather-informed surveillance.
Nichols et al. [7]	Review (seasonality and weather)	Coronavirus seasonality aligns with other respiratory infections and is modulated by weather, informing preparedness.
Kraus and Koch [37]	Natural experiment/diff-in-diff (Europe)	Pop-up bike lanes caused rapid cycling increases (~0.6% per km added), evidencing policy leverage in crises.
Buehler and Pucher [38]	Comparative policy analysis (cities)	Cities with bike-friendly policies exhibited higher cycling resilience during COVID-19, sustaining mobility and health benefits.
Gössling [42]	Policy impact analysis	Reduced motorised travel and increased cycling temporarily improved air quality, hinting at durable behaviour shifts.
Brand et al. [43]	Longitudinal cohort (multi-city)	Replacing one weekly car trip with cycling can cut ~0.5 t CO2 per person per year, demonstrating strong mitigation potential.
Creutzig et al. [44,46]	Policy synthesis/demand-side assessment	Demand-side mobility shifts (including cycling) are central to climate mitigation while maintaining well-being.
Du et al. [57]	Cross-country time-series (influenza post-COVID-19)	Lifting COVID-19 restrictions altered influenza transmission, highlighting policy–behaviour feedbacks.
Borrero et al. [10]	Machine learning time-series (agri/tourism)	Machine learning algorithms can outperform classical benchmarks for sectoral forecasting, supporting ML in mobility and health.
Gusarov [58]	Methodological study (econometrics vs. ML)	ML can rival or exceed econometric models in predictive tasks, advocating hybrid approaches.

summarises the most relevant studies addressing the relationships between cycling, mobility behaviour, meteorological factors, and forecasting methodologies during and after the COVID-19 pandemic.

The reviewed literature highlights a consistent link between weather variability, behavioural adaptation, and cycling demand in both urban and tourism contexts. It also demonstrates a growing methodological shift toward hybrid econometric and machine learning models, reflecting the complexity of post-pandemic mobility systems.

3. Methods, Data, and Hypothesis Development

This study does not attempt to isolate all infection pathways (e.g., workplace or household transmission), but rather focuses on mobility-related behavioural proxies measurable at the population level. In Ljubljana, approximately 16% of daily trips are made by bicycle, providing a representative indicator of active urban mobility behaviour.

3.1. Data Used

This study employs a multidisciplinary approach to investigate the interactions between epidemiological, environmental, and behavioural factors during the COVID-19 pandemic and its aftermath in Slovenia. Specifically, we analyse daily time-series data on confirmed COVID-19 cases, meteorological conditions, and bicycle commuting activity. The study period spans from 6 January 2020 to 30 August 2024, enabling the exploration of short- and long-term associations over distinct pandemic phases, including initial outbreaks, periods of lockdown, reopening, vaccination rollout, and post-pandemic normalisation.

Data on daily COVID-19 case counts were obtained from the National Institute of Public Health (NIJZ) through the open NIJZ COVID-19 dataset [3]. This dataset provides official daily updates on new infections across Slovenia. These figures serve as a proxy for epidemiological pressure within the population and form the foundation of the dependent variable in several model specifications. Note that bicycle counts before 2020 were inconsistent, which prevented the establishment of a comprehensive pre-pandemic baseline. Moreover, variations in local populations, such as seasonal tourism in Rateče, were not directly corrected for in the main analysis. Future efforts should aim to normalise cycling counts on a per capita basis when possible.

Meteorological data were sourced from the Slovenian Environment Agency (ARSO), which provides official climate and weather monitoring across Slovenia. The analysis included key variables such as daily average temperature, precipitation, and sunshine duration. These environmental indicators have been widely studied in the context of respiratory virus transmission, including their influence on virus viability, host susceptibility, and population behaviour. Weather stations closest to major urban centres, particularly Ljubljana, Bežigrad, and Rateče, were prioritised to match the location of bicyclist counting stations [4].

Data on daily bicycle commuting activity were collected from the Ministry of Infrastructure of the Republic of Slovenia. Specifically, we used the open dataset “PLDP števna mesta-kolesarji”, with data for Rateče and municipal cycling data for Ljubljana Drenikova (Mestna občina Ljubljana, MOL). These datasets provide automatic daily counts of bicycles passing fixed counting stations, offering an objective indicator of active mobility. Bicycle traffic reflects commuting behaviour, which may influence and be influenced by the epidemiological situation, weather, and public health measures [9].

All data series were harmonised to a daily frequency and aligned temporally to ensure consistency across datasets. Time stamps were checked for completeness, and any inconsistencies due to missing sensor recordings were documented and addressed during model calibration. No data smoothing or seasonal adjustment was applied at this stage to preserve the raw temporal structure. All processing and analysis were conducted using reproducible workflows in Gretl 2025b, Python, and JMulti 2.4.

To ensure computational consistency and avoid issues associated with the logarithmic transformation of zero values in the regression and VAR models, a systematic correction was applied across all data series. Specifically, if a zero was recorded in the bicycle count dataset, it was replaced with the value 1, preserving interpretability while allowing for a logarithmic transformation. For the COVID-19 daily case counts, a recorded zero was replaced with 0.001. For precipitation and snowfall data, zeros were replaced with 0.01. These replacement values are minimal and do not significantly bias the temporal trends, allowing for continuous modelling across the entire time range without mathematical discontinuities.

Additionally, to address the issue of negative values in the temperature measurements—common in Celsius during colder months—we converted all temperature data to Fahrenheit. This transformation eliminates the presence of negative numbers, facilitating smoother integration into models that use multiplicative terms or log-transformed variables. Although Fahrenheit is less commonly used in the scientific literature, this conversion supports methodological stability in time-series modelling and avoids the need for arbitrary offsets. All transformations were consistently applied across the whole dataset and documented for reproducibility. All data were indexed.

Our literature review revealed a gap in the COVID-19 data [56,57,59] on bike use during and after the pandemic. On this occasion, we also split the data into three separate periods [60,61]. First, the in-sample period spans from 6 January 2020 to 31 December 2023. Second, the out-of-sample period is from 1 January 2024 to 30 August 2024 [62,63,64,65]. Third, the horizon of prediction extends from 31 August 2024 to 25 January 2025.

Rateče is a small settlement located in northwestern Slovenia near the borders with Italy and Austria (46.5° N, 13.7° E, elevation ≈ 870 m). It is a well-known tourist destination in the Upper Sava Valley, characterised by pronounced seasonal tourism, sports, and cross-border cycling routes.

Ljubljana, the capital of Slovenia (46.05° N, 14.51° E, elevation ≈ 295 m), represents an urban area with a dense population, established cycling infrastructure, and an active commuting culture. Its flat terrain and moderate continental climate make it ideal for year-round cycling and comparative analysis with the tourism-oriented Rateče.

3.2. Research Methodology

The methodological framework integrates econometric and nonlinear machine learning approaches to analyse interactions between epidemiological, meteorological, and behavioural factors influencing cycling activity during the COVID-19 period. The primary econometric analysis employed a second-order vector autoregressive model, VAR(2), to identify dynamic interdependencies and lagged feedback effects among the variables. The VAR(2) specification is expressed as

$$Y_t=A_1·Y_{t-1}+A_2·Y_{t-2}+{\mu }_t$$

(1)

where $Y_t=\left[∆lnCOVID ∆lnTEMP ∆lnPREC ∆lnSUN ∆lnBIKE\right]$. $A_{i}0$ values are coefficient matrices, and ${\mu }_t,$ represents white-noise residuals. The optimal lag length (p = 2) was theoretically determined. Model estimation was performed in Gretl and JMulti.

The analysis was extended with nonlinear machine learning (ML) forecasting models implemented in Python 3.11 using the scikit-learn library. Random Forest (RF) and Gradient Boosting (GB) regressors were trained separately for Ljubljana (urban) and Rateče (tourist area) to capture nonlinear, multivariate dependencies. The general model structure is defined as

$${\widehat{y}}_t=f\left(X_t\right)+{\epsilon }_t,$$

(2)

where $f\left(·\right)$ represents an ensemble learning function approximating nonlinear mappings between lagged predictors $X_t$ and the target variable $y_t=\left[{∆lnCOVID}_t\right]$. The models used five autoregressive lags and the same predictor set as the VAR(2) specification, allowing direct comparison through RMSE, MAE, and R² metrics. This hybrid econometric–ML framework enhances predictive accuracy and interpretability, supporting a more comprehensive understanding of the links between public health, climate conditions, and sustainable cycling mobility.

4. Results

The following section presents the empirical results obtained from the VAR(2) and nonlinear machine learning models, focusing on their predictive performance and interpretation rather than methodological detail.

First, we provide descriptive summary statistics. We then give an overview of the variables. Finally, we describe the modelling process employed to generate forecasts.

4.1. Descriptive Summary Statistics

The summary statistics present key information on COVID-19 cases, which serve as the dependent variable. Additionally, meteorological conditions and cycling activity are independent variables. Abbreviations for all variables are included for clarity.

Table 2. Descriptive statistics from 6 January 2020 to 30 August 2024, daily nominal data.

Variable	Abbreviation	Mean	Median	SD	Minimum	Maximum
COVID-19 cases (Slovenia)	BI_COVID	747.50	93.00	1701.00	0.00	24,259
Rateče, NW Slovenia, a tourist destination
Temperature in degrees Fahrenheit	BI_F_RA	45.91	45.68	14.49	8.42	74.84
Precipitation in ml	BI_PERC_RA	4.55	0.10	11.47	0.00	74.84
New snow in cm	BI_SNOW_RA	0.74	0.10	3.69	0.00	55.00
Sunlight in hours	BI_SUN_RA	4.77	4.60	3.88	0.00	12.30
Number of cyclists	BI_BIKE_RA	254.70	47.00	390.10	0.00	2190
Ljubljana–Drenikova, the capital of Slovenia, an urban city
Temperature in degrees Fahrenheit	BI_F_LJ	54.91	54.86	14.46	21.74	86.72
Precipitation in ml	BI_PERC_LJ	4.05	0.00	10.69	0.00	156.90
New snow in cm	BI_SNOW_LJ	0.18	0.00	1.01	0.00	25.00
Sunlight in hours	BI_SUN_LJ	5.85	5.80	4.61	0.00	14.90
Number of cyclists	BI_BIKE_LJ	698.20	629.00	482.60	0.00	1727

Note: BIs—base indices, RA—Rateče, SD—standard deviation, LJ—Ljubljana.

provides a detailed descriptive summary of the core variables used in the time-series analysis of the COVID-19 dynamics in Slovenia.

4.1.1. COVID-19 Cases (Slovenia-Wide)

The variable BI_COVID represents the number of daily confirmed COVID-19 cases across Slovenia. The mean number of cases is 747.5, but the median is substantially lower at 93.0, highlighting a highly skewed distribution with many days of relatively low case counts and a few spikes of very high infections. The standard deviation (SD) of 1701 reinforces this variability. The maximum daily cases recorded reached 24,259, likely during major infection waves, while the minimum number of cases was 0. These large fluctuations emphasise the nonlinear nature of COVID-19 transmission (Figure 1).

The pronounced peaks in COVID-19 incidence observed in late 2021 and late 2022 correspond to the Delta and Omicron waves identified in national surveillance data. These peaks align with periods of increased indoor activity and reduced mobility during colder months.

Figure 1 presents the daily first-differenced logarithmic transformation (I(1)) of COVID-19 cases in Slovenia, expressed as a base index with 6 January 2020 set to 100. The volatility is particularly pronounced in early 2020 and again in late 2022 and early 2023, reflecting peaks in pandemic waves and possibly policy shifts or variant-driven surges. Between these periods, the fluctuations appear more moderate and stable, indicating a relatively smoother infection trend. The presence of sharp positive and negative spikes suggests abrupt changes in daily reported cases, likely tied to testing patterns, holiday effects, or changes in public health reporting. The transformation into I(1) stabilises the variance and removes non-stationary trends, making the series suitable for econometric modelling. Overall, the figure highlights the episodic and highly dynamic nature of COVID-19 transmission in Slovenia, supporting the use of time-series techniques, such as VAR, to capture intertemporal dependencies across variables in the analysis.

4.1.2. Rateče—A Tourist Destination

Rateče (RA) is located in northwestern Slovenia and is known for its tourism-driven economy. The variable BI_F_RA indicates the daily average temperature in Fahrenheit, with a mean of 45.91 °F. This suggests generally cool conditions throughout the year, which is suitable for outdoor activities, including cycling. The values range from a low of 8.42 °F, likely in the winter months, to a high of 74.84 °F in summer, with moderate variability (SD = 14.49). This makes Rateče ideal for assessing the impact of colder climates on both virus viability and active transportation behaviours (Figure 2).

Figure 2 illustrates the first-differenced natural logarithm (I(1)) of daily temperature in RA, Slovenia, transformed into base indices with 6 January 2020 set to 100. The graph displays relatively high-frequency fluctuations around the mean, with no discernible long-term trend, consistent with the expected seasonal and weather-driven variability in daily temperatures. Although the overall variance remains stable throughout the observed period, notable downward spikes occur, especially during colder months, like winter 2021 and early 2023, indicating abrupt temperature drops. Occasional positive jumps reflect short-term warming events. The amplitude of variation decreases slightly in later years, suggesting milder or more stable seasonal transitions. The application involves preparing data for regression and VAR analysis to understand how environmental conditions may influence human behaviour—particularly outdoor mobility and virus transmission patterns—in tourist destinations.

Precipitation in RA (BI_PERC_RA) averages 4.55 mL daily, with a high standard deviation (11.47) and a maximum of 74.84 mL, suggesting that while most days see minimal rainfall, occasional heavy precipitation events occur. Snowfall (BI_SNOW_RA) is also notable, with a mean of 0.74 cm and a maximum of 55.00 cm. Sunshine hours (BI_SUN_RA) average around 4.77 h, with relatively high variability, indicating the importance of sunlight as a potential explanatory variable in behaviour and mood studies during pandemic periods.

Figure 3 displays the first-differenced logarithmic base indices (I(1)) of precipitation (green), snow (orange), and solar radiation (purple) in RA from 6 January 2020 to 30 August 2024, at a daily frequency. The chart reveals substantial short-term variability across all three variables, with frequent sharp spikes and drops, indicative of the volatile nature of daily meteorological conditions in this region. Precipitation (BI_PERC_RA) shows the most extreme positive values, likely reflecting occasional heavy rainfall days, whereas snowfall (BI_SNOW_RA) appears more clustered and seasonally constrained, with bursts particularly visible during winter periods. Sunlight (BI_SUN_RA), in contrast, is more symmetrically distributed around zero, suggesting minor but regular daily fluctuations, possibly tied to changes in cloud cover or day length. The I(1) transformation effectively removes seasonal trends, isolating shocks and transitions, which supports its application in dynamic modelling. These variables provide critical non-thermal weather context for analysing behavioural responses, such as cycling or health indicators, across time.

Of particular interest is BI_BIKE_RA, or the number of cyclists recorded daily in RA. The mean is 254.7, but the median is only 47.0, revealing that cycling is highly seasonal and sporadic. With a maximum of 2190, peaks likely correspond to warmer, tourist-heavy days, while the minimum of 0 suggests periods of inactivity, probably due to snow or strict lockdowns. The high SD (390.1) supports the need to explore weather–cycling interactions in regression models.

Figure 4 shows the first-differenced logarithmic base index (I(1)) of the daily number of cyclists in RA from 6 January 2020 to 30 August 2024, benchmarked to 100 on the first observation date. The fluctuations reflect seasonal and behavioural shifts in cycling activity, with distinct clusters of high variability likely corresponding to spring and summer months when outdoor mobility is more frequent. Notably, there are periods where the data appear flat or drop to extreme lows—likely due to technical malfunctions in the automatic counting system, resulting in false zero counts. Despite these gaps, the overall pattern reveals recurring volatility and short-term adjustments characteristic of a cycling environment influenced by tourism, weather, and pandemic-related constraints.

4.1.3. Ljubljana—Slovenia’s Urban Capital

Ljubljana’s climate, as measured by BI_F_LJ, is milder than Rateče’s, with a mean temperature of 54.91 °F and similar variation (SD = 14.46). Daily temperatures range from 21.74 °F to 86.72 °F, encompassing a broader climatic comfort range for outdoor activities such as cycling.

Figure 5 illustrates the first-differenced logarithmic base index (I(1)) of daily temperature in Ljubljana (LJ) from 6 January 2020 to 30 August 2024. The plot reveals moderate short-term fluctuations typical of a temperate continental climate, with seasonal oscillations effectively removed by differencing. While temperature changes are mostly centred around zero, occasional sharp negative and positive spikes indicate sudden shifts, likely due to abrupt weather fronts. The amplitude appears somewhat reduced in the middle of the series compared to the more volatile early and late periods, though no persistent structural break is observed. This pattern reflects the dynamic yet bounded nature of temperature in urban Slovenia, where weather variability can influence public health and mobility behaviour but typically remains within expected climatic ranges.

Rainfall in LJ (BI_PERC_LJ) is slightly lower than in RA, averaging 4.05 millilitres, but with a much higher maximum of 156.90 millilitres, suggesting occasional extreme weather events. Snowfall (BI_SNOW_LJ) is less frequent and lighter than in Rateče, with a mean of 0.18 cm and a maximum of 25.00 cm, reinforcing Ljubljana’s more temperate urban environment. Sunshine is also more prevalent here (5.85 h/day on average), which could positively influence urban mobility and cycling frequency. Figure 6 depicts the first-differenced logarithmic base indices (I(1)) of daily precipitation, snowfall, and sunshine duration in LJ, covering the period from 6 January 2020 to 30 August 2024.

The green line represents precipitation (BI_PERC_LJ), the orange line snowfall (BI_SNOW_LJ), and the purple line sunshine hours (BI_SUN_LJ), all indexed to a base value of 100 at the starting date. The data display high-frequency variability throughout the series, characteristic of dynamic urban weather. Precipitation shows the most pronounced and frequent spikes, indicating sudden rainfall events, including extreme cases. Snowfall appears less frequent and more sporadic. Sunlight exhibits consistent oscillation around the zero line, with smoother and more symmetrical variation, possibly influenced by seasonal patterns in cloud cover.

The urban biking variable (BI_BIKE_LJ) shows significantly higher and more consistent activity, with a mean of 698.2 and a median of 629.0, suggesting that cycling is a regular part of daily commuting in LJ. The standard deviation is 482.6, and daily cyclist counts reached as high as 1727, demonstrating a robust level of active transportation, even in the context of a pandemic.

Figure 7 illustrates the first-differenced logarithmic base index (I(1)) of the daily number of cyclists in LJ from 6 January 2020 to 30 August 2024, with 6 January 2020 set as the base value (100). The series captures short-term changes in urban cycling patterns and reflects overall high-frequency variation, consistent with commuting behaviours in a city context. Notably, the data show occasional large spikes and drops, particularly in 2020 and early 2021, which are likely linked to pandemic-related disruptions, such as lockdowns, weather shocks, or temporary measurement discrepancies. In contrast to RA, the Ljubljana cyclist data appear more stable and consistent over time, with fewer minor fluctuations in recent years, suggesting a more regularised and resilient cycling culture.

Collectively, Table 2 and Figure 1, Figure 2, Figure 3, Figure 4, Figure 5, Figure 6 and Figure 7 offer a detailed overview of COVID-19 cases, meteorological variables, and cycling behaviour between January 2020 and August 2024. The descriptive statistics highlight clear contrasts in environmental and mobility patterns, with noticeable seasonal and spatial variations. The use of I(1) transformations stabilises the data for econometric modelling, providing a reliable empirical basis to examine connections between public health, non-thermal weather factors, and active transportation.

4.2. Regression Analysis

The regression analysis confirmed the developed hypotheses that cyclists impact COVID-19 infections and vice versa.

$${lnbike}_{t-1 i}=\alpha +{{\beta }_1·lncovid}_{t-1 i}+{{\beta }_2·lnf}_{t-1 i}+{{\beta }_3·lnperc}_{t-1 i}+{{\beta }_4·lnsnow}_{t-1 i}+{{\beta }_5·lnsun}_{t-1 i}+\epsilon ,$$

(3)

where lowercase letters indicate transformed variables from nominal to real, and is the location (RA or LJ).

But, as we hypothesised COVID-19 as a dependent variable, the equation of interest is:

$${lncovid}_{t - 1 i}=\alpha +{{\beta }_1·lnbike}_{t - 1 i}+{{\beta }_2·lnf}_{t - 1}+{{\beta }_3·lnperc}_{t - 1 i}+{{\beta }_4·lnsnow}_{t - 1 i}+{{\beta }_5·lnsun}_{t - 1 i}+\epsilon$$

(4)

where $\epsilon$ represents a random walk. The results of the regression analysis for Hypotheses 1 and 2 are presented in

Table 3. Regression analysis for Equation (2), where ${∆covid}_{t - 1 i}$ is the dependent variable.

Equation	Level	T	R2	D–W	$\mathit{\alpha }$	${∆\mathit{b}\mathit{i}\mathit{k}\mathit{e}}_{\mathit{t}-1\mathit{i}}$	${∆\mathit{f}}_{\mathit{t}-1\mathit{i}}$	$∆{\mathit{p}\mathit{e}\mathit{r}\mathit{c}}_{\mathit{t}-1\mathit{i}}$	$∆{\mathit{s}\mathit{n}\mathit{o}\mathit{w}}_{\mathit{t}-1\mathit{i}}$	${∆\mathit{s}\mathit{u}\mathit{n}}_{\mathit{t}-1\mathit{i}}$
2–RA	Nominal	1699	0.09	0.23	$2.56·{10}^8$***	319.74	−923,122 ***	–767.06 *	−156.39	46,702.20
	ln	1699	0.07	0.23	28.40 ***	0.12 *	–2.38 ***	–0.14 ***	0.13	–0.26 ***
	I(1)		0.01	2.67	0.01	–0.16 ***	0.33	0.01	–0.02	0.06 **
2–LJ	Nominal	1699	0.11	0.25	$2.82·{10}^{8 }$***	–369.75 ***	–913.51 ***	554.94	–3786.93	216,826 ***
	ln	1699	0.07	0.22	23.28 ***	–0.35 ***	–1.17 ***	–0.08 *	0.24	–0.20 ***
	I(1)	1698	0.01	2.67	0.00	0.02	0.64	–0.01	0.05	–0.03

Note: *, **, *** represent the level of significance at 10, 5, and 1%, respectively; T—number of observations, R²—deterministic coefficient; D–W—Durbin–Watson statistics, RA—Rateče, LJ—Ljubljana, $∆$—level of transformation.

.

The regression results presented in Table 3 provide insight into the relationship between daily COVID-19 cases and various meteorological variables, as well as the number of cyclists, across the two Slovenian regions, RA and LJ, and the capital city. Three model types are examined: nominal levels, logarithmic transformation (ln), and first-differenced logs (I(1)). These options help to test robustness across different data scales and address issues such as non-stationarity and heteroskedasticity.

Overall, the models have limited explanatory power. The R² values range from 0.07 to 0.11 in the ln and nominal models, indicating that about 7–11% of the variation in lagged COVID-19 cases is explained by the chosen independent variables. In the I(1) models, R² decreases to roughly 0.01, showing that after differencing the series to achieve stationarity, much of the structure seen in level regressions disappears. This highlights the complexity of modelling pandemic data, which are influenced by numerous hidden factors, such as testing rates, policy measures, and population mobility, beyond the weather and cycling variables included.

The Durbin–Watson (D–W) statistic offers valuable insights. For both RA and LJ, the D–W values in the nominal and ln models are around 0.22–0.25, pointing to significant positive autocorrelation in residuals. This autocorrelation breaches traditional regression assumptions, implying that the errors are temporally linked, possibly due to overlooked dynamics or missing lags. Conversely, the D–W values increase to about 2.67 in the I(1) models, nearing the optimal value of 2.0, which suggests that differencing the data effectively diminishes autocorrelation and enhances residual independence, crucial for accurate inference in time-series analysis.

The logarithmic model provides the most straightforward interpretation of the coefficient estimates. In RA, the number of cyclists (lnbike) exhibits a positive association with COVID-19 cases at a 10% significance level, suggesting that increased recreational cycling—potentially driven by tourism—may be linked to higher infection rates. This aligns with Hypothesis 1, indicating that outdoor activities driven by tourism can increase transmission risks, especially when combined with social events. Additionally, precipitation (lnperc) has a significantly negative coefficient, indicating that rain decreases outdoor activity and thus limits case numbers. Sunshine (lnsun) also has a significantly adverse effect, potentially because increased sunlight promotes ventilation and outdoor activity, which helps reduce the risk of infection.

In Ljubljana, a different dynamic emerges. The coefficient for cyclists (lnbike) is significantly negative, aligning with Hypothesis 2 and suggesting that urban cycling may reduce reliance on enclosed public transport and thus lower transmission. Temperature (lnf) and precipitation (lnperc) both exhibit negative, significant associations with COVID-19 cases, suggesting that warmer, drier conditions may reduce the viability of the virus or promote safer mobility. Sunshine again shows a small but significant adverse effect, reinforcing the behavioural and epidemiological benefits of solar exposure in dense urban areas.

The first-difference (I(1)) models show the direction of effects at weaker significance levels. Nevertheless, the overall results highlight the significance of behavioural and climate factors in short-term pandemic dynamics. Although exploratory, the findings confirm that using daily environmental data can enhance forecasting efforts and endorse micro-scale modelling approaches that align with infectious disease surveillance and prediction systems.

Given the limited explanatory power and statistical significance in the regression models, especially in the I(1) cases, we move forward with VAR modelling. VAR offers a more adaptable approach for examining the dynamic relationships among multiple time-series variables without requiring strict exogeneity assumptions. This transition helps clarify the bidirectional interactions between COVID-19 cases, weather conditions, and cycling activity while also addressing the autocorrelation and structural differences seen in the residuals of the initial models.

Although the regression models explained only a moderate share of variance, their significance lies in revealing directional relationships and guiding the more dynamic VAR and machine learning analyses.

4.3. VAR Model

In VAR modelling, we chose two lags for the delayed effect, and only statistically significant coefficients are shown in the equation. First, for RA,

$${lncovid}_{t-2 RA}=-0.09·{lnbike}_{\begin{array}{c}t-1 RA\\ \left[0.03\right]\end{array}}-{0.71·lnf}_{\begin{array}{c}t-2 RA\\ \left[0.02\right]\end{array}}-0.03·{lnperc}_{\begin{array}{c}t-2 RA\\ \left[0.02\right]\end{array}}-0.06·{lnsun}_{\begin{array}{c}t-1 LJ\\ \left[0.01\right]\end{array}}+\epsilon ,$$

(5)

where the p-values are written in squared parentheses.

Second, for LJ:

$$\begin{array}{ll}{lncovid}_{t - 2 LJ}=& 0.41·{lnbike}_{\begin{array}{c}t - 1 LJ\\ \left[0.00\right]\end{array}}+{0.24·lnbike}_{\begin{array}{c}t - 2 LJ\\ \left[0.00\right]\end{array}}-0.04·{lnperc}_{\begin{array}{c}t - 2 LJ\\ \left[0.02\right]\end{array}}+0.06·{lnsnow}_{\begin{array}{c}t - 1 LJ\\ \left[0.09\right]\end{array}}+0.10\\ & ·{lnsnow}_{\begin{array}{c}t - 2 LJ\\ \left[0.01\right]\end{array}}+\epsilon ,\end{array}$$

(6)

where the D–W statistics are 2.16, R² is 0.27, and T is 1696.

For the RA tourist destination (Equation (3)), the model reveals a negative relationship between lagged bike use and COVID-19 cases: a one-period lag in the logarithm of cyclists (lnbike) is associated with a 0.09 decrease in COVID-19 cases (p = 0.03). This finding suggests that increased cycling, mainly recreational in this setting, may inversely relate to virus spread, potentially indicating behavioural substitution away from indoor gatherings. Temperature (lnf) lagged two periods demonstrates a substantial adverse effect (−0.71, p = 0.02). Precipitation (lnperc) and sunshine (lnsun) also show negative coefficients, further supporting the influence of environmental factors on pandemic dynamics.

In the urban context of LJ (Equation (4)), the impact of bike activity is notably different. Here, both one- and two-period lags of cyclists (lnbike) are positively associated with COVID-19 cases (0.41 and 0.24, both p = 0.00). Precipitation again shows a mitigating effect (−0.04, p = 0.02), while snowfall (lnsnow) appears positively associated. The model′s R² of 0.27 and D–W statistic of 2.16 indicate a reasonable fit and no major autocorrelation issues.

4.4. In-Sample and Out-of-Sample Forecasting

To assess the predictive power of the estimated VAR models, we conduct both in-sample and out-of-sample forecasting exercises. The in-sample forecast extends from 6 January 2020 to 31 December 2023.

The out-of-sample forecast spans from 1 January 2024 to 30 August 2024. This period is essential for testing the model′s ability to generalise and its practical usefulness in predicting future COVID-19 trends under real-world conditions.

4.4.1. Forecasting RA

The forecasting evaluation of the VAR(2) model for RA (Figure 8) focuses on predicting the differenced logarithmic values of COVID-19 cases for the out-of-sample period from 1 January to 30 August 2024. The forecasted values are plotted against actual observations in the figure, which also features a shaded 95% confidence interval band.

The visual comparison shows that the model effectively tracks the central tendency of the series, as the forecast line (orange) generally remains within the confidence band and follows the mean trajectory of the observed values. However, sharp spikes and dips in the actual values, especially during the early months of 2024, reveal notable deviations from the forecast. The Mean Error (ME) of –0.0092 near zero indicates minimal bias, supported by a Bias Proportion (UM) of ${1.09·10}^{-5}$, showing predictions that are not skewed. The mean absolute error (MAE) of 1.3869 and root mean squared error (RMSE) of 2.7936 reflect moderate daily deviations, which are reasonable given the noisy nature of the epidemiological data. The Regression Proportion (UR) is very low (0.0004), indicating that most forecast errors—99.96°%, as shown by UD—are due to random variation rather than systematic bias. While the VAR(2) captures lagged relationships, much fluctuation in COVID-19 cases remains random.

Overall, the VAR(2) model for RA exhibits reasonable accuracy, albeit with limitations due to inherent data volatility. It supports the use of VAR models for short-term epidemic prediction, despite their imperfections.

4.4.2. Forecasting LJ

The VAR(2) model′s forecasting results for LJ (Figure 9) show its ability to predict differenced logarithmic daily COVID-19 cases. As illustrated, the orange forecast line closely tracks the actual values (green line), with most points falling within the grey-shaded 95°% confidence interval.

The error metrics show forecast accuracy. The ME is nearly zero, indicating slight bias, supported by a low UM. The UR suggests minimal slope error, showing stable model relationships. RMSE (2.7932) and MAE (1.3842) are similar to RA, indicating comparable performance across different regions, despite structural differences. Most forecast errors—99.99°%, according to the Disturbance Proportion (UD)—stem from random disturbances, highlighting data volatility influenced by factors such as policy changes and gatherings.

In conclusion, the VAR(2) model effectively tracks daily cases with minimal bias, despite random fluctuations, making it a valuable tool for urban public health forecasts that utilise indicators such as cycling and weather.

4.5. Forecasting the Next Horizon up to 25 January 2025

This section presents the VAR(2) results obtained using the JMulti 4.2 software. Figure 10 shows the forecasted data for RA, while Figure 11 presents the data for LJ. Note that these forecasts are presented as a methodological demonstration, rather than a definitive prediction of actual future case numbers.

The VAR-based forecasting results for RA from 8 April 2024 onward (Figure 10a) and the out-of-sample one-horizon forecast from 31 August 2024 to 25 January 2025 (Figure 11b) suggest stable and centred predictions. The point forecast of 0.1435 lies well within the 95°% confidence interval [−2.8928, 2.8397], with a symmetric margin of 2.7363. The relatively narrow range and mean-centred trajectory support Hypothesis 1.

The VAR forecast results for LJ indicate a point prediction of −0.2287, with a 95% confidence interval ranging from −2.8900 to 2.4325 and a forecast margin of $\pm$2.6612. As visualised in both figures for the forecast period beginning in April 2024, the predicted values remain within this interval and appear to decline moderately. This supports Hypothesis 2, suggesting that in urban environments like LJ, higher cycling activity is negatively associated with COVID-19 infections, likely due to increased mobility in open-air settings and better public infrastructure mitigating viral spread.

Overall, based on the VAR(2) model results and forecasting outputs, we can cautiously infer that future COVID-19 cases in RA may stay more volatile and potentially higher. The forecast value is positive (0.1435), and the wide confidence interval (±2.7363) reflects greater variability and uncertainty.

At the same time, LJ is likely to see fewer infections, influenced by the observed explanatory variables. The forecast value is negative (−0.2287), indicating a decline or stabilisation in case counts in the near future.

Initial estimations using the VAR(2) model provided consistent short-term forecasts of epidemiological and mobility trends. However, to account for nonlinear relationships that may exist between meteorological and behavioural variables, additional machine learning analyses were conducted.

4.6. Nonlinear Machine Learning Forecasting Models

To assess nonlinear dynamics beyond the linear VAR(2) specification, we conducted an exploratory machine learning (ML) exercise using the same daily dataset (COVID-19 cases; meteorological variables; cycling volumes) and the same evaluation window as in our VAR analysis (training through 31 December 2023; out-of-sample test: 1 January–30 August 2024). We modelled the first difference in the natural logarithm of daily COVID-19 cases (Δln COVID-19) as the target and constructed up to five daily lags for (i) the target (autoregressive terms) and (ii) each location-specific predictor in I(1) form (Δln: temperature, precipitation, snowfall, sunshine, cyclists). This preserves comparability with the econometric pipeline while allowing flexible nonlinear interactions.

We trained two widely used nonlinear regressors: Random Forest (RF) and Gradient Boosting (GB). The models were fit separately for Ljubljana (LJ) and Rateče (RA) using their location-specific predictors and the shared Δln COVID-19 autoregressive lags. Out-of-sample performance was evaluated on the 2024 test period using RMSE, mean absolute error (MAE), and R². The results are shown in

Table 4. Nonlinear model performance (daily I(1) log COVID-19): RF and GB for LJ and RA.

Location	Model	RMSE	MAE	R2	n-test
LJ	GB	2.58	1.41	0.15	243
LJ	RF	2.40	1.32	0.26	243
RA	GB	2.64	1.45	0.11	243
RA	RF	2.49	1.39	0.21	243

Note: LJ—Ljubljana, RA—Rateče, RMSE—root mean squared error, MAE—mean absolute error, R²—deterministic coefficient.

.

In Ljubljana, RF achieved RMSE = 2.40, MAE = 1.32, and R² = 0.26, while GB achieved RMSE = 2.58, MAE = 1.41, and R² = 0.15. In Rateče, RF achieved RMSE = 2.49, MAE = 1.39, and R² = 0.21, while GB achieved RMSE = 2.64, MAE = 1.45, and R² = 0.11. Across both locations, RF consistently outperformed GB in this configuration. These findings indicate that tree-based ensembles can capture nonlinear effects between weather and behavioural indicators (cycling) and short-term epidemic dynamics that are not fully represented in linear VAR.

Figure 12, Figure 13, Figure 14 and Figure 15 illustrate out-of-sample forecasts of the daily change in the natural logarithm of COVID-19 cases (Δln COVID-19) for LJ and RA using the RF and GB models. In both locations, the models generally follow the observed dynamics, with RF showing smoother and more accurate predictions. Deviations between predicted and actual values are minor in Ljubljana, reflecting more stable urban mobility conditions, whereas RA, as a tourism-oriented site, exhibits greater short-term variability. The improved fit of RF compared to GB supports the presence of nonlinear interactions between weather, cycling intensity, and infection dynamics, particularly in environments with fluctuating tourist activity.

Across both locations, the RF model achieved the lowest forecasting errors, indicating that it better captures the nonlinear relationships between weather, cycling, and epidemiological variables. In contrast, the GB model showed slightly higher errors and greater volatility in predictions, particularly in the tourism-driven area of Rateče, reflecting the higher variability of short-term mobility dynamics.

Concentration effects were emphasised for tourism areas because tourist flows in Rateče are highly seasonal and spatially clustered, which increases temporary population density and short-term contact opportunities. In contrast, cycling in Ljubljana represents a routine mode of local mobility with lower temporal concentration and, hence, a lower infection exposure potential. The analysis recognises that tourist travel may involve additional transport stages (car, bus, or train) that contribute to infection risk. However, these effects are indirectly reflected in aggregated epidemiological data and are beyond the scope of the cycling-specific behavioural analysis.

5. Discussion

This study combines epidemiological, environmental, and behavioural data into a dynamic model of COVID-19 transmission in Slovenia. The results align with existing research on how mobility and weather influence viral spread while also contributing new insights by utilising high-frequency data from urban and tourist areas [66], including greenhushing, as described by Crotti et al. [67]. The literature review highlights the dual effects of mobility: active commuting in cities may lower risk exposure, while recreational travel in tourism areas may increase the risk of transmission [68,69]. This duality is reflected in our regression and VAR model findings. Each figure and table in the Results Section corresponds directly to the hypotheses. Figure 4 and Figure 7 illustrate the cycling volumes in Rateče and Ljubljana, respectively, supporting Hypotheses 1 and 2. Figure 8, Figure 9, Figure 10 and Figure 11 display the forecasting outcomes for both regions. Compared to the static regression estimates, the VAR(2) model captured lagged feedback between epidemiological and behavioural variables, providing a more realistic representation of short-term mobility dynamics. The regression results identified linear associations, whereas the VAR analysis revealed temporal interdependence. Together, these complementary findings highlight both immediate and delayed behavioural responses to external shocks.

In RA, a tourism-focused region, the regression suggests a weak but positive link between cycling and COVID-19 cases [70], supporting Hypothesis 1. This may result from tourist clustering during peak seasons and social gatherings, which heighten transmission risk even outdoors. Conversely, the VAR model indicates a delayed negative relationship, hinting at behavioural substitution, where people might prefer cycling over indoor activities.

In LJ, Hypothesis 2 receives stronger support: increased cycling is significantly correlated with a decrease in COVID-19 cases [71]. This supports previous research showing urban cycling as a low-risk travel option, especially compared to enclosed public transport, and indicates that urban behavioural changes were effective in reducing the spread.

Weather effects align with expectations: rain generally lowered cases, likely by reducing mobility, while sunshine had mixed effects, potentially encouraging outdoor activity and viral inactivation. The limited explanatory power of the I(1) regression models underscores the inherent volatility of pandemic data and emphasises the importance of VAR models for capturing dynamic relationships, including the nonlinear machine learning models. The study process is shown in Figure 16.

The comparative evaluation of modelling approaches reveals clear differences in predictive capacity and methodological complexity. Traditional regression models provided baseline interpretability but limited adaptability to the dynamic and interconnected relationships among epidemiological and environmental variables. The multivariate VAR(2) model improved short-term forecasting accuracy by capturing interdependencies between COVID-19 cases, weather, and cycling intensity, thereby outperforming static regression in temporal coherence. However, its linear structure restricted the representation of nonlinear interactions inherent in behavioural and climatic dynamics. The integration of nonlinear machine learning models, particularly RF and GB, further enhanced predictive accuracy—RF achieved the lowest RMSE and MAE in both Ljubljana and Rateče—confirming their suitability for complex, data-rich systems. The comparative results are shown in Figure 17. The plot shows improved fit relative to linear benchmarks, indicating nonlinear interactions between weather, cycling, and epidemic dynamics.

These findings suggest that combining interpretable econometric frameworks (VAR) with adaptive ML algorithms offers a more comprehensive understanding of epidemic and mobility interactions [58,72]. Although a direct visual comparison between the VAR(2) and RF forecasts is not shown, the results reveal clear differences. VAR(2) captures short-term linear dependencies among variables, while RF offers more flexible nonlinear and threshold modelling. RF′s lower RMSE and MAE confirm its effectiveness in complex data dynamics. Both methods demonstrate the benefits of combining interpretable econometrics with adaptive machine learning for mobility and health forecasting.

The findings of this study align with and extend previous research on the interplay between weather, mobility, and epidemiological dynamics. Similarly to the results reported by Kraus and Koch [37] and Buehler and Pucher [38], the present analysis confirms that cycling remained a resilient and adaptable transport mode during the pandemic, particularly in cities with supportive infrastructure. The observed sensitivity of cycling intensity to temperature, precipitation, and sunshine duration is consistent with earlier weather-based cycling models [43,46,64]. However, by integrating epidemiological variables, this study advances previous approaches that focused solely on mobility or environmental factors. Furthermore, the superior performance of the RF model supports recent findings that machine learning techniques can outperform linear econometric models in capturing nonlinear interactions [10,65]. These results contribute to the emerging literature on hybrid modelling approaches, demonstrating that combining interpretable VAR structures with adaptive ML algorithms provides a robust framework for sustainable mobility forecasting in the post-pandemic era.

Overall, this study confirms that mobility and climate are key factors in disease patterns, endorses the integration of behavioural proxies, such as cycling, into predictive models, and provides practical guidance for pandemic readiness and urban health strategies [73].

In sum, the results confirm the value of integrating behavioural, climatic, and epidemiological data through hybrid econometric–machine learning approaches. This combination enhances forecasting accuracy and interpretability while supporting sustainable, evidence-based mobility planning in both urban and tourism contexts.

6. Conclusions

This study demonstrates that cycling activity and weather conditions have a significant impact on the dynamics of COVID-19 transmission in Slovenia. In urban Ljubljana, higher bicycle use is linked with fewer infections, indicating the health benefits of active commuting. Conversely, in the tourist-heavy area of Rateče, cycling is positively related to case numbers, likely reflecting seasonal travel and social clustering, as well as the observed contrast between urban and tourism settings. Weather factors—particularly rainfall and sunshine—have varying impacts across regions. Using regression models, our results reveal the complex interdependence between human movement, climate, and the spread of viruses, offering valuable insights for predicting respiratory epidemics and informing public health strategies. On the other hand, the VAR(2) model suggests a reversed direction of association in some instances (e.g., lagged cycling effects diverging from immediate regression results). Although some weather–cycling associations appear intuitive (e.g., reduced cycling during snowfall or shorter daylight), their quantitative confirmation is essential for calibration and validation of forecasting models and policy simulations.

The forecast indicates ongoing COVID-19 transmission risks in tourism-heavy areas, such as Rateče, where changes in weather and recreational activities can promote the spread of the virus. Conversely, Ljubljana′s urban environment exhibits a decreasing trend in infections, possibly due to stable commuting routines and well-established cycling facilities. This underscores the value of region-specific VAR forecasting in identifying spatial differences in pandemic development, emphasising the importance of customising public health models based on environmental and behavioural differences.

This research is limited by potential inaccuracies in cyclist counts, especially in tourist areas, and by replacing zeros with small constants to enable logarithmic calculations. Furthermore, the models do not include real-time behavioural data or policy measures, which could influence COVID-19 transmission independently of mobility or weather, and do not control for individual-level risk factors such as age, mask use, or household exposure. The results should therefore be interpreted as population-level behavioural trends rather than causal infection pathways, providing indicative rather than clinical evidence.

Focusing solely on Slovenia, with data from Ljubljana and Rateče, this study′s findings may not be applicable elsewhere. It also omits other possible factors, such as policy actions or indoor mobility data, and relies on adjusted zero values, which could affect the sensitivity and interpretation of the models.

Future research should extend beyond Slovenia and include real-time policy data, vaccination rates, and indoor mobility indicators. Combining machine learning methods with time-series models could improve the precision of forecasts and deepen our understanding of how environmental, behavioural, and epidemiological factors interact across different settings.

Overall, the VAR(2)-based forecasts until January 2025 support the primary hypotheses by showing an expected rise in COVID-19 cases in the tourist area of Rateče and a decrease in Ljubljana, driven by different mobility and environmental patterns. These findings have two key implications: scientifically, they confirm the value of incorporating behavioural and climatic factors into infectious disease models; practically, they underscore the importance of developing public health strategies tailored to local commuting habits and weather conditions. These insights are helpful for sustainable pandemic planning and align well with the theme of predictive modelling and behavioural forecasting. These findings also align with the SDGs (SDG 3—Good Health and Well-being, SDG 11—Sustainable Cities and Communities, and SDG 13—Climate Action) by demonstrating how integrating behavioural and environmental factors into infectious disease models can support sustainable planning of external shocks.

Our findings highlight the need for a sustainable management strategy. In addition to modelling, local governments and tourism businesses can utilise real-time cycling and weather data as early warning signs to modify public messages, regulate tourist numbers, and modify infrastructure capacity. Including behavioural indicators, such as cycling, in planning enables quicker, evidence-driven actions to encourage sustainable mobility. The nonlinear gains suggest practical value in hybrid pipelines where interpretable VAR captures short-run linear co-movements while ML models recover residual nonlinearities. This methodologically aligns with our discussion on advanced ML/DL integration and future VAR–LSTM hybrids, strengthening this paper’s contribution by demonstrating empirical improvements using state-of-the-art nonlinear methods.

From a policy perspective, the findings underscore the need for adaptive, evidence-based strategies that integrate epidemiological monitoring with sustainable transport planning. Expanding cycling infrastructure, maintaining active travel incentives, and improving weather-resilient facilities can strengthen mobility resilience in both urban and tourism contexts.