Introduction
Background
Hemorrhagic fever with renal syndrome (HFRS), also known as epidemic hemorrhagic fever, is an important infectious disease caused by hantavirus infection and transmitted by rodents, posing a serious threat to human health [
1]. Rodents are the main hosts of hantaviruses [
2]. Hantavirus is transmitted to humans primarily through inhalation of aerosols from the urine, feces, and saliva of infected rodents [
3] and can also be transmitted through the digestive tract and via direct contact [
4]. Clinical symptoms of HFRS include fever, hemorrhage, headache, and renal impairment, with the course of a typical case divided into 5 stages: fever, hypotensive shock, oliguria, polyuria, and recovery [
5,
6].
In recent years, an estimated 200,000 people worldwide have been affected by HFRS each year [
7]. Cases are distributed largely in Asia and Europe, with China reporting the highest number and accounting for 90% of global cases [
8]. Moreover, cases have been reported in 31 of 34 provinces, autonomous regions, municipalities, or special administrative regions in China [
9]. Shandong Province is among the provinces with the highest number of HFRS cases in China [
10]. Weifang, one source of HFRS in Shandong Province, has seen a gradual expansion of affected areas since the first case was reported in 1974 and now represents a high-incidence region for the disease [
11].
The prevalence of HFRS is influenced by multiple factors, including socioeconomic conditions, healthcare availability, and the ecological environment [
12]. Meteorological conditions play a crucial role in HFRS transmission, particularly through effects on crop growth, hantavirus activity, and daily human behaviors. Precipitation and temperature are key determinants of HFRS incidence. Specifically, precipitation influences vegetation growth and hantavirus spread, which in turn affects transmission. Additionally, temperature fluctuations can impact rodent populations, influencing their reproductive cycles and maturity [
13].
Ecological factors also contribute significantly to the spread of HFRS by altering rodent population density, geographic distribution, and the virus carriage rate among these animals [
14]. Furthermore, a nonlinear relationship has been observed between the normalized difference vegetation index (NDVI) and HFRS risk. Extremes in NDVI, whether high or low, can affect rodent survival, which subsequently influences the risk of disease transmission to humans [
15].
Current research on HFRS determinants has mostly focused on host animals, climate conditions, or their combination. Few studies have integrated host, climate, and economic factors in a comprehensive analysis. For example, previous exploration of HFRS in Weifang has focused mainly on epidemiological characteristics and the impact of climate change on HFRS [
16], with relatively scarce research examining economic and ecological factors. On this basis, the present study uses wavelet analysis [
17], a generalized additive model (GAM), and structural equation modeling (SEM) to investigate economic, ecological, and climatic factors associated with HFRS in Weifang, Shandong Province, from 2013–2021; to explore the incidence of HFRS; and to predict the timing of cases, thereby providing a theoretical basis for accurate prevention and control measures.
Materials and Methods
Study Area
Weifang is a prefecture-level city under the jurisdiction of Shandong Province, China. Located in the central part of the Shandong Peninsula, it has a warm temperate, monsoon-influenced, semi-humid continental climate. The topography rises from north to south, with a total area of 16,167.23 square kilometers. As of 2022, the city has jurisdiction over 4 districts and 2 counties and administers 6 county-level cities. At the end of 2023, the permanent population of Weifang was 9.3695 million, with a regional gross domestic product (R. GDP) of 760.601 billion yuan.
Data Collection
HFRS incidence and rodent density
All cases of HFRS in Weifang from January 1, 2013, to December 31, 2021, were obtained from the National Disease Surveillance System of the Chinese Center for Disease Control and Prevention. The dataset included key variables such as gender, age, population classification, current address, case classification, and date of onset. Rodent population monitoring information included the number of effective traps, the number of rodents captured, and rodent species. Rodent density was calculated as (number of rodents captured/number of active traps)×100%. Data from 2017 onward were available as monthly figures.
Data processing and interpolation
To ensure consistency in temporal resolution across the study period (2013–2021), we applied data interpolation methods to address differences in time granularity. For rodent density data prior to 2017, which were available at a lower temporal resolution (e.g., quarterly or annually), we used the adjacent midpoint method to interpolate monthly values. The interpolation formula was: missing value=(previous valid value+next valid value)/2.
This approach allowed us to generate monthly estimates for rodent density from 2013 to 2016, ensuring compatibility with the monthly data available from 2017 onward. Similarly, for other variables with inconsistent temporal resolutions, we applied the same interpolation method to maintain uniformity in the dataset. This preprocessing step enabled continuous time-series analyses, including GAM and wavelet analysis, without introducing biases due to temporal mismatches [
18].
Meteorological Data
Meteorological data were obtained from the China Meteorological Science Data Sharing Service Network (
https://data.cma.cn/). The data included monthly average temperature (tmean, ℃), monthly minimum temperature (tmin, ℃), monthly maximum temperature (tmax, ℃), monthly average precipitation (Ap, mm), monthly average relative humidity (Rh, %), and monthly average wind speed (Ff, m/s). Population size and R. GDP indicators were obtained from the Weifang Statistical Yearbook (
http://tjj.weifang.gov.cn/). These data included population (×10
3), R. GDP (billion yuan), total grain output (10,000 tons), and other economic indicators (
Table 1).
Data Analysis
In this study, a GAM was used to examine the associations between HFRS incidence and rodent density, temperature, Rh, precipitation, population, gross regional product, and total food production. Because HFRS is a low-incidence condition and therefore represents a small-probability event, a Poisson link function was applied to account for the discrete nature of the data. The generalized cross-validation (GCV) index was used as the model selection criterion, with a lower GCV value indicating a better-fitting model. To ensure that the distribution of the response variable approximated a normal distribution, the variable was log-transformed. The optimal model was established as follows: log[Yi]=β0+f1(tmeani)+f2(log yieldi−1)+f3(Rhi)+f4(log Average rodent densityi)+εi,
where Yi is the number of HFRS cases in month i; β0 is the model intercept; tmeani is the average temperature in month i; yieldi−1 is the previous month’s total grain yield; Rhi is the average Rh in month i; Average.rodent densityi is the average rodent density in month i; εi is the random error term; and f1, f2, f3, and f4 are natural spline smoothing functions, each with 4 degrees of freedom.
This study used a Bayesian time-series model to predict the incidence of HFRS. The Bayesian method is a statistical inference approach that integrates prior information with observed data to update beliefs and make predictions, offering improved flexibility and adaptability. Similar Bayesian and artificial intelligence-based approaches have been successfully applied to predict infectious disease trends, demonstrating their effectiveness in epidemiological forecasting [
19]. Prior to analysis, the dataset was divided into a training set (January 2013–December 2019) and a testing set (January 2020–December 2021) to validate model fit and assess predictive performance. A key advantage of this model is its reliance on probability distributions rather than point estimates, which promotes adaptability and mitigates the risk of overfitting. Common indicators for assessing model fit include root mean square error (RMSE), mean absolute percentage error (MAPE), and the coefficient of determination (
R2), with smaller RMSE and MAPE values indicating better fit, whereas a larger
R2 value is preferable. By incorporating prior information, the Bayesian method demonstrates greater flexibility and adaptability than traditional approaches.
SEM was then applied to explore the associations of the number of HFRS cases with mean rodent density, climate (tmean and Rh), and economy (yield). Model fit was assessed using the comparative fit index (CFI) and RMSE of approximation (RMSEA). The CFI ranges from 0 to 1, with higher values indicating better model fit; an RMSEA value closer to 0 also indicates better fit.
All statistical analyses were performed with the “biwavelet,” “mgcv,” “CausalImpact,” “lavaan,” and “corrplot” packages in R ver. 4.2.1 (R Foundation for Statistical Computing). The confidence intervals (CIs) for all 2-sided statistical tests were 95%.
Results
Descriptive Data
Weifang had 2,118 recorded HFRS cases from January 2013 to December 2021. The highest number of cases was reported in 2013, totaling 388. Among all cases, the number of male patients (
n=1,442) was significantly greater than that of female patients (
n=523), with a male-to-female ratio of 2.76:1. The age at HFRS onset was most frequently 40 to 69 years, accounting for 69.1% of all cases. The most affected occupational groups included farmers, workers, and students, with farmers (1,726) accounting for 87.8% (
Table 2). The trend in HFRS incidence in Weifang from 2013–2021 showed a rapid decline from 2013–2016, followed by a brief period of stability between 2017 and 2018. This was followed by a downward trend from 2019–2020, with a slight increase in cases observed in 2021. Notably, the lowest number of cases was recorded in 2020. Rodent density closely mirrored the trend for HFRS incidence. Additionally, the overall incidence exhibited significant seasonality, with lower counts observed from July to September and peak cases between October and December (
Figure 1). The distributions of monthly minimum temperature, Rh, and precipitation exhibited clear cyclical and seasonal patterns (
Figure 2), with mean monthly minimum temperature, Rh, and precipitation of 9.65 °C, 62.37%, and 54.24 mm, respectively.
Multivariate Correlation Analysis
Multivariate correlation analysis revealed that, among economic factors, GDP, crop cultivated area, total grain production, and green space area were highly correlated (
r>0.8). Mean air temperature, minimum air temperature, maximum air temperature, and air pressure also exhibited high correlations (
r>0.8). Mean rodent density was correlated (
r>0.5) with the densities of brown rats and small house mice (
Figure 2).
Wavelet Correlation between HFRS and Rodent Density
Wavelet analysis indicated a correlation between HFRS incidence and the population density of small house mice from 2013–2016 and a correlation between HFRS incidence and the population density of brown rats from 2017–2021 (
Figure 3). The occurrence of HFRS can be divided into 2 phases: 2013–2016, when the main hosts were small house mice, and 2017–2021, when the main hosts were brown rats.
HFRS Incidence in Relation to Climate and Economy
The GAM analysis revealed a positive correlation between monthly average rodent density and HFRS incidence, indicating that higher rodent density significantly increases the risk of HFRS outbreaks. Regarding meteorological factors, both monthly mean temperature (tmean) and monthly mean Rh exhibited nonlinear associations with HFRS incidence, specifically U-shaped relationships with distinct inflection points at approximately 11.64 °C for temperature and 68.31% for humidity. Below these thresholds, the factors were positively correlated with incidence, whereas above them, the correlations became negative.
The nonlinear relationships between these key predictors—tmean, Rh, and average rodent density—and HFRS incidence are shown in
Figure 4 through GAM smoothing curves. Temperature displayed a U-shaped relationship with incidence, peaking near 11.64 °C; Rh showed an inverted U-shaped pattern, peaking around 68.31%; and average rodent density maintained a consistent positive linear correlation. These findings corroborate the statistical model results presented in
Table 3, further validating the model. With respect to economic factors, a clear inflection point was observed between the previous month’s total grain yield (
yieldi−1) and HFRS incidence, characterized by an initial negative correlation followed by a positive correlation beyond the inflection point, forming a U-shaped relationship (
Figure 4). Regarding risk ratios (RRs), the RR for monthly average rodent density was 0.94 (95% CI, 0.78–1.13); for tmean, 2.09 (95% CI, 1.51–2.88); for monthly average Rh, 1.28 (95% CI, 0.95–1.75); and for the previous month’s total grain yield, 0.54 (95% CI, 0.24–119.07). All estimates are summarized in
Table 3.
The Bayesian Prediction Model
The factors influencing HFRS occurrence identified above (average rodent density, tmean, Rh, and
yieldi−1) were incorporated into the Bayesian prediction model. The model’s fitting performance is illustrated in
Figure 5, where the triangular dashed line represents the actual number of cases, the solid square line represents the predicted values, and the shaded area indicates the 95% CI. Notably, the predicted values closely aligned with the observed data, demonstrating a strong model fit. The validation results confirmed that the established model accurately predicted HFRS occurrence in Weifang during 2020–2021, with performance metrics of RMSE=7.36, MAPE=0.28, and
R2=0.65.
Pathways Influencing HFRS Incidence
The SEM results clarify the pathways influencing HFRS occurrence. As shown in
Figure 6, the latent variable “climate” (comprising Rh, average temperature, and rainfall) exerted a positive effect on average rodent density (path coefficient, +0.698). Conversely, the direct path from climate to HFRS incidence had a negative coefficient (−0.402). The direct paths from R. GDP and average rodent density to HFRS were also negative, with coefficients of −0.650 and −0.093, respectively.
Discussion
Prevalence of HFRS
A total of 2,118 cases of HFRS were reported in Weifang from 2013 to 2021. Overall, reported cases displayed a general downward trend, with a rebound observed in 2017. This finding may relate to climate change, shifts in rodent habitat, and population vaccination coverage. Among reported HFRS cases, the number of male patients was significantly higher than that of female patients. The age of onset was predominantly 40 to 69 years, and farmers were the most affected occupational group, aligning with prior studies [
19]. This pattern may be explained by the greater likelihood of adult males to be exposed to infected rodents through occupational activities. Related occupations, such as herding, also face an increased risk of infection [
20].
Shift in Primary Host Animal
In Weifang, mice were the primary animal hosts of HFRS from 2013–2016; however, brown rats became the dominant host species from 2017–2021. This shift may be associated with the city’s urban–rural development during that period, including the urbanization of rural areas and the renovation of rural toilets and household sewage systems. Such human activities can alter community structure, species distribution, and the population density of host animals. Urbanization processes influence ecological quality and dynamics at different stages of development [
21], thereby modifying vector populations and transmission patterns. Additionally, the significant decrease in total grain production after 2017 may have further contributed to this shift in host species. Beyond environmental changes, improvements in living conditions driven by economic development have also impacted host habitats and influenced population dynamics [
22]. A GAM analysis demonstrated that rodent density, temperature, Rh, and total grain yield significantly affected the prevalence of HFRS, further supporting our observations.
Potential Drivers of Seasonal Incidence Pattern
Weifang exhibits pronounced seasonal variations in HFRS incidence, with peak cases occurring annually from October to December and relatively low incidence from July to September. This epidemiological pattern likely results from the combined influence of agricultural cycles, rodent ecology, and human activities. The autumn harvest season (October–December) represents a critical period of heightened risk. First, large-scale grain harvesting and storage provide abundant food sources for rodents, leading to rapid population growth and increased proximity to human dwellings. Second, declining temperatures drive rodents—such as the black-striped field mouse—to migrate from fields into warmer indoor environments such as houses and granaries, substantially increasing human exposure to virus-contaminated excreta. At the same time, concentrated indoor grain processing following the harvest further elevates the risk of aerosol transmission within enclosed spaces [
23]. In contrast, incidence levels are lower during the summer months (July–September). Agricultural activities at this time focus primarily on field management, with rodents widely dispersed across open terrain, markedly reducing opportunities for human-rodent contact.
Influence of Climatic Factors on the Incidence of HFRS
This study employed SEM to elucidate the pathways through which climatic factors influence the incidence of HFRS. As shown in
Figure 6, the latent variable “Atmosphere” (comprising Rh, average temperature, and rainfall) demonstrated a weak positive indirect effect on HFRS through rodent density: the path coefficient from Atmosphere to rodent density was −0.165 and that from rodent density to HFRS was −0.093, yielding an indirect effect of approximately +0.015. This finding aligns with established ecological mechanisms in which moderate climatic conditions promote rodent population growth, thereby indirectly increasing transmission risk, consistent with observations from Weifang [
24]. However, the direct path from Atmosphere to HFRS had a negative coefficient (−0.402), which may reflect residual effects after controlling for rodent density or limitations in capturing complex climatic interactions due to data constraints. This provides a plausible explanation for inconsistencies across studies: for instance, our results partially align with those of Lin et al. [
25], whereas Li et al. [
26] reported a persistent negative correlation between temperature and HFRS, potentially attributable to regional variations in climatic conditions and human behavior. Temperature primarily affects HFRS by modifying rodent habitat and activity, with an optimal reproductive range of 10–25 °C [
11]; however, extreme temperatures may directly reduce human outdoor exposure. Regarding humidity, a nonlinear relationship with HFRS was observed—positive below the 68.31% Rh threshold but negative above it—consistent with the findings of Xiao et al. [
27,
28] and Liang et al. [
29]. This suggests that moderate humidity increases rodent density, whereas excessive rainfall disrupts habitats. Additionally, R. GDP exhibited a strong direct inhibitory effect on HFRS (path coefficient, −0.650), underscoring the influence of socioeconomic factors in disease control. In summary, the SEM results indicate that the indirect climatic effect via rodents, although modest, is positive, whereas the direct negative path warrants further investigation into residual or confounding mechanisms.
Influence of the Economy on HFRS Incidence
The present study revealed a nonlinear relationship between the previous month’s total grain yield and the number of HFRS cases. A turning point was observed in total grain production, with the correlation initially negative and becoming positive beyond that point. This study also found that economic development is negatively associated with the incidence of HFRS, consistent with the findings of Xiao et al. [
27]. Previous research has shown that economic development plays important roles in the occurrence, spread, prevention, and control of infectious diseases [
30]. This finding supports broader evidence that socioeconomic factors interact with meteorological conditions to influence disease transmission patterns. Rapid economic development has substantially improved living conditions and hygiene, reducing the likelihood of human contact with rodents and thus lowering the risk of HFRS. In addition, increased public awareness of the disease further contributes to limiting its spread.
Modeling of the Prediction of HFRS Onset Time
The model’s predictions closely aligned with observations at multiple time points, accurately capturing fluctuations in case counts and reflecting the dynamic behavior of HFRS incidence. We project that, assuming other conditions remain unchanged, HFRS incidence will continue to exhibit periodic fluctuations in the coming years. Discrepancies between predicted and observed values at certain time points may arise from the model’s inability to fully account for the complex factors influencing HFRS incidence, including spatial heterogeneity and external shocks. Future research should consider incorporating additional factors to increase the predictive accuracy and undertake model optimization and validation to ensure robustness across regions and time periods. Model adjustments may also be necessary to better accommodate the complexity and uncertainty of HFRS incidence at specific time points.
Although this study provides a comprehensive analysis of the HFRS epidemic using multiple epidemiological and statistical methods, several limitations remain. For example, because it focuses on a single city (Weifang), its representativeness is limited, and it lacks comparative analysis with other regions. This limitation may affect the broader applicability of the findings. Moreover, the research’s focus on Weifang without incorporating a wider regional perspective may further limit the generalizability of the results. In addition, although the Bayesian time-series model demonstrated strong predictive performance, it did not include spatial factors in the analysis. Future studies could improve predictive accuracy and model applicability by expanding the scope of data collection, integrating dynamic monitoring of host behavior and environmental factors, and adopting other innovative approaches.
