Tag: statistics

Sci Rep. 2026 May 13. doi: 10.1038/s41598-026-49743-1. Online ahead of print.

ABSTRACT

Rumor spreading has become a critical social issue with the widespread use of social media platforms. This study develops a stochastic fractional delay differential equation (SFDDE) model to describe rumor propagation in a population divided into four compartments: susceptible [Formula: see text], spreaders [Formula: see text], counter-rumor spreaders [Formula: see text], and stiflers [Formula: see text]. The proposed model ensures nonnegativity and boundedness of solutions for nonnegative initial conditions. Rigorous analytical investigations establish the local and global stability of both the Rumor-Free Equilibrium (RFE) and the Rumor-Present Equilibrium (RPE), with the reproduction number identified as a key threshold parameter. Supported by classical stability theorems, the model’s positivity, boundedness, local and global dynamics, and sensitivity around the reproduction number are systematically examined. Furthermore, the Generalized Nonstandard Finite Difference (GL-NSFD) method is employed to obtain accurate and dynamically consistent numerical approximations, demonstrating the model’s reliability and efficiency through simulations and graphical validation.

PMID:42129419 | DOI:10.1038/s41598-026-49743-1

Sci Rep. 2026 May 13;16(1):15067. doi: 10.1038/s41598-026-50965-6.

ABSTRACT

Acute SARS-CoV-2 infection has been implicated in the development of endothelial dysfunction and metabolic alterations. These disturbances may contribute to the pathophysiology of post-COVID-19 syndrome (PCS), a multifaceted condition characterized by persistent symptoms, including neuropsychiatric symptoms. The diagnosis of PCS primarily relies on symptom-based criteria. Here, we aimed to identify biomarkers associated with PCS and disease severity. This prospective single-center cohort study investigated soluble blood biomarkers related to endothelial dysfunction and amino acid, fatty acid, carnitine, eicosanoid and resolvin metabolism in individuals post-acute SARS-CoV-2 infection with or without PCS compared with individuals without documented SARS-CoV-2 infection. Additionally, we explored the association between these biomarkers and PCS-related fatigue severity as assessed by the Multidimensional Fatigue Inventory (MFI). At a median of 37.4 weeks after SARS-CoV-2 infection, participants with prior infection showed higher levels of soluble thrombomodulin (TM) and L-lactate dehydrogenase (LDH) than those without previous infection. Alterations in arginine biosynthesis and taurine and hypotaurine metabolism indicate disruption of the NO-metabolism. These findings were made in participants without and with symptoms of PCS. In participants with PCS-related high fatigue severity, concentrations of the polyunsaturated fatty acid (PUFA) linoleic acid (LA), and the monounsaturated fatty acids (MUFAs) oleic acid (OA) and palmitoleic acid (PA) were higher than in participants with low fatigue severity. Alterations in markers of endothelial dysfunction and NO-metabolism are detectable at a median of 37.4 weeks after SARS-CoV-2 infection independent of PCS-related fatigue severity. Additionally, in individuals with high PCS-related fatigue severity, specific fatty acid alterations were observed.

PMID:42129413 | DOI:10.1038/s41598-026-50965-6

Sci Rep. 2026 May 13. doi: 10.1038/s41598-026-52453-3. Online ahead of print.

ABSTRACT

Coal and gas outburst represents a highly destructive dynamic phenomenon inherent in deep coal mining operations. Currently, outburst prediction frameworks rely heavily on a uniform critical threshold system recommended by national regulations. However, within heterogeneous coal seams characterized by complex geological conditions, this universal approach frequently leads to “low-index outburst” incidents or excessive engineering redundancy, significantly undermining the intrinsic safety of mine operations. To address this core scientific bottleneck, the present study establishes a theoretical methodology for the quantitative determination of sensitive prediction indicators and proposes a hierarchical optimization framework for both regional and local critical thresholds. By integrating long-term historical statistics, laboratory kinetic tests of gas desorption, and in-situ multi-point tracking and verification, the critical thresholds undergo scientific calibration and site-specific alignment. Empirical research conducted on the No. 1 coal seam of the Miluo Coal Mine in Guizhou demonstrates that, at the regional prediction level, gas content and gas pressure exhibit equivalent sensitivity, with established critical values of 8.0 m³/t and 0.74 MPa, respectively. Furthermore, the sensitivity hierarchy for local prediction indicators was determined as [Formula: see text]. Significantly, the finalized local thresholds ([Formula: see text]= 0.47 mL/(g·min^0.5), [Formula: see text]= 184 Pa, and S= 6.0 kg/m) are more stringent than the recommendations set forth in the Detailed Rules for Prevention and Control of Coal and Gas Outburst. The proposed prediction system effectively standardizes disaster characterization in complex coal seams and provides strategic guidance for coal mining enterprises to establish precision-based, site-specific outburst prevention standards. Coal and gas outbursts constitute a highly destructive dynamic phenomenon inherent in deep coal mining operations. Current outburst prediction frameworks largely depend on a uniform critical threshold system mandated by national regulations. However, in heterogeneous coal seams characterized by complex geological conditions, this universal approach frequently leads to “low-index outburst” incidents or excessive engineering redundancy, significantly undermining the intrinsic safety of mining operations. To resolve this fundamental scientific bottleneck, the present study establishes a theoretical methodology for the quantitative determination of sensitive prediction indicators and proposes a hierarchical optimization framework for both regional and local critical thresholds. By integrating long-term historical statistics, laboratory kinetic tests of gas desorption, and in-situ multi-point tracking and verification, the critical thresholds undergo rigorous scientific calibration and site-specific alignment. Empirical research conducted on the No. 1 coal seam of the Miluo Coal Mine in Guizhou demonstrates that, at the regional prediction level, gas content (w) and gas pressure (p) exhibit equivalent sensitivity, with established critical values of 8.0 m³/t and 0.74 MPa, respectively. Furthermore, the sensitivity hierarchy for local prediction indicators was established as [Formula: see text]. Significantly, the finalized local thresholds ([Formula: see text]= 0.47 mL/(g·min^0.5), [Formula: see text]= 184 Pa, and S= 6.0 kg/m) are more stringent than the standards set forth in the Detailed Rules for Prevention and Control of Coal and Gas Outburst. The proposed prediction system effectively standardizes hazard characterization in complex coal seams and provides strategic guidance for coal mining enterprises to establish precision-based, site-specific outburst prevention standards.

PMID:42129399 | DOI:10.1038/s41598-026-52453-3

Sci Rep. 2026 May 13. doi: 10.1038/s41598-026-53061-x. Online ahead of print.

ABSTRACT

Accurate representation of CO over India remains challenging because of large uncertainties in emissions, atmospheric transport, and sparse in‑situ measurements. This study examines the impact of assimilating MOPITT total column CO retrievals into the Weather Research and Forecasting model coupled with Chemistry (WRF‑Chem) using the Gridpoint Statistical Interpolation (GSI) system for October-December 2019, a period strongly influenced by post‑monsoon crop‑residue burning and stagnant meteorology over northern India. Model performance is evaluated against independent TROPOMI CO columns and MOPITT vertical profiles. The control simulation (WRF‑CNTL) shows a persistent positive bias, overestimating TROPOMI CO by about 0.4-0.6 × 10¹⁸ molecules cm⁻² across the Indo‑Gangetic Plain. Assimilation (WRF‑DA) markedly reduces these biases and better captures observed spatial and temporal variability. Normalized mean bias decreases from 33.5% to 14.4%, while the index of agreement increases from 0.45 in the control to 0.72 in the data assimilation run. Comparisons with MOPITT profiles indicate that assimilation lowers near‑surface CO by 40-100 ppbv and reduces profile errors by 40-60% in the lower troposphere. These results show that MOPITT CO assimilation effectively constrains regional CO distributions and substantially enhances WRF‑Chem performance over India.

PMID:42129394 | DOI:10.1038/s41598-026-53061-x

Int J Impot Res. 2026 May 13. doi: 10.1038/s41443-026-01283-y. Online ahead of print.

ABSTRACT

Most studies on the impact of vitamin D on sex hormones focus on specific populations, such as older males, Asian males, or those with certain health conditions. Limited evidence exists on the relationship between vitamin D and sex hormones in American women. This cross-sectional analysis used National Health and Nutrition Examination Survey (NHANES) data to explore the association between serum vitamin D levels and sex hormones levels in women. Data from NHANES (2021-2023) were analyzed. Participants were categorized by serum vitamin D levels: Deficient (<50 nmol/L), Insufficient (50-74.99 nmol/L), and Adequate ( ≥ 75 nmol/L). One-way ANOVA and Chi-square tests were used for comparisons, and linear regression evaluated associations. Our analysis specifically focused on a subset of 3181 women aged 18 years and older (18-80 years). Women in the adequate vitamin D group had lower body mass index (BMI) (29.16 vs. 32.10 kg/m², p < 0.001), lower total testosterone (24.10 vs. 32.28 ng/dL, p < 0.001), progesterone (139.05 vs. 229.73 ng/dL, p < 0.001), estrone sulfate (687.10 vs. 1023.08 pg/mL, p < 0.001), and dehydroepiandrosterone sulfate (DHEAS) (66.41 vs. 100.56 µg/dL, p < 0.001) compared to the deficient vitamin D group. They also had higher sex hormone-binding globulin (SHBG) (70.37 vs. 58.55 nmol/L, p < 0.001), follicle-stimulating hormone (FSH) (50.30 vs. 23.99 mIU/mL, p < 0.001), and luteinizing hormone (LH) (26.39 vs. 16.64 mIU/mL, p < 0.001) compared to the deficient vitamin D group. Linear regression revealed that higher serum vitamin D was inversely associated with 17α-hydroxyprogesterone (Beta = -0.85, P = 0.023), androstenedione (Beta = -0.181, p < 0.001), anti-Müllerian hormone (Beta = -0.238, p < 0.001), DHEAS (Beta = -0.204, p < 0.001), total testosterone (Beta = -0.080, P = 0.042), while showing a positive association with follicle-stimulating hormone (Beta = 0.260, p < 0.001) and luteinizing hormone (Beta = 0.208, p < 0.001). Serum vitamin D levels were negatively associated with testosterone and estradiol in American women, particularly in older individuals.

PMID:42129376 | DOI:10.1038/s41443-026-01283-y

Pediatr Res. 2026 May 13. doi: 10.1038/s41390-026-04952-2. Online ahead of print.

ABSTRACT

BACKGROUND: There is a well-established link between growth and future health, but it is uncertain whether early life growth and well-being in adolescence are associated. We hypothesized that individuals with slower growth during infancy or childhood had a lower degree of well-being at age 18 years.

METHODS: This population-based study examined early life growth in relation to adolescent well-being in the GrowUp_1974&1990Gothenburg cohorts (n = 4319). Individual growth trajectories were modeled using the Quadratic-Exponential-Pubertal-Stop (QEPS) model, based on longitudinal height data. Well-being was assessed using the Gothenburg Well-being in Adolescence scale.

RESULTS: Associations between early life growth (birth size, height at ages 2, 4, and 7 years, and growth change) and adolescent well-being were uniformly small (β ranging from -0.2 to 0.2), with narrow confidence intervals and low explained variance (R² ≤ 1%). However, in the 1974 cohort, males born large for gestational age reported higher total well-being than peers born appropriate or small for gestational age, while females born large for gestational age by weight reported lower mood and self-esteem.

CONCLUSION: Differences in self-reported well-being at age 18 years associated with early-life growth were small and probably of minimal clinical importance, providing relevant information for healthcare professionals and parents.

IMPACT: This population-based study, with longitudinal growth data from over 4,000 Swedish adolescents, born in 1974 and 1990, showed that early life growth is of limited importance for self-reported well-being at age 18. There is a well-established link between growth and future health, but our results suggest that early deviations in physical growth are unlikely to have substantial implications for adolescent well-being in relatively healthy populations. The study’s findings may offer reassurance to clinicians and parents concerned about the long-term psychological consequences of early growth variations.

PMID:42129372 | DOI:10.1038/s41390-026-04952-2

Sci Rep. 2026 May 13;16(1):15046. doi: 10.1038/s41598-026-51334-z.

ABSTRACT

Studies have shown how air pollution and temperature affect blood pressure. We investigated the combined effect of air pollution and temperature on blood pressure in a cohort of older German women. We conducted a cross-sectional analysis of systolic (SBP) and diastolic blood pressure (DBP) data from follow-up 3 (2012-2013) of the Study on the influence of Air pollution on lung function inflammation and ageing (SALIA) cohort. Short-term data on daily air pollutants and temperature were obtained from the German Weather Bureau and the German Environment Agency. A generalized additive model was used to capture their combined effect. Stratified analyses were performed to quantify the variation in the estimated effects. The core model was adjusted for potential covariates. We observed a combined association of temperature and air pollution with blood pressure. We found that lower temperatures and higher levels of air pollutants such as PM_2.5 and NO₂ were associated with higher SBP and DBP. However, higher O₃ exposure was generally associated with lower SBP and DBP. Stratified analyses showed that the associations between temperature, air pollution, and blood pressure were stronger among women living in urban areas and those with lower socio-economic status. The combined effect of low ambient temperature and high air pollution substantially increased BP among older German women.

PMID:42129347 | DOI:10.1038/s41598-026-51334-z

Sci Rep. 2026 May 13. doi: 10.1038/s41598-026-51718-1. Online ahead of print.

ABSTRACT

Investigation of in utero, tissue-specific molecular pathways contributing to prenatal programming of childhood-onset asthma is needed to develop effective, targeted prevention strategies. We aimed to examine the relationship between predicted gene expression in placenta and childhood-onset asthma and to compare relationships between childhood- and adult-onset asthma. Asthma genome-wide association study published summary statistics were obtained from the UK Biobank and published placental gene expression quantitative trait loci were obtained from the Rhode Island Child Health Study. We used S-PrediXcan to evaluate and compare associations between placental predicted gene expression and childhood- and adult-onset asthma and to determine whether signals were placenta-specific. Among 8,038 tested placental predicted expression-asthma associations, we identified 56 (0.7%) genes only significantly associated with childhood-onset asthma, 12 (0.1%) genes only significantly associated with adult-onset asthma, and 18 (0.2%) shared genes. Predicted expression of several genes (ACTL9, AMN, C9orf38, C11orf30, CTSE, EFCAB13, EIF4E1B, FN1, GLS2, IL6, IVL, LZIC, MAN2A2, MEGT1, RACGAP1, SMAD6, SPATA5, TMEM25, VTI1B, WDR19) was not significantly associated with childhood- or adult-onset asthma in any non-placental tissue, suggesting that the associations may be placenta-specific. This study identified alterations in predicted expression of placental genes associated with transcriptional pathways critical to the development of asthma. We identified unique and shared pathways, particularly related to immune regulation, associated with childhood- and adult-onset. This expands our understanding of the fetal origins of asthma, highlights the placenta as an informative tissue in understanding asthma pathogenesis, and identifies target genes to prioritize for future functional studies.

PMID:42129325 | DOI:10.1038/s41598-026-51718-1

Sci Rep. 2026 May 13. doi: 10.1038/s41598-026-52632-2. Online ahead of print.

ABSTRACT

This study focuses on the vessel normalization window of anlotinib to preliminarily explore the optimal intervention timing for combining anlotinib with whole brain radiotherapy (WBRT) in treating brain metastases from non-small cell lung cancer (NSCLC). We aimed to explore the feasibility of combining anlotinib with WBRT based on the hypothesized vascular normalization window, and to investigate potential associations with intracranial tumor control, iPFS, and quality of life in patients with NSCLC brain metastases. This study was designed as a prospective, non-randomized, single-center cohort study. From Feb 8, 2024, to Sep 30, 2025, a total of 38 patients with NSCLC brain metastases diagnosed by the Department of Oncology, the Fifth Affiliated Hospital of Chengdu University of Traditional Chinese Medicine, were prospectively recruited. Anlotinib was used as the intervention measure in this study. According to whether the patients received anlotinib or not, they were divided into the experimental group (anlotinib combined with WBRT) and the control group (sole WBRT), with 19 patients in each group. In the experimental group, the vascular normalization time window of anlotinib, which is 5 to 7 days, was precisely utilized. The specific medication regimen was to start taking 8 mg of anlotinib 5 days before the initiation of WBRT and continue the medication until the end of WBRT. In contrast, the control group received only WBRT. The primary and secondary endpoint indicators of the patients in both groups were followed up regularly. The primary endpoint indicators included the intracranial objective response rate (iORR) and iPFS, while the secondary endpoint indicators included the intracranial disease control rate (iDCR), quality of life, and adverse reactions. The Kaplan-Meier method was used to draw the survival curve.Meanwhile, the clinical characteristics of the patients in both groups, such as gender, age, primary tumor site, T stage, N stage, and the number of brain metastases, were collected. Univariate analysis was used to screen out the prognostic factors that might affect iPFS. Then, the factors with statistical differences (P < 0.10) in the univariate analysis were taken as independent variables, and further Cox multivariate regression analysis was carried out to explore the independent prognostic factors affecting iPFS. The test standard P value was < 0.05. From Feb 8, 2024, to Sep 30, 2025, a total of 38 patients diagnosed with brain metastases from NSCLC by the Oncology Department of the Fifth Affiliated Hospital of Chengdu University of Traditional Chinese Medicine were prospectively recruited and included in the statistical analysis. The median follow-up time was 15.2 months (95% CI: 9.02-21.37). The results showed that the experimental group had better iORR (57.90% vs. 15.79%, P = 0.017) and iDCR (100% vs. 73.68%, P = 0.046) compared to the control group, with statistically differences. Compared with the control group, the experimental group showed a advantage in iPFS (6.7 months vs. 4.27 months, P = 0.038), and the median iPFS was extended by an additional 2.43 months. The results of subgroup analysis showed that the iPFS of patients with ≥ 3 brain metastases and patients with < 3 brain metastases were 6.3 months and 6.7 months, respectively, and there was no significant difference between the two groups (P = 0.723). The iPFS was longer in patients with less than 3 metastases than those with more than 3 metastases (11.73 months vs. 3.17 months, P = 0.035). After WBRT, the iPFS of NSCLC patients with brain metastases who received anti-tumor therapy was improved compared with those who did not receive anti-tumor therapy (8.67 months vs. 3.80 months, P = 0.040). In terms of quality of life, the experimental group showed better outcomes in functional status, symptom domains, and overall health compared to the control group over time. Regarding adverse reactions, the main ones included decreased appetite, fatigue, nausea and vomiting, hypertension, Myelosuppression, dizziness, headache, and abnormal liver function indicators. Grade ≥ 3 adverse reactions primarily included anemia, agranulocytosis, leukopenia, thrombocytopenia, cognitive impairment and abnormal liver function indicators, most of which were tolerable after symptomatic treatment. Univariate regression analysis of the overall population indicated that antitumor therapy after WBRT (P = 0.078) and the number of organ metastases (P = 0.038) were clinically relevant factors affecting iPFS. Further multivariate Cox regression analysis revealed that antitumor therapy after WBRT (P = 0.047) and the number of organ metastases (P = 0.028) were independent prognostic factors influencing iPFS. In this exploratory cohort, low-dose (8 mg) anlotinib administered 5-7 days prior to WBRT was associated with higher iORR, iDCR, and longer iPFS relative to WBRT alone in patients with NSCLC brain metastases. This combination regimen showed a manageable safety profile and trends toward improved quality of life. Subgroup analyses suggested that patients with < 3 organ metastases or those receiving post-WBRT antitumor therapy tended to have prolonged iPFS. Multivariate Cox regression identified post-WBRT antitumor therapy and number of organ metastases as potential independent prognostic factors for iPFS in this cohort. These findings are hypothesis-generating and require validation in larger randomized controlled trials.

PMID:42129320 | DOI:10.1038/s41598-026-52632-2

Sci Rep. 2026 May 13. doi: 10.1038/s41598-026-52297-x. Online ahead of print.

ABSTRACT

Nigeria faces a significant energy deficit (61.2% electricity access), hindering progress toward SDG 7 (Affordable and Clean Energy) and SDG 13 (Climate Action). Despite geothermal potential, comprehensive assessments of low-enthalpy resources (that is, subsurface temperatures below 100 ℃) in transitional geological environments (TGEs) – basement-sedimentary contact zones with mixed conductive-advective heat transfer – remain underexplored. This study uses high-resolution aeromagnetic data interpretation with statistical modeling to delineate geothermal potential within the Egbako-Share axis of North-Central, Nigeria. Spectral analysis adopting centroid depth technique from 40 overlapping blocks was employed to estimate Curie Point Depths (CPD), geothermal gradients (GTG), and heat flow (HF). Statistical modeling – including correlation analysis, multiple regression, PCA, and spatial autocorrelation (Moran’s I, Getis-Ord Gi*) – provided a robust framework for resource assessment and risk evaluation. The analysis revealed significant geothermal resources with CPD ranging from 26 to 46 km (mean: 38 ± 6 km), GTG of 13-23 °C/km (mean: 16 ± 2 °C/km), and HF values of 31-57 mW/m² (mean: 39 ± 6 mW/m²). Strong negative correlations between CPD and both GTG (r = -0.892, p < 0.001) and HF (r = -0.891, p < 0.001) were established, with the regression model explaining 79.5% of HF variance. PCA identified 12 high-potential geothermal zones for low-enthalpy development. Under a conceptual scenario assuming full development of all 12 zones, modelled capacity could range from approximately 15 to 25 MW, with scenario-based annual CO₂ emission reductions of 85,000-140,000 t/year (subject to confirmatory drilling and feasibility studies), supporting Nigeria’s SDG 7, SDG 13, and related development targets.

PMID:42129299 | DOI:10.1038/s41598-026-52297-x