Environmental Synchronization Between Background Galactic Cosmic Radiation and the Non-Random Timing of Viral Outbreak Emergence

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Increasing evidence from heliophysics and atmospheric science suggests that Galactic Cosmic Ray (GCRs) flux—modulated by solar magnetic activity and Earth–atmosphere coupling—constitutes a persistent background source of ionizing radiation and may represent an overlooked environmental driver capable of organizing biological phenomena across multiple timescales. As a ubiquitous component of the planetary radiation environment, GCRs continuously interact with biological systems, providing a plausible environmental context for large-scale temporal modulation without implying direct deterministic causation. Methods : A total of 514 viral outbreak events (EM-DAT, 1964 to 2025) and GCRs intensity data (Oulu Cosmic Ray Station) were analyzed using SARIMA forecasting, PELT change-point detection, Granger causality, cross-spectral and Wavelet Transform Coherence (WTC), and a Vector Error Correction Model with exogenous harmonic components (VECMX). These methods were applied within an environmental–ecological time-series framework to evaluate whether large-scale GCRS variability aligns with population-level viral outbreak dynamics. Harmonic structures corresponding to the Hale (~22-year), Schwabe (~11-year), annual/semi-annual, and Quasi-Biennial Oscillation (QBO) cycles were incorporated to assess phase synchronization, ecological timing cues, and long-range temporal alignment between cosmic radiation variability and viral emergence patterns. Results : GCRs variability significantly Granger-caused viral outbreak occurrence across all tested lags up to 12 months (p < 0.05), with maximal significance within the first four months (p < 0.0001), while no reverse causality was detected. Spectral coherence revealed robust phase-locked coupling at the Hale and Schwabe solar cycles (coherence = 0.91 and 0.85, respectively), indicating long-term synchronization. Additional statistically significant coherence was identified at quasi-biennial, annual, and semi-annual timescales, consistent with GCRs secondary particles modulation by the Quasi-Biennial Oscillation and seasonal atmospheric shielding. WTC demonstrated sustained coherence at the ≈11-year Schwabe periodicity. Burst detection analysis further showed clustering of viral outbreak onsets during periods of low solar activity, notably around the 2009 and 2019 solar minima. Conditional harmonic VECMX and SARIMA projections indicate a renewed increase in GCRs intensity toward ~2030, coinciding with the anticipated solar cycle A<0, 25/26 minimum and a corresponding phase-aligned rise in viral outbreak activity. Conclusions : Global viral outbreak dynamics exhibit statistically robust, multi-scale synchronization with GCRs variability. While GCRs are unlikely to act as direct causal agents, they may function as environmental timing cues or permissive triggers that modulate viral emergence or ecological susceptibility windows. Incorporation of heliophysical indicators as contextual environmental risk modifiers may enhance early-warning systems and global outbreak preparedness when integrated with conventional epidemiological surveillance frameworks. Ecological Modeling Astrobiology Atmospheric Sciences Epidemiology Viral outbreaks galactic cosmic rays global viral pandemics synchronization solar cycle and Hale cycle Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Introduction The ability to forecast the sudden emergence of viral pandemics remains one of the most challenging real-world problems. While traditional models focus mainly on the human–animal–environment interface, these frameworks often struggle to account for the abrupt, synchronized shifts in viral outbreak observed globally. The impact of COVID-19 alone caused trillions of dollars of economic loss with millions of lives lost [ 1 – 3 ]. The unpredictable magnitude of these viral pandemics indicate that our existing models may miss critical feedbacks that can aid in early warning [ 4 ]. Conventional terrestrial parameters such as population density, zoonotic spillover events, and global travel patterns may be insufficient to account for sudden, coordinated surges in viral activity or the accelerated genetic shifts observed in emerging viral pandemics (Fig. 1 A) [ 5 – 7 ]. Also, as the world becomes increasingly complex and interconnected, the threat posed by such pandemics grows even more. The speed and scale of global interactions will amplify the impact of localized outbreaks to escalate into worldwide crises, placing humanity at greater risk in the future [ 8 ]. The inability of traditional factors alone to predict the abrupt changes in viral outbreak emergence suggests the influence of external factors [ 1 , 5 ]. In this context, Galactic Cosmic Rays (GCRs) emerge as a possibly critical modulators, interacting with the biosphere. The solar cycle intensity and magnetic field, regulates the flux of GCRs reaching Earth, with periods of solar minimum allowing increased GCRs radiation to penetrate the atmosphere [ 9 , 10 ]. This interaction may contribute to global-scale shifts in viral mutation rates and transmissibility, providing a potential explanation for the synchronized, abrupt changes observed during major pandemics. This study aims to study the longitudinal relationship between GCRs flux and viral outbreaks events through advanced time-series analysis. The primary objectives are to evaluate variable synchronicity through cross-spectral coherence, cross-wavelet coherence (WTC), and Granger causality, with a project long-term phase-aligned dynamics (2026–2046) via a conditional harmonic Vector Error Correction Model with exogenous components (VECMX). Galactic Cosmic Rays and Solar Weather The solar heliosphere is a vast, complex tailed bubble-like region of space dominated by the Sun's magnetic field and the outward flow of the solar winds. It acts as the solar system’s primary defense against the interstellar medium and GCRs. The GCRs are high-energy particles originating from outside the solar system, primarily accelerated by supernova shockwaves within the Milky Way [ 11 ]. The GCRs consist mostly of ionized postively charged protons which can drift across solar magnetic field [ 11 ]. Variations GCRs flux arise from complex interactions between solar activity through heliospheric magnetic field (HMF), solar wind intensity and Earth atmospheric processes that influence GCRs propagation and its secondary particle production (Fig. 1 B). The 11-year solar cycle modulate the intensity of the solar winds, here during solar maximum, the Sun’s stronger magnetic field and denser solar wind deflect GCRs, leading to lower intensities on Earth [ 12 ]. Conversely, solar minimum sees a significant increase in GCRs exposure, these particles, along with their secondary particle cascades, represent a potential source of genotoxic stress capable of damaging DNA and RNA [ 13 ]. The solar dynamo is a highly complex, nonlinear process that generates multiple overlapping cycles of solar magnetic activities [ 14 ]. While the 11-year Schwabe cycle governs sunspot variability, it is superimposed by another complex 22-year Hale magnetic cycle, during which the Sun’s global magnetic polarity reverses and returns to its original state. This polarity reversal, occurring near solar maximum, introduces differences between successive solar cycles and significantly influences heliospheric conditions and GCRs flux [ 15 ]. Solar cycle morphology frequently exhibits a double-peaked maximum, commonly referred to as the Gnevyshev Gap, which is primarily attributed to hemispheric asymmetry and the temporal separation of magnetic flux emergence [ 16 ]. In contrast, GCRs modulation displays a well-established dependence on solar cycle intensity and the Hale magnetic cycle which is more apparent in solar minimum, where drift effects dominate. During positive polarity epochs (A > 0), GCRs enter primarily through the solar polar regions, producing a flat-topped maximum, whereas during negative polarity epochs (A < 0), transport along the heliospheric current sheet (HCS) and leads to a sharper GCRs peak on Earth [ 15 , 16 ]. Biological impact of Galactic Cosmic Rays The biological impact of GCRs is primarily governed by their high linear energy transfer (LET) and high ionizing potential, characterized by dense energy deposition along the tracks of the charged particles as they traverse biological matter [ 17 , 18 ]. Unlike low-LET radiation such as X-rays or gamma rays, GCRs and particularly heavy ions with high charge and energy (HZE) like carbon atoms (C), oxygen (O), neon (Ne), silicon (Si), calcium (Ca), and iron (Fe) can produce dense ionization columns that induce complex, clustered genetic lesions that are difficult for cellular mechanisms to repair [ 18 , 19 ]. When primary GCRs interact with the Earth’s atmosphere, they undergo nuclear spallation. This process generates secondary particle cascades, including neutrons, protons, pions, and muons [ 19 ]. Neutrons, despite being uncharged, possess high Relative Biological Effectiveness (RBE) (Fig. 1 B). Because they are highly penetrating, they frequently collide with hydrogen nuclei in biological tissue, producing recoil protons that can cause localized, high-density damage [ 19 – 21 ]. These secondary cascades can penetrate the troposphere, contributing to a continuous background of ionizing radiation that fluctuates with solar activities and Earth atmospheric conditions [ 22 , 23 ]. The resulting genetic damage may occur via two primary pathways, in which high-energy particles directly strike DNA, causing double-strand breaks (DSBs) and locally multiply damaged sites (LMDS) [ 19 , 24 ]. The radiation can induce the radiolysis of water molecules, generating reactive oxygen species (ROS) such as hydroxyl radicals (⋅OH). These radicals cause oxidative base modifications and systemic oxidative stress [ 19 ]. In the context of viral dynamics, GCR-induced mutagenic pressure may alter viral quasispecies structure. At moderate levels, such mutational stress could enhance viral diversification, potentially facilitating reactivation or amplification. However, if the mutation rate exceeds the error-threshold, viral populations may enter an error-catastrophe regime [ 24 ]. Furthermore, GCRs flux is modulated by solar cycle and the Hale Cycle. During solar minima, the weakened HMF allows for increased GCRs penetration into the inner solar system [ 16 ]. These periods of elevated GCRs flux, particularly during specific solar magnetic polarities (A 0), have been hypothesized to act as external mutagenic drivers that may promote abrupt viral genetic shifts, potentially enhancing viral virulence or facilitating zoonotic spillover events [ 25 , 26 ]. In host populations, chronic exposure to GCR-induced secondary radiation can theoretically lead to altered immune responsiveness, potentially compromising the host’s ability to clear emerging viral variants [ 19 , 27 – 30 ]. Materials and Methods Data The cosmic ray data were obtained on 26 July 2025 from the Oulu Cosmic Ray Station, which provides long-term monitoring of GCRs intensity using ground-based neutron monitors ( https://cosmicrays.oulu.fi/ ). These measurements represent the flux of high-energy charged particles originating outside the solar system and modulated by heliospheric and atmospheric processes [ 31 ]. Viral outbreak data were obtained on the same date from the Emergency Events Database (EM-DAT), a comprehensive global repository maintained by the Centre for Research on the Epidemiology of Disasters (CRED), which systematically records natural disasters, including viral epidemics ( https://www.emdat.be/ ) [ 32 , 33 ]. For this study, viral outbreaks were analyzed using the reported start date of each outbreak event as the temporal reference. The combined dataset spans the period from 1 October 1964 (1964-10-01T00:00:00Z) to 1 March 2025 (2025-03-01T00:00:00Z) and comprises 514 discrete viral outbreak events. Viral outbreaks were treated as a point process, allowing for multiple outbreak occurrences on the same calendar date. When repeated events shared the same start date, they were preserved and counted to quantify event multiplicity. Viral event intensity was quantified by aggregating the number of outbreak events occurring on the same date. These time series were visualized jointly to assess long-term temporal patterns in cosmic radiation intensity alongside viral outbreak frequency. Seasonal Autoregressive Integrated Moving Average (SARIMA) A seasonal autoregressive integrated moving average model [ 34 ], SARIMA(1,0,1)×(1,0,1,11), was fitted to the yearly GCRs radiation time series using statsmodels.tsa.statespace.SARIMAX, with an 11-year seasonal period corresponding to the solar cycle. Annual GCRs measurements were obtained by resampling the data to yearly resolution, with linear interpolation applied to fill missing years prior to model fitting. Stationarity and invertibility constraints were relaxed to allow flexible parameter estimation. Stationarity of the series was assessed using standard unit-root diagnostics prior to model fitting. Model performance was evaluated using the Akaike Information Criterion (AIC) (AIC = 644.981). The fitted model was used to generate a 10-year GCRs radiation forecasts, with 95% confidence intervals derived from the model’s predictive distribution. Local maxima and minima in the forecasted series were identified using scipy.signal.find_peaks. Observed values, forecasts, confidence intervals, and identified peaks and troughs were visualized using matplotlib, with the x-axis scaled in 5-year intervals to emphasize long-term behavior. Cross-Spectral Coherence, Burst Detection, and Granger Causality Monthly radiation and viral event counts were aggregated into a continuous monthly time series. Months without recorded events were zero-filled, representing absence of the documented viral outbreak events rather than confirmed zero incidence; however, this assumption may bias short-term variability. The Abrupt changes in viral event frequency were identified using the Pruned Exact Linear Time (PELT) change-point detection algorithm implemented in the ruptures package [ 35 ]. Cross-spectral coherence [ 36 ] between GCRs radiation and viral outbreak events counts was computed using scipy.signal.coherence, with frequencies converted to periods expressed in months. Statistical significance was assessed using a permutation-based surrogate approach. Viral outbreak events counts were randomly shuffled 1,000 times to generate a null distribution of coherence values, and empirical p-values were calculated as the fraction of surrogate coherences exceeding the observed value. Periods exceeding a coherence threshold of 0.8 and the 95th percentile of the surrogate distribution were considered significant. Also, Granger causality analysis [ 37 ] was performed on the monthly series using lags up to 12 months. Both forward (radiation to events) and reverse (events to radiation) directions were tested to assess directional predictability, with p-values below 0.05 considered indicative of significant Granger causality. Cross-Wavelet Coherence and Phase Analysis To resolve time-varying periodic synchronization between GCRs radiation and viral event frequancy, the author performed WTC using the pycwt library [ 38 ]. Both monthly time series were standardized (z-score normalization) to ensure the wavelet power reflected relative oscillations rather than absolute magnitudes. The analysis utilized a Morlet mother wavelet (dimensionless frequency ω0 = 6) with a sub-octave resolution of dj = 1/12 and a starting scale (s0) of two months. Statistical significance was established at the 95% confidence level against a red-noise background. To prevent misinterpretation of edge effects arising from the finite length of the time series, a Cone of Influence (COI) was calculated; data outside this boundary were excluded from periodic interpretation. Phase relationships were visualized via quiver plots on the coherence spectrum. The orientation of the phase arrows indicates the lead/lag relationship: right-pointing arrows signify in-phase synchronization, while left-pointing arrows signify anti-phase synchronization. Conditional Harmonic VECMX Projection Prior to Vector Error Correction Model (VECM) estimation, the Johansen cointegration test was [ 39 ] applied to the monthly GCRs and viral outbreak event series using statsmodels.tsa.vector_ar.vecm.coint_johansen. Thirteen lagged differences (k_ar_diff = 13), corresponding approximately to one annual cycle, and no deterministic trend (det_order = 0) were specified. Both trace and maximum-eigenvalue statistics were evaluated against 90%, 95%, and 99% critical values. A cointegration rank of one was identified and used in subsequent VECM estimation. To capture long-term phase relationships between GCRs and viral outbreak event counts, a conditional harmonic with exogenous variables (VECMX) [ 40 ] was implemented. Monthly series were standardized and augmented with exogenous harmonic components representing Hale (21.33-year), Schwabe (10.67-year), Quasi-Biennial Oscillation (QBO) (1.94-year), annual, semiannual cycles, informed by heliophysical theory and prior spectral coherence analysis. Each cycle was expressed using sine and cosine terms to encode phase information. The VECMX employed 13 lagged differences, a cointegration rank of one, and a constant term in the cointegration relation. Projections were generated for a 20-year horizon (2026–2046), with a 12-month rolling mean applied to emphasize dominant cyclical behavior. Predicted GCRs and viral event series were normalized using MinMaxScaler to facilitate comparison. Phase alignment between projected GCRs intensity and viral event frequency was further assessed using cross-correlation analysis of the normalized, smoothed projection series. Cross-correlation functions were computed over the full range of possible lags, and the lag corresponding to the maximum correlation was interpreted as the dominant phase offset between the two signals at monthly resolution. All analyses were conducted on a Linux system using Python 3.12 and standard scientific libraries, including pandas, numpy, matplotlib, scipy, ruptures, and statsmodels. Result and Discussion Although the timing of major viral outbreaks has long been an enigma in modern medicine [4-7], this study provides a possible statistical framework for outbreak prediction. By synthesizing spectral coherence, Granger causality, and cross-wavelet coherence analyses, the result shows that global viral crises are significantly coupled with fluctuations in GCRs flux. This relationship—driven primarily by solar cycle and Sun magnetic cycle harmonic components—suggests that what was once viewed as stochastic unpredictability can possibly be a predictable temporal pattern. Here, (Figure 2) visually demonstrates a temporal alignment between peaks in the start of viral outbreak activity and intervals of elevated GCRs intensity. The (Figure 3 and Table 1) highlight a predicted surge in GCRs intensity around 2030, likely coinciding with the transition into the next 25/26 solar minimum [41,42]. In this context, viral outbreak emergence may not represent random epidemiological noise, but rather a phenomenon that exhibits synchronization with external GCRs and its solar and atmospheric modulators. As shown in the analysis, GCRs activity significantly "Granger-causes" viral events across all 12 tested lags (p < 0.05), with the strongest significance (p 0.21). This lack of feedback may indicate that the relationship is unidirectional (Table 2). The GCRs may contain predictive information that precedes the viral outbreaks. The persistent significance up to a 12-month lag may suggest a priming period, where solar and Earth atmospheric conditions may influence the terrestrial environment or viral outbreak well before they reaches a detectable threshold. Also, burst detection mapping of viral outbreak events against GCRs intensity identifies a clustering of burst occurrences during periods of low solar activity, most notably around the solar minima of approximately 2009 and 2019 (Figure 4A). Moreover, the spectral coherence analysis identifies statistically robust associations at multiple characteristic timescales. Prominent long-term periodicities corresponding to the Hale magnetic cycle (21.33 years) and the Schwabe cycle (10.67 years) exhibit high coherence values of 0.91 and 0.85, respectively, indicating a possible phase-locked behavior between solar variability and the analyzed viral outbreak signal. At shorter timescales, a high coherence is observed at the semi-annual cycle (0.50 years), with a coherence value of 0.95 (p = 0.000), consistent with a possibly seasonal modulation processes (Figure 4B, Table 3). In addition, a coherent spectral band spanning 1.94–2.37 years aligns closely with the known periodicity of the QBO [43]. In addition, the WTC analysis provides a dynamic, time-resolved evidence for the synchronization between GCRs variability and viral outbreak events. Unlike stationary spectral methods, the wavelet framework explicitly captures how shared periodicities emerge, persist, and intermittently strengthen or weaken across the full duration of the study period. The predominance of phase-locked regions, represented by contiguous dark-red coherence domains, indicates extended intervals during which both signals evolve in a tightly coupled manner. Notably, a persistent high-coherence band centered around the 11-year periodicity extends across the temporal axis (Figure 5), indicating that the Schwabe solar cycle may act as a stable and recurrent modulator of the viral outbeark events rather than a transient or episodic influence. Also, the 20-year conditional harmonic projection (2026–2046) demonstrates a persistent and coherent phase alignment between the projected GRCs radiation signal and the projected viral outbreak trajectories. Across the forecast horizon, peaks and troughs in the projected viral outbreak event consistently track the phase evolution of the GCRs radiation harmonics. Rather than predicting the exact events, this model shows that future viral trends continue to mirror historical radiation cycles. These findings may suggest that global viral outbreaks can be organized around predictable GCRs rhythms instead of occurring at random (Figure 6A, Figure 6B). As shown in the SARIMA forecast (Table 1), GCRs flux intensity is predicted to rise steadily toward a peak around 2030, a corresponding increase in the frequency of viral outbreaks can be anticipated based on established periodic rhythms. Independent experimental and theoretical studies provide external support for the biological plausibility of the statistical associations observed in the present analysis. Mehta et al. demonstrated that exposure to simulated GCRs, including high-energy protons and heavy ions, that can directly induce reactivation of latent human cytomegalovirus (CMV) in vitro, leading to a significant increase in viral copy number without requiring major genomic sequence alterations [44]. Instead, radiation exposure triggered transcriptional activation of lytic-phase viral genes, indicating that ionizing radiation can act as a functional switch from latency to active replication. These findings support the hypothesis that fluctuations in GCRs intensity may influence viral activity through reactivation or amplification mechanisms rather than de novo viral emergence, consistent with the lead–lag structure identified in the Granger causality and wavelet analyses. Complementary theoretical work proposed that variations in cosmic ray flux and solar activity represent underappreciated environmental drivers of emerging viral infectious diseases and argued for their integration into global early-warning surveillance systems [45]. Their study highlights that periods of solar minima coincide with several major viral emergence events. This framework aligns with this finding that viral outbreak timing may be phase-locked to dominant solar and heliomagnetic cycles, particularly the Schwabe cycle and Hale cycle. Together, these studies provide convergent biological and conceptual support for the hypothesis that GCRs variability may contain predictive information relevant to viral outbreak dynamics [44-46]. Beyond the dominant decadal solar-cycle harmonics, this analysis identifies statistically significant coherence between viral outbreak and GCRs variability within the quasi-biennial (≈1.9–2.4 years) and annual/semi-annual cycles. The quasi-biennial periodicity aligns with the QBO, a primary mode of equatorial stratospheric variability. The QBO is known to modulate the vertical coupling between the stratosphere and troposphere, influencing global circulation and the transport of trace gases and aerosols [47-50]. The QBO modulates the dynamical coupling between the tropical stratosphere and the extratropics through the Holton–Tan effect. During the easterly QBO phase, enhanced upward propagation of planetary waves weakens the polar vortex, whereas the westerly phase is associated with a stronger, more stable vortex [49-55]. Numerous studies have shown that the atmospheric response to solar variability is phase-dependent on the QBO, with statistically significant signals often emerging when stratified by QBO phase [50-55]. While the QBO does not alter the incoming flux of GCRs, it can regulate how solar-driven perturbations are dynamically expressed within the middle and lower atmosphere [56]. Similarly, the high coherence at annual and semi-annual scales may reflect the seasonal modulation of GCRs flux. This flux is governed by the Earth's orbital position within the HCS and seasonal changes in Earth atmospheric shielding [54-57]. However, such coherence may also arise from climatologically favorable viral outbreak seasons, during which intrinsic seasonal drivers dominate transmission dynamics, potentially producing apparent synchronization independent of heliophysical forcing [58,59]. By integrating these results, a multilevel coupling framework emerges; while long-term solar variability establishes the the long term risk, shorter-term oscillations like the QBO or seasonal cycles may regulate the specific timing of viral outbreak emergence. The increased GCRs flux and its secondary particle production has been linked to changes in the polar vortex strength which can impacted by QBO phases [60-63]. Moreover, recent research indicates that the Sun is entering a period of prolonged low solar activity, potentially marking the onset of a modern Grand Solar Minimum. The Sun has completed solar cycle 24, which was the weakest cycle observed in over a century, and solar cycle 25, which began in 2020, has exhibited a notably slow start in generating active regions and flares [64]. During 2020, the Sun experienced 115 spotless days (78% of the year), exceeding previous space-age records and indicating a continued suppression of sunspot formation. If this trend persists, the extended periods of minimal solar activity will correspond to conditions analogous to historical grand solar minima, such as the Sporer (ca. 1440–1460), Maunder (ca. 1687–1703), and Dalton (ca. 1809–1821) minima [64-67]. Prolonged low solar activity, increases GCRs flux, which may partly explain the occurrence of the two major 21st-century pandemics—Swine Flu (2009) and COVID-19 (2019)—both coinciding with solar minima and separated by approximately 10 years. Nevertheless, while the combined SARIMA, spectral coherence, and conditional harmonic VECMX framework offers a mechanistically informed approach to modeling GCR–viral event dynamics, several limitations must be acknowledged. Both SARIMA and VECMX are fundamentally linear and rely on stationarity of differenced series; consequently, unmodeled nonlinear interactions, regime shifts, or structural breaks—arising from abrupt solar variability, climatic transitions, or epidemiological changes—may bias parameter estimates and inferred associations. The conditional harmonic VECMX further constrains system dynamics by imposing phase alignment with predefined solar and seasonal cycles, which, although physically motivated, may fail to capture transient, stochastic, or non-canonical solar influences and complex heliospheric–atmospheric couplings. Interpolation of missing data in both GCRs and outbreak time series may introduce artificial smoothness, induce spurious trends, or attenuate short-term variability, thereby affecting time- and frequency-domain analyses. Spectral coherence and Granger causality inferences are sensitive to surrogate construction, lag selection, windowing, and significance thresholding, and extensive testing across scales and frequencies increases the risk of inflated nominal significance despite correction efforts. Long-horizon projections, particularly those extending to 20 years, remain highly sensitive to unmodeled exogenous changes, including shifts in surveillance practices, public health interventions, viral evolution, climate dynamics, and future solar behavior, and should therefore be interpreted as phase-informed scenario trajectories rather than deterministic predictions. Also, viral outbreak data derived from EM-DAT—especially in the pre-2000 period—are subject to substantial reporting biases which may distort long-term trends and further bias estimated relationships. Finaly, to substantiate any causal interpretation, targeted laboratory or experimental research is highly required to assess whether GCR-associated atmospheric ionization or perturbations can meaningfully influence viral persistence, activation, or host susceptibility. Conclusion This study shows that global viral outbreak frequency exhibits statistically significant phase coherence with GCRs flux, implying a possible structured temporal organization rather than purely stochastic behavior. This coherence corresponds to dominant heliophysical periodicities, including the solar cycle and Hale magnetic cycle. While these findings may suggest that viral activity may be conditioned by interacting heliophysical and atmospheric rhythms acting as background modulators alongside established ecological and epidemiological drivers, further mechanistic, experimental, and epidemiological studies are required to substantiate and interpret these associations. Declarations Conflict of Interest The author declares that there are no conflicts of interest. Acknowledgements The author wishes to express his gratitude to the Oulu Cosmic Ray Station (University of Oulu) for providing the long-term monitoring data of GCRs intensity and also to Centre for Research on the Epidemiology of Disasters (CRED) for maintaining the Emergency Events Database (EM-DAT), which was instrumental in providing the viral outbreak records used in this analysis. Funding: This research received no specific grant from any funding agency Ethical Approval and Institutional Review Board (IRB) Ethical approval was not required for this study. The research involves the secondary analysis of publicly available, aggregated, and de-identified environmental and epidemiological data. No human participants were involved, and no identifiable personal data were accessed or processed. Author Contributions Alamin Mustafa solely contributed to the conceptualization, methodology, investigation, data curation, formal analysis, resources, software, validation, visualization, project administration, supervision, and writing (original draft and review & editing). Data Availability: The raw data supporting the findings of this study are available from the Oulu Cosmic Ray Station and the EM-DAT database. The specific datasets processed and analyzed for this study are available from the corresponding author upon reasonable request. References 1. The true death toll of COVID-19: estimating global excess mortality. Geneva: World Health Organization; 2021 ( https://www.who.int/data/stories/the-true-death-toll-of-covid-19-estimating-global-excess-mortality). 2. The impact of COVID-19 on health and care workers: a closer look at deaths. Geneva: World Health Organization; 2021 ( https://apps.who.int/iris/handle/10665/345300). 3. Agarwal R, Gopinth G, Farrar J, Hatchett R, Sands P. A global strategy to manage the long-term risks of COVID-19. Washington (DC): International Monetary Fund; 2022 (IMF Working Paper 22/68; https://doi.org/10.5089/9798400205996.001 4. Ioannidis JPA, Cripps S, Tanner MA. Forecasting for COVID-19 has failed. Int J Forecast. 2022 Apr-Jun;38(2):423-438. doi: 10.1016/j.ijforecast.2020.08.004. Epub 2020 Aug 25. PMID: 32863495; PMCID: PMC7447267. https://doi.org/10.1016/j.ijforecast.2020.08.004 PMid:32863495 PMCid:PMC7447267 5. Abdullrahman, M. (2022) Possible Association between Space Weather Variables, and the World's COVID-19 Cases. Journal of Biosciences and Medicines, 10, 64-76. doi: 10.4236/jbm.2022.105006. https://doi.org/10.4236/jbm.2022.105006 6. McMichael, A. (2004) Environmental and Social Influences on Emerging Infectious Diseases: Past, Present and Future. Philosophical Transactions of the Royal Society B Biological Sciences, 359, 1049-1058. https://doi.org/10.1098/rstb.2004.1480 PMid:15306389 PMCid:PMC1693387 7. Chizhevsky, A. (1976) The Terrestrial Echo of Solar Storms. Mysl, Moscow. First Published in 1936. 8.Helbing D. Globally networked risks and how to respond. Nature. 2013 May 2;497(7447):51-9. doi: 10.1038/nature12047. PMID: 23636396. https://doi.org/10.1038/nature12047 PMid:23636396 9. Towers S. Sunspot activity and influenza pandemics: a statistical assessment of the purported association. Epidemiol Infect. 2017 Oct;145(13):2640-2655. doi: 10.1017/S095026881700173X. Epub 2017 Aug 29. PMID: 28847318; PMCID: PMC9148804. https://doi.org/10.1017/S095026881700173X PMid:28847318 PMCid:PMC9148804 10. Towers S. Sunspot activity and influenza pandemics: a statistical assessment of the purported association. Epidemiology & Infection. 2017 Oct;145(13):2640-55. https://doi.org/10.1017/S095026881700173X PMid:28847318 PMCid:PMC9148804 11. Potgieter MS. Solar modulation of cosmic rays. Living Reviews in Solar Physics. 2013 Dec;10(1):3. https://doi.org/10.12942/lrsp-2013-3 12. Rahmanifard F, Jordan AP, De Wet WC, Schwadron NA, Wilson JK, Owens MJ, Spence HE, Riley P. Evidence from galactic cosmic rays that the Sun has likely entered a secular minimum in solar activity. Space Weather. 2022 Feb;20(2):e2021SW002796. https://doi.org/10.1029/2021SW002796 13. Sage E, Shikazono N. Radiation-induced clustered DNA lesions: Repair and mutagenesis. Free Radical Biology and Medicine. 2017 Jun 1;107:125-35. https://doi.org/10.1016/j.freeradbiomed.2016.12.008 PMid:27939934 14. Käpylä MJ, Käpylä PJ, Olspert N, Brandenburg A, Warnecke J, Karak BB, Pelt J. Multiple dynamo modes as a mechanism for long-term solar activity variations. Astronomy & Astrophysics. 2016 May 1;589:A56. https://doi.org/10.1051/0004-6361/201527002 15. Oh S, Yi Y. Variations in Solar Parameters and Cosmic Rays with Solar Magnetic Polarity. The Astrophysical Journal. 2017 Apr 27;840(1):14. https://doi.org/10.3847/1538-4357/aa6c62 16. Ross E, Chaplin WJ. The behaviour of galactic cosmic-ray intensity during solar activity cycle 24. Solar physics. 2019 Jan;294(1):8. https://doi.org/10.1007/s11207-019-1397-7 PMid:30872867 PMCid:PMC6383758 17. Durante M, Cucinotta FA. Physical basis of radiation protection in space travel. Reviews of modern physics. 2011 Oct 1;83(4):1245-81. https://doi.org/10.1103/RevModPhys.83.1245 18. Sweet M, Mishima K, Harada M, Kurita K, Iikura H, Tasaki S, Kikuchi N. Simulation Study on Dose and LET of Neutron Irradiation for Biological Experiments Using Spallation, Reactor, and Compact Neutron Sources. Quantum Beam Science. 2025 Apr 8;9(2):11. https://doi.org/10.3390/qubs9020011 19. Giovanetti A, Tortolici F, Rufini S. Why Do the Cosmic Rays Induce Aging?. Frontiers in physiology. 2020 Aug 12;11:955. https://doi.org/10.3389/fphys.2020.00955 PMid:32903447 PMCid:PMC7434975 20. Simonsen LC, Slaba TC, Guida P, Rusek A. NASA's first ground-based Galactic Cosmic Ray Simulator: Enabling a new era in space radiobiology research. PLoS biology. 2020 May 19;18(5):e3000669. https://doi.org/10.1371/journal.pbio.3000669 PMid:32428004 PMCid:PMC7236977 21. Li M, Gonon G, Buonanno M, Autsavapromporn N, De Toledo SM, Pain D, Azzam EI. Health risks of space exploration: targeted and nontargeted oxidative injury by high-charge and high-energy particles. Antioxidants & redox signaling. 2014 Mar 20;20(9):1501-23. https://doi.org/10.1089/ars.2013.5649 PMid:24111926 PMCid:PMC3936510 22. Mertens CJ, Meier MM, Brown S, Norman RB, Xu X. NAIRAS aircraft radiation model development, dose climatology, and initial validation. 23. Hassanpour M, Rezaie M, Heydarizade Y, Rashed Iqbal Faruque M, Hassanpour M. Production of secondary particles from cosmic ray interactions in the earth's atmosphere: Implications for annual effective dose, 14C/12C ratio, and magnetic field effects. PLoS One. 2025 Oct 23;20(10):e0328915. doi: 10.1371/journal.pone.0328915. PMID: 41129520; PMCID: PMC12548846. https://doi.org/10.1371/journal.pone.0328915 PMid:41129520 PMCid:PMC12548846 24. Ward JF. DNA damage produced by ionizing radiation in mammalian cells: identities, mechanisms of formation, and reparability. Progress in nucleic acid research and molecular biology. 1988 Jan 1;35:95-125. https://doi.org/10.1016/S0079-6603(08)60611-X PMid:3065826 25. Wickramasinghe NC. Is the 2019 novel coronavirus related to a spike of cosmic rays?. Advances in Genetics. 2020 Jan 1;106:119-22. https://doi.org/10.1016/bs.adgen.2020.06.003 PMCid:PMC7529058 26. de Groen PC. Muons, mutations, and planetary shielding. Frontiers in astronomy and space sciences. 2022 Nov 23;9:1067491. https://doi.org/10.3389/fspas.2022.1067491 PMid:36688079 PMCid:PMC9854335 27. Norbury JW, Schimmerling W, Slaba TC, Azzam EI, Badavi FF, Baiocco G, Benton E, Bindi V, Blakely EA, Blattnig SR, Boothman DA. Galactic cosmic ray simulation at the NASA Space Radiation Laboratory. Life sciences in space research. 2016 Feb 1;8:38-51. https://doi.org/10.1016/j.lssr.2016.02.001 PMid:26948012 PMCid:PMC5771487 28. Winer DA, Du H, Kim J, Chang V, Burke M, Winer S, Costes SV, Frippiat JP, Sams C, Paul AM, Wu H. Astroimmunology: the effects of spaceflight and its associated stressors on the immune system. Nature Reviews Immunology. 2025 Oct 16:1-24. https://doi.org/10.1038/s41577-025-01226-6 PMid:41102553 29. Wadhwa A, Moreno-Villanueva M, Crucian B, Wu H. Synergistic interplay between radiation and microgravity in spaceflight-related immunological health risks. Immunity & Ageing. 2024 Jul 20;21(1):50. https://doi.org/10.1186/s12979-024-00449-w PMid:39033285 PMCid:PMC11264846 30. Shearer WT, Zhang S, Reuben JM, Lee BN, Butel JS. Effects of radiation and latent virus on immune responses in a space flight model. Journal of allergy and clinical immunology. 2005 Jun 1;115(6):1297-303. https://doi.org/10.1016/j.jaci.2005.03.003 PMid:15940150 31. Poluianov S, Usoskin I, Ibragimov A. Data management at the Oulu cosmic ray station. Proceedings of NMDB@ Home 2020. 2021 Jun 1. https://doi.org/10.38072/2748-3150/p25 32. Delforge, D., Wathelet, V., Below, R., Lanfredi Sofia, C., Tonnelier, M., van Loenhout, J. A. F. & Speybroeck, N.: EM-DAT: The Emergency Events Database, International Journal of Disaster Risk Reduction, 105509, https://doi.org/10.1016/j.ijdrr.2025.105509, 2025. https://doi.org/10.1016/j.ijdrr.2025.105509 33. EM-DAT, CRED / UCLouvain, 2025, Brussels, Belgium - www.emdat.be (Accssed on 26 July 2026) 34. Ghysels E, Osborn DR, Rodrigues PM. Forecasting seasonal time series. Handbook of economic forecasting. 2006 Jan 1;1:659-711. https://doi.org/10.1016/S1574-0706(05)01013-X 35. Wambui GD, Waititu GA, Wanjoya A. The power of the pruned exact linear time (PELT) test in multiple changepoint detection. American Journal of Theoretical and Applied Statistics. 2015 Nov;4(6):581. https://doi.org/10.11648/j.ajtas.20150406.30 36. White LB, Boashash B. Cross spectral analysis of nonstationary processes. IEEE Transactions on Information Theory. 2002 Aug 6;36(4):830-5. https://doi.org/10.1109/18.53742 37. Shojaie A, Fox EB. Granger causality: A review and recent advances. Annual Review of Statistics and Its Application. 2022 Mar 7;9(1):289-319 https://doi.org/10.1146/annurev-statistics-040120-010930 PMid:37840549 PMCid:PMC10571505 38. Grinsted A, Moore JC, Jevrejeva S. Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear processes in geophysics. 2004 Nov 18;11(5/6):561-6. https://doi.org/10.5194/npg-11-561-2004 39. Dwyer GP. The Johansen tests for cointegration. White Paper. 2015 Apr;516 40. Usman M, Loves L, Russel E, Ansori M, Warsono W, Widiarti W, Wamiliana W. Analysis of some energy and economics variables by using VECMX model in Indonesia. International Journal of Energy Economics and Policy. 2022;12(2):91-102. https://doi.org/10.32479/ijeep.11897 41. Petrie GJ. Global solar photospheric and coronal magnetic field over activity cycles 21-25. Journal of Space Weather and Space Climate. 2024;14:5. https://doi.org/10.1051/swsc/2024005 42. Zharkova V. Modern Grand Solar Minimum will lead to terrestrial cooling. Temperature. 2020 Jul 2;7(3):217-22. https://doi.org/10.1080/23328940.2020.1796243 PMid:33117860 PMCid:PMC7575229 43. Valva C, Gerber EP. The QBO, the annual cycle, and their interactions: Isolating periodic modes with Koopman analysis. Journal of Climate. 2025 Jun 3. https://doi.org/10.1175/JCLI-D-24-0411.1 44. Mehta SK, Diak DM, Bustos-Lopez S, Nelman-Gonzalez M, Chen X, Plante I, Stray SJ, Tandon R, Crucian BE. Effect of Simulated Cosmic Radiation on Cytomegalovirus Reactivation and Lytic Replication. International Journal of Molecular Sciences. 2024 Sep 26;25(19):10337. https://doi.org/10.3390/ijms251910337 PMid:39408667 PMCid:PMC11477029 45. Qu J. Is sunspot activity a factor in influenza pandemics? Rev Med Virol. 2016; 26(5): 309-313. https://doi.org/10.1002/rmv.1887 PMid:27136236 46. Qu J, Wickramasinghe NC. The world should establish an early warning system for new viral infectious diseases by space‐weather monitoring. MedComm. 2020 Dec;1(3):423-6. https://doi.org/10.1002/mco2.20 PMid:32838395 PMCid:PMC7404868 47. Diallo MA, Ploeger F, Hegglin MI, Ern M, Grooß JU, Khaykin S, Riese M. Stratospheric water vapour and ozone response to the quasi-biennial oscillation disruptions in 2016 and 2020. Atmospheric chemistry and physics. 2022 Nov 8;22(21):14303-21. https://doi.org/10.5194/acp-22-14303-2022 48. Gray LJ, Beer J, Geller M, Haigh JD, Lockwood M, Matthes K, Cubasch U, Fleitmann D, Harrison G, Hood L, Luterbacher J. Solar influences on climate. Reviews of Geophysics. 2010 Dec;48(4). https://doi.org/10.1029/2009RG000282 49. Baldwin MP, Gray LJ, Dunkerton TJ, Hamilton K, Haynes PH, Randel WJ, Holton JR, Alexander MJ, Hirota I, Horinouchi T, Jones DB. The quasi‐biennial oscillation. Reviews of Geophysics. 2001 May;39(2):179-229. https://doi.org/10.1029/1999RG000073 50. Bazilevskaya GA, Usoskin IG, Flückiger EO, Harrison RG, Desorgher L, Bütikofer R, Krainev MB, Makhmutov VS, Stozhkov YI, Svirzhevskaya AK, Svirzhevsky NS. Cosmic ray induced ion production in the atmosphere. Space Science Reviews. 2008 Jun;137(1):149-73. https://doi.org/10.1007/s11214-008-9339-y 51. Sunkara E, Seo KH, Mengist CK, Ratnam MV, Niranjan Kumar K, Venkata Chalapathi G. Role of QBO and MJO in Sudden Stratospheric Warmings: A Case Study. Atmosphere. 2024 Dec 5;15(12):1458. https://doi.org/10.3390/atmos15121458 52. Svensmark H. Cosmoclimatology: a new theory emerges. Astronomy & Geophysics. 2007 Feb 1;48(1):1-8. https://doi.org/10.1111/j.1468-4004.2007.48118.x 53. Usoskin IG, Kovaltsov GA, Mishev AL. Updated model of cosmic-ray-induced ionization in the atmosphere (CRAC: CRII_v3): Improved yield function and lookup tables. 54. Holton JR, Austin J. The influence of the equatorial QBO on sudden stratospheric warmings. Journal of Atmospheric Sciences. 1991 Feb 15;48(4):607-18. https://doi.org/10.1175/1520-0469(1991)0482.0.CO;2 55. Schmidt C, Küchelbacher L, Wüst S, Bittner M. OH airglow observations with two identical spectrometers: benefits of increased data homogeneity in the identification of variations induced by the 11-year solar cycle, the QBO, and other factors. Atmospheric Measurement Techniques. 2023 Oct 4;16(19):4331-56. https://doi.org/10.5194/amt-16-4331-2023 56. Li KF, Tung KK. Quasi‐biennial oscillation and solar cycle influences on winter Arctic total ozone. Journal of Geophysical Research: Atmospheres. 2014 May 27;119(10):5823-35. https://doi.org/10.1002/2013JD021065 57. Lockwood M, Owens MJ, Barnard LA, Haines C, Scott CJ, McWilliams KA, Coxon JC. Semi-annual, annual and Universal Time variations in the magnetosphere and in geomagnetic activity: 1. Geomagnetic data. Journal of Space Weather and Space Climate. 2020;10:23. https://doi.org/10.1051/swsc/2020023 58. Bloom-Feshbach K, Alonso WJ, Charu V, Tamerius J, Simonsen L, Miller MA, Viboud C. Latitudinal variations in seasonal activity of influenza and respiratory syncytial virus (RSV): a global comparative review. PloS one. 2013 Feb 14;8(2):e54445. https://doi.org/10.1371/journal.pone.0054445 PMid:23457451 PMCid:PMC3573019 59. Geoghegan JL, Walker PJ, Duchemin JB, Jeanne I, Holmes EC. Seasonal drivers of the epidemiology of arthropod-borne viruses in Australia. PLoS Neglected Tropical Diseases. 2014 Nov 20;8(11):e3325. https://doi.org/10.1371/journal.pntd.0003325 PMid:25412443 PMCid:PMC4239014 60. Veretenenko S, Ogurtsov M. Stratospheric polar vortex as a possible reason for temporal variations of solar activity and galactic cosmic ray effects on the lower atmosphere circulation. Advances in Space Research. 2014 Dec 15;54(12):2467-77. https://doi.org/10.1016/j.asr.2013.09.001 61. Veretenenko S. Stratospheric polar vortex as an important link between the lower atmosphere circulation and solar activity. Atmosphere. 2022 Jul 18;13(7):1132. https://doi.org/10.3390/atmos13071132 62. Zharkova V. Modern Grand Solar Minimum will lead to terrestrial cooling. Temperature (Austin). 2020 Aug 4;7(3):217-222. doi: 10.1080/23328940.2020.1796243. PMID: 33117860; PMCID: PMC7575229. https://doi.org/10.1080/23328940.2020.1796243 PMid:33117860 PMCid:PMC7575229 63. Brown LP, Charlery J, Voutchkov M. Investigating the Apparent Link between Cosmic Ray Muon Flux, Sudden Stratospheric Warming and Dry Season Rainfall over Jamaica. Atmospheric and Climate Sciences. 2019 Sep 10;9(4):662-82. https://doi.org/10.4236/acs.2019.94041 64. Taricco C, Arnone E, Rubinetti S, Bizzarri I, Agafonova NY, Aglietta M, Antonioli P, Ashikhmin VV, Bari G, Bruno G, Dobrynina EA. Exploration of the stratosphere with cosmic-ray muons detected underground. Physical Review Research. 2022 Jun;4(2):023226. https://doi.org/10.1103/PhysRevResearch.4.023226 65. Mörner NA. The approaching new grand solar minimum and little ice age climate conditions. Natural Science. 2015 Nov 16;7(11):510-8. https://doi.org/10.4236/ns.2015.711052 66. Hao YQ, Shi H, Xiao Z, Zhang DH. Weak ionization of the global ionosphere in solar cycle 24. InAnnales Geophysicae 2014 Jul 21 (Vol. 32, No. 7, pp. 809-816). Copernicus GmbH. https://doi.org/10.5194/angeo-32-809-2014 67. Elias AG, de Adler NO. Forecast of solar maximum and minimum dates for solar cycles 23 to 29. Annals of Geophysics. 1998 Nov 25;41(1). https://doi.org/10.4401/ag-3790 Tables Table 1: Decade-Ahead SARIMA Forecast (2026–2035) of Predicted GCRs Flux Intensity with 95% Confidence Intervals Year Predicted Value [cts/min] Lower 95% CI Upper 95% CI Feature 2026 5703.49 5404.72 6002.25 2027 5779.74 5273.77 6285.71 2028 5828.32 5180.48 6476.16 2029 5870.19 5108.36 6632.03 2030 5876.80 5017.65 6735.95 Peak 2031 5868.73 4923.76 6813.70 2032 5789.41 4767.28 6811.55 2033 5657.03 4564.44 6749.63 2034 5509.97 4352.37 6667.57 2035 5426.33 4208.29 6644.36 Table 2: Summary of Granger Causality Tests for GCRs Levels and Viral Outbreak Events across 12 Lags Lag Radiation → Events (p-value) Events → Radiation (p-value) 1 0.0000*** 0.8422 2 0.0000*** 0.8007 3 0.0000*** 0.2750 4 0.0000*** 0.3552 5 0.0003*** 0.3473 6 0.0008*** 0.4236 7 0.0014** 0.4635 8 0.0010** 0.5079 9 0.0032** 0.3634 10 0.0030** 0.4197 11 0.0059** 0.5030 12 0.0375* 0.2140 Table 3: Spectral Coherence Analysis Identifying Significant Periodicities and Possibly Associated with Solar/Atmospheric Cycles Period (Years) Coherence P-Value Possible Cycle Description 21.33 0.91 0.001 Hale Cycle (Solar Magnetic) 10.67 0.85 0.007 Schwabe Cycle (11-Year Solar) 2.37 0.81 0.010 Quasi-Biennial Oscillation (QBO) 2.13 0.83 0.003 Quasi-Biennial Oscillation (QBO) 1.94 0.89 0.003 Quasi-Biennial Oscillation (QBO) 1.02 0.84 0.004 Annual Cycle 0.97 0.81 0.001 Annual Variation 0.65 0.81 0.007 Intra-annual signal 0.51 0.86 0.005 Semi-annual signal 0.50 0.95 0.000 Semi-annual Cycle 0.37 0.82 0.003 seasonal harmonic 0.30 0.83 0.003 seasonal harmonic 0.30 0.91 0.001 seasonal harmonic 0.30 0.92 0.002 seasonal harmoni 0.29 0.91 0.002 High-frequency variation 0.24 0.89 0.000 Quarterly signal (~3 months) 0.21 0.84 0.009 High-frequency jitter 0.21 0.80 0.009 High-frequency jitter Additional Declarations The authors declare no competing interests. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8834986","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":588610842,"identity":"85846bec-1b78-4809-ab44-7ec806f61b53","order_by":0,"name":"Alamin Mustafa","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8UlEQVRIiWNgGAWjYDACdiBOYLDhYWNmbP/wAchhYyekhRmsJU2On735GOMMkBZmYrQwMBw2luw5lsbMgxDBDfibmZ9ueLjjcOKGGzlmj21+bZPnY2Zg/PAxB7cWicNsZjcSz6SDtJgb5/bdNmxjZmCWnLkNjzWHGYBa2qxBWgykc3tuMwK1sDHz4tEif5j9G1ALM0SLZc9te4JaDA7zgGxxBntfmuHH7USCWgwP85QBtYAD+bBhb8Pt5DZmxma8fpE73r7t5s82cFQ2Pvjx57bt/Pbmgx8+4vM+CmBsA5MNxKoHgT+kKB4Fo2AUjIKRAgD4EFTiJ5jl2QAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0003-1129-6284","institution":"MBBS, Faculty of Medicine, Al-Neelain University, Khartoum, Sudan","correspondingAuthor":true,"prefix":"","firstName":"Alamin","middleName":"","lastName":"Mustafa","suffix":""}],"badges":[],"createdAt":"2026-02-10 00:36:22","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-8834986/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8834986/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102375453,"identity":"2ea0a558-3372-4f09-a4b5-cd5b288a54ee","added_by":"auto","created_at":"2026-02-11 05:19:44","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":449295,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eA: Missing GCRs Inputs in Pandemic Response, B: Linear Energy Transfer Characteristics of Primary and Secondary Cosmic-Ray Particles\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-8834986/v1/461828f262e09e7a8f173fef.png"},{"id":102404159,"identity":"544fb7f1-a208-4b9d-9559-59a7493f7fc8","added_by":"auto","created_at":"2026-02-11 11:01:34","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":468738,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTemporal Co-variation Between Cosmic Rays Radiation Intensity and Viral Outbreak Frequency\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-8834986/v1/932c3eed4a7de4273d5092f1.png"},{"id":102375451,"identity":"01131ae7-e772-4143-a5a6-91146bc5c673","added_by":"auto","created_at":"2026-02-11 05:19:44","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":153829,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eGCRs Forecast Model with 95% Confidence Interval and Peak Predictions\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-8834986/v1/7daab7cd73a98ec98549f0f4.png"},{"id":102397927,"identity":"8a4a4987-166d-4623-8eb7-d0946e65e344","added_by":"auto","created_at":"2026-02-11 10:20:11","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":355948,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eA; Poisson Burst Prediction Mapping of Viral Outbreak Events against GCRs Intensity Flux. B; Cross-Spectral Coherence Analysis with Shuffle Surrogate Noise Floor Testing for Periodic Synchronization Validation.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-8834986/v1/2536b402c0da20ef5ed51795.png"},{"id":102375454,"identity":"4c77b8c2-b4c4-4c61-9aba-0950ca790a64","added_by":"auto","created_at":"2026-02-11 05:19:44","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":791615,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCross-Wavelet Coherence and Phase Locking between Monthly GCRs and Viral outbreak Event Activity.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-8834986/v1/bbdde7ffa8ea96a2c3953bd6.png"},{"id":102375457,"identity":"86e58c16-80c5-44f9-a33e-e226344d3b15","added_by":"auto","created_at":"2026-02-11 05:19:44","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":221297,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eA; Long-Term Harmonic VECMX Projection (2026–2046) of GCRS and Predicted Viral outbreak Event Phases. B; Cross-Correlation Profile Identifying Zero-Month Phase Lag for Synchronous Variation Between GCRs and Viral Outbreak Frequency\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-8834986/v1/3d2a132b6cb39fe664be96ef.png"},{"id":102404746,"identity":"b9791ee1-7e2a-4dd9-a62d-6c8f9221d437","added_by":"auto","created_at":"2026-02-11 11:08:04","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3438010,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8834986/v1/f0771a81-4eee-4517-b59a-942286b38a61.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eEnvironmental Synchronization Between Background Galactic Cosmic Radiation and the Non-Random Timing of Viral Outbreak Emergence\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe ability to forecast the sudden emergence of viral pandemics remains one of the most challenging real-world problems. While traditional models focus mainly on the human\u0026ndash;animal\u0026ndash;environment interface, these frameworks often struggle to account for the abrupt, synchronized shifts in viral outbreak observed globally. The impact of COVID-19 alone caused trillions of dollars of economic loss with millions of lives lost [\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. The unpredictable magnitude of these viral pandemics indicate that our existing models may miss critical feedbacks that can aid in early warning [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Conventional terrestrial parameters such as population density, zoonotic spillover events, and global travel patterns may be insufficient to account for sudden, coordinated surges in viral activity or the accelerated genetic shifts observed in emerging viral pandemics (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eA) [\u003cspan additionalcitationids=\"CR6\" citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Also, as the world becomes increasingly complex and interconnected, the threat posed by such pandemics grows even more. The speed and scale of global interactions will amplify the impact of localized outbreaks to escalate into worldwide crises, placing humanity at greater risk in the future [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe inability of traditional factors alone to predict the abrupt changes in viral outbreak emergence suggests the influence of external factors [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. In this context, Galactic Cosmic Rays (GCRs) emerge as a possibly critical modulators, interacting with the biosphere. The solar cycle intensity and magnetic field, regulates the flux of GCRs reaching Earth, with periods of solar minimum allowing increased GCRs radiation to penetrate the atmosphere [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. This interaction may contribute to global-scale shifts in viral mutation rates and transmissibility, providing a potential explanation for the synchronized, abrupt changes observed during major pandemics. This study aims to study the longitudinal relationship between GCRs flux and viral outbreaks events through advanced time-series analysis. The primary objectives are to evaluate variable synchronicity through cross-spectral coherence, cross-wavelet coherence (WTC), and Granger causality, with a project long-term phase-aligned dynamics (2026\u0026ndash;2046) via a conditional harmonic Vector Error Correction Model with exogenous components (VECMX).\u003c/p\u003e\n\u003ch3\u003eGalactic Cosmic Rays and Solar Weather\u003c/h3\u003e\n\u003cp\u003eThe solar heliosphere is a vast, complex tailed bubble-like region of space dominated by the Sun's magnetic field and the outward flow of the solar winds. It acts as the solar system\u0026rsquo;s primary defense against the interstellar medium and GCRs. The GCRs are high-energy particles originating from outside the solar system, primarily accelerated by supernova shockwaves within the Milky Way [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. The GCRs consist mostly of ionized postively charged protons which can drift across solar magnetic field [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Variations GCRs flux arise from complex interactions between solar activity through heliospheric magnetic field (HMF), solar wind intensity and Earth atmospheric processes that influence GCRs propagation and its secondary particle production (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eB). The 11-year solar cycle modulate the intensity of the solar winds, here during solar maximum, the Sun\u0026rsquo;s stronger magnetic field and denser solar wind deflect GCRs, leading to lower intensities on Earth [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Conversely, solar minimum sees a significant increase in GCRs exposure, these particles, along with their secondary particle cascades, represent a potential source of genotoxic stress capable of damaging DNA and RNA [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe solar dynamo is a highly complex, nonlinear process that generates multiple overlapping cycles of solar magnetic activities [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. While the 11-year Schwabe cycle governs sunspot variability, it is superimposed by another complex 22-year Hale magnetic cycle, during which the Sun\u0026rsquo;s global magnetic polarity reverses and returns to its original state. This polarity reversal, occurring near solar maximum, introduces differences between successive solar cycles and significantly influences heliospheric conditions and GCRs flux [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Solar cycle morphology frequently exhibits a double-peaked maximum, commonly referred to as the Gnevyshev Gap, which is primarily attributed to hemispheric asymmetry and the temporal separation of magnetic flux emergence [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. In contrast, GCRs modulation displays a well-established dependence on solar cycle intensity and the Hale magnetic cycle which is more apparent in solar minimum, where drift effects dominate. During positive polarity epochs (A\u0026thinsp;\u0026gt;\u0026thinsp;0), GCRs enter primarily through the solar polar regions, producing a flat-topped maximum, whereas during negative polarity epochs (A\u0026thinsp;\u0026lt;\u0026thinsp;0), transport along the heliospheric current sheet (HCS) and leads to a sharper GCRs peak on Earth [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eBiological impact of Galactic Cosmic Rays\u003c/h2\u003e \u003cp\u003eThe biological impact of GCRs is primarily governed by their high linear energy transfer (LET) and high ionizing potential, characterized by dense energy deposition along the tracks of the charged particles as they traverse biological matter [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Unlike low-LET radiation such as X-rays or gamma rays, GCRs and particularly heavy ions with high charge and energy (HZE) like carbon atoms (C), oxygen (O), neon (Ne), silicon (Si), calcium (Ca), and iron (Fe) can produce dense ionization columns that induce complex, clustered genetic lesions that are difficult for cellular mechanisms to repair [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. When primary GCRs interact with the Earth\u0026rsquo;s atmosphere, they undergo nuclear spallation. This process generates secondary particle cascades, including neutrons, protons, pions, and muons [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Neutrons, despite being uncharged, possess high Relative Biological Effectiveness (RBE) (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eB). Because they are highly penetrating, they frequently collide with hydrogen nuclei in biological tissue, producing recoil protons that can cause localized, high-density damage [\u003cspan additionalcitationids=\"CR20\" citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. These secondary cascades can penetrate the troposphere, contributing to a continuous background of ionizing radiation that fluctuates with solar activities and Earth atmospheric conditions [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe resulting genetic damage may occur via two primary pathways, in which high-energy particles directly strike DNA, causing double-strand breaks (DSBs) and locally multiply damaged sites (LMDS) [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. The radiation can induce the radiolysis of water molecules, generating reactive oxygen species (ROS) such as hydroxyl radicals (\u0026sdot;OH). These radicals cause oxidative base modifications and systemic oxidative stress [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. In the context of viral dynamics, GCR-induced mutagenic pressure may alter viral quasispecies structure. At moderate levels, such mutational stress could enhance viral diversification, potentially facilitating reactivation or amplification. However, if the mutation rate exceeds the error-threshold, viral populations may enter an error-catastrophe regime [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Furthermore, GCRs flux is modulated by solar cycle and the Hale Cycle. During solar minima, the weakened HMF allows for increased GCRs penetration into the inner solar system [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. These periods of elevated GCRs flux, particularly during specific solar magnetic polarities (A\u0026thinsp;\u0026lt;\u0026thinsp;0 or A\u0026thinsp;\u0026gt;\u0026thinsp;0), have been hypothesized to act as external mutagenic drivers that may promote abrupt viral genetic shifts, potentially enhancing viral virulence or facilitating zoonotic spillover events [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. In host populations, chronic exposure to GCR-induced secondary radiation can theoretically lead to altered immune responsiveness, potentially compromising the host\u0026rsquo;s ability to clear emerging viral variants [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan additionalcitationids=\"CR28 CR29\" citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e"},{"header":"Materials and Methods","content":"\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003eData\u003c/h2\u003e \u003cp\u003eThe cosmic ray data were obtained on 26 July 2025 from the Oulu Cosmic Ray Station, which provides long-term monitoring of GCRs intensity using ground-based neutron monitors (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://cosmicrays.oulu.fi/\u003c/span\u003e\u003cspan address=\"https://cosmicrays.oulu.fi/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e). These measurements represent the flux of high-energy charged particles originating outside the solar system and modulated by heliospheric and atmospheric processes [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. Viral outbreak data were obtained on the same date from the Emergency Events Database (EM-DAT), a comprehensive global repository maintained by the Centre for Research on the Epidemiology of Disasters (CRED), which systematically records natural disasters, including viral epidemics (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.emdat.be/\u003c/span\u003e\u003cspan address=\"https://www.emdat.be/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e) [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. For this study, viral outbreaks were analyzed using the reported start date of each outbreak event as the temporal reference. The combined dataset spans the period from 1 October 1964 (1964-10-01T00:00:00Z) to 1 March 2025 (2025-03-01T00:00:00Z) and comprises 514 discrete viral outbreak events. Viral outbreaks were treated as a point process, allowing for multiple outbreak occurrences on the same calendar date. When repeated events shared the same start date, they were preserved and counted to quantify event multiplicity. Viral event intensity was quantified by aggregating the number of outbreak events occurring on the same date. These time series were visualized jointly to assess long-term temporal patterns in cosmic radiation intensity alongside viral outbreak frequency.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eSeasonal Autoregressive Integrated Moving Average (SARIMA)\u003c/h3\u003e\n\u003cp\u003eA seasonal autoregressive integrated moving average model [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e], SARIMA(1,0,1)\u0026times;(1,0,1,11), was fitted to the yearly GCRs radiation time series using statsmodels.tsa.statespace.SARIMAX, with an 11-year seasonal period corresponding to the solar cycle. Annual GCRs measurements were obtained by resampling the data to yearly resolution, with linear interpolation applied to fill missing years prior to model fitting. Stationarity and invertibility constraints were relaxed to allow flexible parameter estimation. Stationarity of the series was assessed using standard unit-root diagnostics prior to model fitting. Model performance was evaluated using the Akaike Information Criterion (AIC) (AIC\u0026thinsp;=\u0026thinsp;644.981). The fitted model was used to generate a 10-year GCRs radiation forecasts, with 95% confidence intervals derived from the model\u0026rsquo;s predictive distribution. Local maxima and minima in the forecasted series were identified using scipy.signal.find_peaks. Observed values, forecasts, confidence intervals, and identified peaks and troughs were visualized using matplotlib, with the x-axis scaled in 5-year intervals to emphasize long-term behavior.\u003c/p\u003e\n\u003ch3\u003eCross-Spectral Coherence, Burst Detection, and Granger Causality\u003c/h3\u003e\n\u003cp\u003eMonthly radiation and viral event counts were aggregated into a continuous monthly time series. Months without recorded events were zero-filled, representing absence of the documented viral outbreak events rather than confirmed zero incidence; however, this assumption may bias short-term variability. The Abrupt changes in viral event frequency were identified using the Pruned Exact Linear Time (PELT) change-point detection algorithm implemented in the ruptures package [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. Cross-spectral coherence [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e] between GCRs radiation and viral outbreak events counts was computed using scipy.signal.coherence, with frequencies converted to periods expressed in months. Statistical significance was assessed using a permutation-based surrogate approach. Viral outbreak events counts were randomly shuffled 1,000 times to generate a null distribution of coherence values, and empirical p-values were calculated as the fraction of surrogate coherences exceeding the observed value. Periods exceeding a coherence threshold of 0.8 and the 95th percentile of the surrogate distribution were considered significant. Also, Granger causality analysis [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e] was performed on the monthly series using lags up to 12 months. Both forward (radiation to events) and reverse (events to radiation) directions were tested to assess directional predictability, with p-values below 0.05 considered indicative of significant Granger causality.\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eCross-Wavelet Coherence and Phase Analysis\u003c/h2\u003e \u003cp\u003eTo resolve time-varying periodic synchronization between GCRs radiation and viral event frequancy, the author performed WTC using the pycwt library [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. Both monthly time series were standardized (z-score normalization) to ensure the wavelet power reflected relative oscillations rather than absolute magnitudes. The analysis utilized a Morlet mother wavelet (dimensionless frequency ω0\u0026thinsp;=\u0026thinsp;6) with a sub-octave resolution of dj\u0026thinsp;=\u0026thinsp;1/12 and a starting scale (s0) of two months. Statistical significance was established at the 95% confidence level against a red-noise background. To prevent misinterpretation of edge effects arising from the finite length of the time series, a Cone of Influence (COI) was calculated; data outside this boundary were excluded from periodic interpretation. Phase relationships were visualized via quiver plots on the coherence spectrum. The orientation of the phase arrows indicates the lead/lag relationship: right-pointing arrows signify in-phase synchronization, while left-pointing arrows signify anti-phase synchronization.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eConditional Harmonic VECMX Projection\u003c/h3\u003e\n\u003cp\u003ePrior to Vector Error Correction Model (VECM) estimation, the Johansen cointegration test was [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e] applied to the monthly GCRs and viral outbreak event series using statsmodels.tsa.vector_ar.vecm.coint_johansen. Thirteen lagged differences (k_ar_diff\u0026thinsp;=\u0026thinsp;13), corresponding approximately to one annual cycle, and no deterministic trend (det_order\u0026thinsp;=\u0026thinsp;0) were specified. Both trace and maximum-eigenvalue statistics were evaluated against 90%, 95%, and 99% critical values. A cointegration rank of one was identified and used in subsequent VECM estimation. To capture long-term phase relationships between GCRs and viral outbreak event counts, a conditional harmonic with exogenous variables (VECMX) [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e] was implemented. Monthly series were standardized and augmented with exogenous harmonic components representing Hale (21.33-year), Schwabe (10.67-year), Quasi-Biennial Oscillation (QBO) (1.94-year), annual, semiannual cycles, informed by heliophysical theory and prior spectral coherence analysis. Each cycle was expressed using sine and cosine terms to encode phase information. The VECMX employed 13 lagged differences, a cointegration rank of one, and a constant term in the cointegration relation. Projections were generated for a 20-year horizon (2026\u0026ndash;2046), with a 12-month rolling mean applied to emphasize dominant cyclical behavior. Predicted GCRs and viral event series were normalized using MinMaxScaler to facilitate comparison. Phase alignment between projected GCRs intensity and viral event frequency was further assessed using cross-correlation analysis of the normalized, smoothed projection series. Cross-correlation functions were computed over the full range of possible lags, and the lag corresponding to the maximum correlation was interpreted as the dominant phase offset between the two signals at monthly resolution. All analyses were conducted on a Linux system using Python 3.12 and standard scientific libraries, including pandas, numpy, matplotlib, scipy, ruptures, and statsmodels.\u003c/p\u003e"},{"header":"Result and Discussion","content":"\u003cp\u003eAlthough the timing of major viral outbreaks has long been an enigma in modern medicine [4-7], this study provides a possible statistical framework for outbreak prediction. By synthesizing spectral coherence, Granger causality, and cross-wavelet coherence analyses, the result shows that global viral crises are significantly coupled with fluctuations in GCRs flux. This relationship\u0026mdash;driven primarily by solar cycle and Sun magnetic cycle harmonic components\u0026mdash;suggests that what was once viewed as stochastic unpredictability can possibly be a predictable temporal pattern. Here, (Figure 2) visually demonstrates a temporal alignment between peaks in the start of viral outbreak activity and intervals of elevated GCRs intensity. The (Figure 3 and Table 1) highlight a predicted surge in GCRs intensity around 2030, likely coinciding with the transition into the next 25/26 solar minimum [41,42].\u003c/p\u003e\n\u003cp\u003eIn this context, viral outbreak emergence may not represent random epidemiological noise, but rather a phenomenon that exhibits synchronization with external GCRs and its solar and atmospheric modulators. As shown in the analysis, GCRs activity significantly \u0026quot;Granger-causes\u0026quot; viral events across all 12 tested lags (p \u0026lt; 0.05), with the strongest significance (p \u0026lt; 0.0001) occurring in the first four months. Conversely, there is no statistical significance to suggest that viral events influence GCRs flux (p \u0026gt; 0.21). This lack of feedback may indicate that the relationship is unidirectional (Table 2). The GCRs may contain predictive information that precedes the viral outbreaks. The persistent significance up to a 12-month lag may suggest a priming period, where solar and Earth atmospheric conditions may influence the terrestrial environment or viral outbreak well before they reaches a detectable threshold. Also, burst detection mapping of viral outbreak events against GCRs intensity identifies a clustering of burst occurrences during periods of low solar activity, most notably around the solar minima of approximately 2009 and 2019 (Figure 4A). Moreover, the spectral coherence analysis identifies statistically robust associations at multiple characteristic timescales. Prominent long-term periodicities corresponding to the Hale magnetic cycle (21.33 years) and the Schwabe cycle (10.67 years) exhibit high coherence values of 0.91 and 0.85, respectively, indicating a possible phase-locked behavior between solar variability and the analyzed viral outbreak signal. At shorter timescales, a high coherence is observed at the semi-annual cycle (0.50 years), with a coherence value of 0.95 (p = 0.000), consistent with a possibly seasonal modulation processes (Figure 4B, Table 3). In addition, a coherent spectral band spanning 1.94\u0026ndash;2.37 years aligns closely with the known periodicity of the QBO [43].\u003c/p\u003e\n\u003cp\u003eIn addition, the WTC analysis provides a dynamic, time-resolved evidence for the synchronization between GCRs variability and viral outbreak events. Unlike stationary spectral methods, the wavelet framework explicitly captures how shared periodicities emerge, persist, and intermittently strengthen or weaken across the full duration of the study period. The predominance of phase-locked regions, represented by contiguous dark-red coherence domains, indicates extended intervals during which both signals evolve in a tightly coupled manner. Notably, a persistent high-coherence band centered around the 11-year periodicity extends across the temporal axis (Figure 5), indicating that the Schwabe solar cycle may act as a stable and recurrent modulator of the viral outbeark events rather than a transient or episodic influence. Also, the 20-year conditional harmonic projection (2026\u0026ndash;2046) demonstrates a persistent and coherent phase alignment between the projected GRCs radiation signal and the projected viral outbreak trajectories. Across the forecast horizon, peaks and troughs in the projected viral outbreak event consistently track the phase evolution of the GCRs radiation harmonics. Rather than predicting the exact events, this model shows that future viral trends continue to mirror historical radiation cycles. These findings may suggest that global viral outbreaks can be organized around predictable GCRs rhythms instead of occurring at random (Figure 6A, Figure 6B). As shown in the SARIMA forecast (Table 1), GCRs flux intensity is predicted to rise steadily toward a peak around 2030, a corresponding increase in the frequency of viral outbreaks can be anticipated based on established periodic rhythms.\u003c/p\u003e\n\u003cp\u003eIndependent experimental and theoretical studies provide external support for the biological plausibility of the statistical associations observed in the present analysis. Mehta et al. demonstrated that exposure to simulated GCRs, including high-energy protons and heavy ions, that can directly induce reactivation of latent human cytomegalovirus (CMV) in vitro, leading to a significant increase in viral copy number without requiring major genomic sequence alterations [44]. Instead, radiation exposure triggered transcriptional activation of lytic-phase viral genes, indicating that ionizing radiation can act as a functional switch from latency to active replication. These findings support the hypothesis that fluctuations in GCRs intensity may influence viral activity through reactivation or amplification mechanisms rather than de novo viral emergence, consistent with the lead\u0026ndash;lag structure identified in the Granger causality and wavelet analyses. Complementary theoretical work proposed that variations in cosmic ray flux and solar activity represent underappreciated environmental drivers of emerging viral infectious diseases and argued for their integration into global early-warning surveillance systems [45]. Their study highlights that periods of solar minima coincide with several major viral emergence events. This framework aligns with this finding that viral outbreak timing may be phase-locked to dominant solar and heliomagnetic cycles, particularly the Schwabe cycle and Hale cycle. Together, these studies provide convergent biological and conceptual support for the hypothesis that GCRs variability may contain predictive information relevant to viral outbreak dynamics [44-46].\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eBeyond the dominant decadal solar-cycle harmonics, this analysis identifies statistically significant coherence between viral outbreak and GCRs variability within the quasi-biennial (\u0026asymp;1.9\u0026ndash;2.4 years) and annual/semi-annual cycles. The quasi-biennial periodicity aligns with the QBO, a primary mode of equatorial stratospheric variability. The QBO is known to modulate the vertical coupling between the stratosphere and troposphere, influencing global circulation and the transport of trace gases and aerosols [47-50]. The QBO modulates the dynamical coupling between the tropical stratosphere and the extratropics through the Holton\u0026ndash;Tan effect. During the easterly QBO phase, enhanced upward propagation of planetary waves weakens the polar vortex, whereas the westerly phase is associated with a stronger, more stable vortex [49-55]. Numerous studies have shown that the atmospheric response to solar variability is phase-dependent on the QBO, with statistically significant signals often emerging when stratified by QBO phase [50-55]. While the QBO does not alter the incoming flux of GCRs, it can regulate how solar-driven perturbations are dynamically expressed within the middle and lower atmosphere [56]. Similarly, the high coherence at annual and semi-annual scales may reflect the seasonal modulation of GCRs flux. This flux is governed by the Earth\u0026apos;s orbital position within the HCS and seasonal changes in Earth atmospheric shielding [54-57]. \u0026nbsp;However, such coherence may also arise from climatologically favorable viral outbreak seasons, during which intrinsic seasonal drivers dominate transmission dynamics, potentially producing apparent synchronization independent of heliophysical forcing [58,59]. By integrating these results, a multilevel coupling framework emerges; while long-term solar variability establishes the the long term risk, shorter-term oscillations like the QBO or seasonal cycles may regulate the specific timing of viral outbreak emergence. The increased GCRs flux and its secondary particle production has been linked to changes in the polar vortex strength which can impacted by QBO phases [60-63].\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eMoreover, recent research indicates that the Sun is entering a period of prolonged low solar activity, potentially marking the onset of a modern Grand Solar Minimum. The Sun has completed solar cycle 24, which was the weakest cycle observed in over a century, and solar cycle 25, which began in 2020, has exhibited a notably slow start in generating active regions and flares [64]. During 2020, the Sun experienced 115 spotless days (78% of the year), exceeding previous space-age records and indicating a continued suppression of sunspot formation. If this trend persists, the extended periods of minimal solar activity will correspond to conditions analogous to historical grand solar minima, such as the Sporer (ca. 1440\u0026ndash;1460), Maunder (ca. 1687\u0026ndash;1703), and Dalton (ca. 1809\u0026ndash;1821) minima [64-67]. Prolonged low solar activity, increases GCRs flux, which may partly explain the occurrence of the two major 21st-century pandemics\u0026mdash;Swine Flu (2009) and COVID-19 (2019)\u0026mdash;both coinciding with solar minima and separated by approximately 10 years.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eNevertheless, while the combined SARIMA, spectral coherence, and conditional harmonic VECMX framework offers a mechanistically informed approach to modeling GCR\u0026ndash;viral event dynamics, several limitations must be acknowledged. Both SARIMA and VECMX are fundamentally linear and rely on stationarity of differenced series; consequently, unmodeled nonlinear interactions, regime shifts, or structural breaks\u0026mdash;arising from abrupt solar variability, climatic transitions, or epidemiological changes\u0026mdash;may bias parameter estimates and inferred associations. The conditional harmonic VECMX further constrains system dynamics by imposing phase alignment with predefined solar and seasonal cycles, which, although physically motivated, may fail to capture transient, stochastic, or non-canonical solar influences and complex heliospheric\u0026ndash;atmospheric couplings. Interpolation of missing data in both GCRs and outbreak time series may introduce artificial smoothness, induce spurious trends, or attenuate short-term variability, thereby affecting time- and frequency-domain analyses. Spectral coherence and Granger causality inferences are sensitive to surrogate construction, lag selection, windowing, and significance thresholding, and extensive testing across scales and frequencies increases the risk of inflated nominal significance despite correction efforts. Long-horizon projections, particularly those extending to 20 years, remain highly sensitive to unmodeled exogenous changes, including shifts in surveillance practices, public health interventions, viral evolution, climate dynamics, and future solar behavior, and should therefore be interpreted as phase-informed scenario trajectories rather than deterministic predictions. Also, viral outbreak data derived from EM-DAT\u0026mdash;especially in the pre-2000 period\u0026mdash;are subject to substantial reporting biases which may distort long-term trends and further bias estimated relationships. Finaly, to substantiate any causal interpretation, targeted laboratory or experimental research is highly required to assess whether GCR-associated atmospheric ionization or perturbations can meaningfully influence viral persistence, activation, or host susceptibility.\u0026nbsp;\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThis study shows that global viral outbreak frequency exhibits statistically significant phase coherence with GCRs flux, implying a possible structured temporal organization rather than purely stochastic behavior. This coherence corresponds to dominant heliophysical periodicities, including the solar cycle and Hale magnetic cycle. While these findings may suggest that viral activity may be conditioned by interacting heliophysical and atmospheric rhythms acting as background modulators alongside established ecological and epidemiological drivers, further mechanistic, experimental, and epidemiological studies are required to substantiate and interpret these associations.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eConflict of Interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe author declares that there are no conflicts of interest.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe author wishes to express his gratitude to the Oulu Cosmic Ray Station (University of Oulu) for providing the long-term monitoring data of GCRs intensity and also to Centre for Research on the Epidemiology of Disasters (CRED) for maintaining the Emergency Events Database (EM-DAT), which was instrumental in providing the viral outbreak records used in this analysis.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research received no specific grant from any funding agency\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthical Approval and Institutional Review Board (IRB)\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eEthical approval was not required for this study. The research involves the secondary analysis of publicly available, aggregated, and de-identified environmental and epidemiological data. No human participants were involved, and no identifiable personal data were accessed or processed.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAlamin Mustafa solely contributed to the conceptualization, methodology, investigation, data curation, formal analysis, resources, software, validation, visualization, project administration, supervision, and writing (original draft and review \u0026amp; editing).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe raw data supporting the findings of this study are available from the Oulu Cosmic Ray Station and the EM-DAT database. The specific datasets processed and analyzed for this study are available from the corresponding author upon reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003cp\u003e1. The true death toll of COVID-19: estimating global excess mortality. Geneva: World Health Organization; 2021 ( https://www.who.int/data/stories/the-true-death-toll-of-covid-19-estimating-global-excess-mortality).\u003c/p\u003e\n\u003cp\u003e2. The impact of COVID-19 on health and care workers: a closer look at deaths. Geneva: World Health Organization; 2021 ( https://apps.who.int/iris/handle/10665/345300).\u003c/p\u003e\n\u003cp\u003e3. Agarwal R, Gopinth G, Farrar J, Hatchett R, Sands P. A global strategy to manage the long-term risks of COVID-19. Washington (DC): International Monetary Fund; 2022 (IMF Working Paper 22/68;\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.5089/9798400205996.001\u003c/p\u003e\n\u003cp\u003e4. Ioannidis JPA, Cripps S, Tanner MA. Forecasting for COVID-19 has failed. Int J Forecast. 2022 Apr-Jun;38(2):423-438. doi: 10.1016/j.ijforecast.2020.08.004. Epub 2020 Aug 25. PMID: 32863495; PMCID: PMC7447267.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1016/j.ijforecast.2020.08.004\u003c/p\u003e\n\u003cp\u003ePMid:32863495 PMCid:PMC7447267\u003c/p\u003e\n\u003cp\u003e5. Abdullrahman, M. (2022) Possible Association between Space Weather Variables, and the World\u0026apos;s COVID-19 Cases. Journal of Biosciences and Medicines, 10, 64-76. doi: 10.4236/jbm.2022.105006.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.4236/jbm.2022.105006\u003c/p\u003e\n\u003cp\u003e6. McMichael, A. (2004) Environmental and Social Influences on Emerging Infectious Diseases: Past, Present and Future. Philosophical Transactions of the Royal Society B Biological Sciences, 359, 1049-1058.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1098/rstb.2004.1480\u003c/p\u003e\n\u003cp\u003ePMid:15306389 PMCid:PMC1693387\u003c/p\u003e\n\u003cp\u003e7. Chizhevsky, A. (1976) The Terrestrial Echo of Solar Storms. Mysl, Moscow. First Published in 1936.\u003c/p\u003e\n\u003cp\u003e8.Helbing D. Globally networked risks and how to respond. Nature. 2013 May 2;497(7447):51-9. doi: 10.1038/nature12047. PMID: 23636396.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1038/nature12047\u003c/p\u003e\n\u003cp\u003ePMid:23636396\u003c/p\u003e\n\u003cp\u003e9. Towers S. Sunspot activity and influenza pandemics: a statistical assessment of the purported association. Epidemiol Infect. 2017 Oct;145(13):2640-2655. doi: 10.1017/S095026881700173X. Epub 2017 Aug 29. PMID: 28847318; PMCID: PMC9148804.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1017/S095026881700173X\u003c/p\u003e\n\u003cp\u003ePMid:28847318 PMCid:PMC9148804\u003c/p\u003e\n\u003cp\u003e10. Towers S. Sunspot activity and influenza pandemics: a statistical assessment of the purported association. Epidemiology \u0026amp; Infection. 2017 Oct;145(13):2640-55.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1017/S095026881700173X\u003c/p\u003e\n\u003cp\u003ePMid:28847318 PMCid:PMC9148804\u003c/p\u003e\n\u003cp\u003e11. Potgieter MS. Solar modulation of cosmic rays. Living Reviews in Solar Physics. 2013 Dec;10(1):3.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.12942/lrsp-2013-3\u003c/p\u003e\n\u003cp\u003e12. Rahmanifard F, Jordan AP, De Wet WC, Schwadron NA, Wilson JK, Owens MJ, Spence HE, Riley P. Evidence from galactic cosmic rays that the Sun has likely entered a secular minimum in solar activity. Space Weather. 2022 Feb;20(2):e2021SW002796.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1029/2021SW002796\u003c/p\u003e\n\u003cp\u003e13. Sage E, Shikazono N. Radiation-induced clustered DNA lesions: Repair and mutagenesis. Free Radical Biology and Medicine. 2017 Jun 1;107:125-35.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1016/j.freeradbiomed.2016.12.008\u003c/p\u003e\n\u003cp\u003ePMid:27939934\u003c/p\u003e\n\u003cp\u003e14. K\u0026auml;pyl\u0026auml; MJ, K\u0026auml;pyl\u0026auml; PJ, Olspert N, Brandenburg A, Warnecke J, Karak BB, Pelt J. Multiple dynamo modes as a mechanism for long-term solar activity variations. Astronomy \u0026amp; Astrophysics. 2016 May 1;589:A56.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1051/0004-6361/201527002\u003c/p\u003e\n\u003cp\u003e15. Oh S, Yi Y. Variations in Solar Parameters and Cosmic Rays with Solar Magnetic Polarity. The Astrophysical Journal. 2017 Apr 27;840(1):14.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.3847/1538-4357/aa6c62\u003c/p\u003e\n\u003cp\u003e16. Ross E, Chaplin WJ. The behaviour of galactic cosmic-ray intensity during solar activity cycle 24. Solar physics. 2019 Jan;294(1):8.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1007/s11207-019-1397-7\u003c/p\u003e\n\u003cp\u003ePMid:30872867 PMCid:PMC6383758\u003c/p\u003e\n\u003cp\u003e17. Durante M, Cucinotta FA. Physical basis of radiation protection in space travel. Reviews of modern physics. 2011 Oct 1;83(4):1245-81.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1103/RevModPhys.83.1245\u003c/p\u003e\n\u003cp\u003e18. Sweet M, Mishima K, Harada M, Kurita K, Iikura H, Tasaki S, Kikuchi N. Simulation Study on Dose and LET of Neutron Irradiation for Biological Experiments Using Spallation, Reactor, and Compact Neutron Sources. Quantum Beam Science. 2025 Apr 8;9(2):11.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.3390/qubs9020011\u003c/p\u003e\n\u003cp\u003e19. Giovanetti A, Tortolici F, Rufini S. Why Do the Cosmic Rays Induce Aging?. Frontiers in physiology. 2020 Aug 12;11:955.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.3389/fphys.2020.00955\u003c/p\u003e\n\u003cp\u003ePMid:32903447 PMCid:PMC7434975\u003c/p\u003e\n\u003cp\u003e20. Simonsen LC, Slaba TC, Guida P, Rusek A. NASA\u0026apos;s first ground-based Galactic Cosmic Ray Simulator: Enabling a new era in space radiobiology research. PLoS biology. 2020 May 19;18(5):e3000669.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1371/journal.pbio.3000669\u003c/p\u003e\n\u003cp\u003ePMid:32428004 PMCid:PMC7236977\u003c/p\u003e\n\u003cp\u003e21. Li M, Gonon G, Buonanno M, Autsavapromporn N, De Toledo SM, Pain D, Azzam EI. Health risks of space exploration: targeted and nontargeted oxidative injury by high-charge and high-energy particles. Antioxidants \u0026amp; redox signaling. 2014 Mar 20;20(9):1501-23.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1089/ars.2013.5649\u003c/p\u003e\n\u003cp\u003ePMid:24111926 PMCid:PMC3936510\u003c/p\u003e\n\u003cp\u003e22. Mertens CJ, Meier MM, Brown S, Norman RB, Xu X. NAIRAS aircraft radiation model development, dose climatology, and initial validation.\u003c/p\u003e\n\u003cp\u003e23. Hassanpour M, Rezaie M, Heydarizade Y, Rashed Iqbal Faruque M, Hassanpour M. Production of secondary particles from cosmic ray interactions in the earth\u0026apos;s atmosphere: Implications for annual effective dose, 14C/12C ratio, and magnetic field effects. PLoS One. 2025 Oct 23;20(10):e0328915. doi: 10.1371/journal.pone.0328915. PMID: 41129520; PMCID: PMC12548846.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1371/journal.pone.0328915\u003c/p\u003e\n\u003cp\u003ePMid:41129520 PMCid:PMC12548846\u003c/p\u003e\n\u003cp\u003e24. Ward JF. DNA damage produced by ionizing radiation in mammalian cells: identities, mechanisms of formation, and reparability. Progress in nucleic acid research and molecular biology. 1988 Jan 1;35:95-125.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1016/S0079-6603(08)60611-X\u003c/p\u003e\n\u003cp\u003ePMid:3065826\u003c/p\u003e\n\u003cp\u003e25. Wickramasinghe NC. Is the 2019 novel coronavirus related to a spike of cosmic rays?. Advances in Genetics. 2020 Jan 1;106:119-22.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1016/bs.adgen.2020.06.003\u003c/p\u003e\n\u003cp\u003ePMCid:PMC7529058\u003c/p\u003e\n\u003cp\u003e26. de Groen PC. Muons, mutations, and planetary shielding. Frontiers in astronomy and space sciences. 2022 Nov 23;9:1067491.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.3389/fspas.2022.1067491\u003c/p\u003e\n\u003cp\u003ePMid:36688079 PMCid:PMC9854335\u003c/p\u003e\n\u003cp\u003e27. Norbury JW, Schimmerling W, Slaba TC, Azzam EI, Badavi FF, Baiocco G, Benton E, Bindi V, Blakely EA, Blattnig SR, Boothman DA. Galactic cosmic ray simulation at the NASA Space Radiation Laboratory. Life sciences in space research. 2016 Feb 1;8:38-51.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1016/j.lssr.2016.02.001\u003c/p\u003e\n\u003cp\u003ePMid:26948012 PMCid:PMC5771487\u003c/p\u003e\n\u003cp\u003e28. Winer DA, Du H, Kim J, Chang V, Burke M, Winer S, Costes SV, Frippiat JP, Sams C, Paul AM, Wu H. Astroimmunology: the effects of spaceflight and its associated stressors on the immune system. Nature Reviews Immunology. 2025 Oct 16:1-24.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1038/s41577-025-01226-6\u003c/p\u003e\n\u003cp\u003ePMid:41102553\u003c/p\u003e\n\u003cp\u003e29. Wadhwa A, Moreno-Villanueva M, Crucian B, Wu H. Synergistic interplay between radiation and microgravity in spaceflight-related immunological health risks. Immunity \u0026amp; Ageing. 2024 Jul 20;21(1):50.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1186/s12979-024-00449-w\u003c/p\u003e\n\u003cp\u003ePMid:39033285 PMCid:PMC11264846\u003c/p\u003e\n\u003cp\u003e30. Shearer WT, Zhang S, Reuben JM, Lee BN, Butel JS. Effects of radiation and latent virus on immune responses in a space flight model. Journal of allergy and clinical immunology. 2005 Jun 1;115(6):1297-303.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1016/j.jaci.2005.03.003\u003c/p\u003e\n\u003cp\u003ePMid:15940150\u003c/p\u003e\n\u003cp\u003e31. Poluianov S, Usoskin I, Ibragimov A. Data management at the Oulu cosmic ray station. Proceedings of NMDB@ Home 2020. 2021 Jun 1.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.38072/2748-3150/p25\u003c/p\u003e\n\u003cp\u003e32. Delforge, D., Wathelet, V., Below, R., Lanfredi Sofia, C., Tonnelier, M., van Loenhout, J. A. F. \u0026amp; Speybroeck, N.: EM-DAT: The Emergency Events Database, International Journal of Disaster Risk Reduction, 105509, https://doi.org/10.1016/j.ijdrr.2025.105509, 2025.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1016/j.ijdrr.2025.105509\u003c/p\u003e\n\u003cp\u003e33. EM-DAT, CRED / UCLouvain, 2025, Brussels, Belgium - www.emdat.be (Accssed on 26 July 2026)\u003c/p\u003e\n\u003cp\u003e34. Ghysels E, Osborn DR, Rodrigues PM.\u0026nbsp;Forecasting seasonal time series. Handbook of economic forecasting. 2006 Jan 1;1:659-711.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1016/S1574-0706(05)01013-X\u003c/p\u003e\n\u003cp\u003e35. Wambui GD, Waititu GA, Wanjoya A. The power of the pruned exact linear time (PELT) test in multiple changepoint detection. American Journal of Theoretical and Applied Statistics. 2015 Nov;4(6):581.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.11648/j.ajtas.20150406.30\u003c/p\u003e\n\u003cp\u003e36. White LB, Boashash B. Cross spectral analysis of nonstationary processes. IEEE Transactions on Information Theory. 2002 Aug 6;36(4):830-5.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1109/18.53742\u003c/p\u003e\n\u003cp\u003e37. Shojaie A, Fox EB. Granger causality: A review and recent advances. Annual Review of Statistics and Its Application. 2022 Mar 7;9(1):289-319\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1146/annurev-statistics-040120-010930\u003c/p\u003e\n\u003cp\u003ePMid:37840549 PMCid:PMC10571505\u003c/p\u003e\n\u003cp\u003e38. Grinsted A, Moore JC, Jevrejeva S. Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear processes in geophysics. 2004 Nov 18;11(5/6):561-6.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.5194/npg-11-561-2004\u003c/p\u003e\n\u003cp\u003e39. Dwyer GP. The Johansen tests for cointegration. White Paper. 2015 Apr;516\u003c/p\u003e\n\u003cp\u003e40. Usman M, Loves L, Russel E, Ansori M, Warsono W, Widiarti W, Wamiliana W. Analysis of some energy and economics variables by using VECMX model in Indonesia. International Journal of Energy Economics and Policy. 2022;12(2):91-102.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.32479/ijeep.11897\u003c/p\u003e\n\u003cp\u003e41. Petrie GJ. Global solar photospheric and coronal magnetic field over activity cycles 21-25. Journal of Space Weather and Space Climate. 2024;14:5.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1051/swsc/2024005\u003c/p\u003e\n\u003cp\u003e42. Zharkova V. Modern Grand Solar Minimum will lead to terrestrial cooling. Temperature. 2020 Jul 2;7(3):217-22.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1080/23328940.2020.1796243\u003c/p\u003e\n\u003cp\u003ePMid:33117860 PMCid:PMC7575229\u003c/p\u003e\n\u003cp\u003e43. Valva C, Gerber EP. The QBO, the annual cycle, and their interactions: Isolating periodic modes with Koopman analysis. Journal of Climate. 2025 Jun 3.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1175/JCLI-D-24-0411.1\u003c/p\u003e\n\u003cp\u003e44. Mehta SK, Diak DM, Bustos-Lopez S, Nelman-Gonzalez M, Chen X, Plante I, Stray SJ, Tandon R, Crucian BE. Effect of Simulated Cosmic Radiation on Cytomegalovirus Reactivation and Lytic Replication. International Journal of Molecular Sciences. 2024 Sep 26;25(19):10337.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.3390/ijms251910337\u003c/p\u003e\n\u003cp\u003ePMid:39408667 PMCid:PMC11477029\u003c/p\u003e\n\u003cp\u003e45. Qu J. Is sunspot activity a factor in influenza pandemics? Rev Med Virol. 2016; 26(5): 309-313.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1002/rmv.1887\u003c/p\u003e\n\u003cp\u003ePMid:27136236\u003c/p\u003e\n\u003cp\u003e46. Qu J, Wickramasinghe NC. The world should establish an early warning system for new viral infectious diseases by space‐weather monitoring. MedComm. 2020 Dec;1(3):423-6.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1002/mco2.20\u003c/p\u003e\n\u003cp\u003ePMid:32838395 PMCid:PMC7404868\u003c/p\u003e\n\u003cp\u003e47. Diallo MA, Ploeger F, Hegglin MI, Ern M, Groo\u0026szlig; JU, Khaykin S, Riese M. Stratospheric water vapour and ozone response to the quasi-biennial oscillation disruptions in 2016 and 2020. Atmospheric chemistry and physics. 2022 Nov 8;22(21):14303-21.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.5194/acp-22-14303-2022\u003c/p\u003e\n\u003cp\u003e48. Gray LJ, Beer J, Geller M, Haigh JD, Lockwood M, Matthes K, Cubasch U, Fleitmann D, Harrison G, Hood L, Luterbacher J. Solar influences on climate. Reviews of Geophysics. 2010 Dec;48(4).\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1029/2009RG000282\u003c/p\u003e\n\u003cp\u003e49. Baldwin MP, Gray LJ, Dunkerton TJ, Hamilton K, Haynes PH, Randel WJ, Holton JR, Alexander MJ, Hirota I, Horinouchi T, Jones DB. The quasi‐biennial oscillation. Reviews of Geophysics. 2001 May;39(2):179-229.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1029/1999RG000073\u003c/p\u003e\n\u003cp\u003e50. Bazilevskaya GA, Usoskin IG, Fl\u0026uuml;ckiger EO, Harrison RG, Desorgher L, B\u0026uuml;tikofer R, Krainev MB, Makhmutov VS, Stozhkov YI, Svirzhevskaya AK, Svirzhevsky NS. Cosmic ray induced ion production in the atmosphere. Space Science Reviews. 2008 Jun;137(1):149-73.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1007/s11214-008-9339-y\u003c/p\u003e\n\u003cp\u003e51. Sunkara E, Seo KH, Mengist CK, Ratnam MV, Niranjan Kumar K, Venkata Chalapathi G. Role of QBO and MJO in Sudden Stratospheric Warmings: A Case Study. Atmosphere. 2024 Dec 5;15(12):1458.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.3390/atmos15121458\u003c/p\u003e\n\u003cp\u003e52. Svensmark H. Cosmoclimatology: a new theory emerges. Astronomy \u0026amp; Geophysics. 2007 Feb 1;48(1):1-8.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1111/j.1468-4004.2007.48118.x\u003c/p\u003e\n\u003cp\u003e53. Usoskin IG, Kovaltsov GA, Mishev AL. Updated model of cosmic-ray-induced ionization in the atmosphere (CRAC: CRII_v3): Improved yield function and lookup tables.\u003c/p\u003e\n\u003cp\u003e54. Holton JR, Austin J. The influence of the equatorial QBO on sudden stratospheric warmings. Journal of Atmospheric Sciences. 1991 Feb 15;48(4):607-18.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1175/1520-0469(1991)048\u0026lt;0607:TIOTEQ\u0026gt;2.0.CO;2\u003c/p\u003e\n\u003cp\u003e55. Schmidt C, K\u0026uuml;chelbacher L, W\u0026uuml;st S, Bittner M. OH airglow observations with two identical spectrometers: benefits of increased data homogeneity in the identification of variations induced by the 11-year solar cycle, the QBO, and other factors. Atmospheric Measurement Techniques. 2023 Oct 4;16(19):4331-56.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.5194/amt-16-4331-2023\u003c/p\u003e\n\u003cp\u003e56. Li KF, Tung KK. Quasi‐biennial oscillation and solar cycle influences on winter Arctic total ozone. Journal of Geophysical Research: Atmospheres. 2014 May 27;119(10):5823-35.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1002/2013JD021065\u003c/p\u003e\n\u003cp\u003e57. Lockwood M, Owens MJ, Barnard LA, Haines C, Scott CJ, McWilliams KA, Coxon JC. Semi-annual, annual and Universal Time variations in the magnetosphere and in geomagnetic activity: 1. Geomagnetic data. Journal of Space Weather and Space Climate. 2020;10:23.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1051/swsc/2020023\u003c/p\u003e\n\u003cp\u003e58. Bloom-Feshbach K, Alonso WJ, Charu V, Tamerius J, Simonsen L, Miller MA, Viboud C. Latitudinal variations in seasonal activity of influenza and respiratory syncytial virus (RSV): a global comparative review. PloS one. 2013 Feb 14;8(2):e54445.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1371/journal.pone.0054445\u003c/p\u003e\n\u003cp\u003ePMid:23457451 PMCid:PMC3573019\u003c/p\u003e\n\u003cp\u003e59. Geoghegan JL, Walker PJ, Duchemin JB, Jeanne I, Holmes EC. Seasonal drivers of the epidemiology of arthropod-borne viruses in Australia. PLoS Neglected Tropical Diseases. 2014 Nov 20;8(11):e3325.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1371/journal.pntd.0003325\u003c/p\u003e\n\u003cp\u003ePMid:25412443 PMCid:PMC4239014\u003c/p\u003e\n\u003cp\u003e60. Veretenenko S, Ogurtsov M. Stratospheric polar vortex as a possible reason for temporal variations of solar activity and galactic cosmic ray effects on the lower atmosphere circulation. Advances in Space Research. 2014 Dec 15;54(12):2467-77.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1016/j.asr.2013.09.001\u003c/p\u003e\n\u003cp\u003e61. Veretenenko S. Stratospheric polar vortex as an important link between the lower atmosphere circulation and solar activity. Atmosphere. 2022 Jul 18;13(7):1132.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.3390/atmos13071132\u003c/p\u003e\n\u003cp\u003e62. Zharkova V. Modern Grand Solar Minimum will lead to terrestrial cooling. Temperature (Austin). 2020 Aug 4;7(3):217-222. doi: 10.1080/23328940.2020.1796243. PMID: 33117860; PMCID: PMC7575229.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1080/23328940.2020.1796243\u003c/p\u003e\n\u003cp\u003ePMid:33117860 PMCid:PMC7575229\u003c/p\u003e\n\u003cp\u003e63. Brown LP, Charlery J, Voutchkov M. Investigating the Apparent Link between Cosmic Ray Muon Flux, Sudden Stratospheric Warming and Dry Season Rainfall over Jamaica. Atmospheric and Climate Sciences. 2019 Sep 10;9(4):662-82.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.4236/acs.2019.94041\u003c/p\u003e\n\u003cp\u003e64. Taricco C, Arnone E, Rubinetti S, Bizzarri I, Agafonova NY, Aglietta M, Antonioli P, Ashikhmin VV, Bari G, Bruno G, Dobrynina EA. Exploration of the stratosphere with cosmic-ray muons detected underground. Physical Review Research. 2022 Jun;4(2):023226.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.1103/PhysRevResearch.4.023226\u003c/p\u003e\n\u003cp\u003e65. M\u0026ouml;rner NA. The approaching new grand solar minimum and little ice age climate conditions. Natural Science. 2015 Nov 16;7(11):510-8.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.4236/ns.2015.711052\u003c/p\u003e\n\u003cp\u003e66. Hao YQ, Shi H, Xiao Z, Zhang DH. Weak ionization of the global ionosphere in solar cycle 24. InAnnales Geophysicae 2014 Jul 21 (Vol. 32, No. 7, pp. 809-816). Copernicus GmbH.\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.5194/angeo-32-809-2014\u003c/p\u003e\n\u003cp\u003e67. Elias AG, de Adler NO.\u0026nbsp;Forecast of solar maximum and minimum dates for solar cycles 23 to 29. Annals of Geophysics. 1998 Nov 25;41(1).\u003c/p\u003e\n\u003cp\u003ehttps://doi.org/10.4401/ag-3790\u003c/p\u003e"},{"header":"Tables","content":"\u003cp\u003e\u003cstrong\u003eTable 1: Decade-Ahead SARIMA Forecast (2026\u0026ndash;2035) of Predicted GCRs Flux Intensity with 95% Confidence Intervals\u003c/strong\u003e\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"3\" cellpadding=\"0\" width=\"99%\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 9px;\"\u003e\n \u003cp\u003eYear\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 36px;\"\u003e\n \u003cp\u003ePredicted Value [cts/min]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003eLower 95% CI\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003eUpper 95% CI\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003eFeature\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 9px;\"\u003e\n \u003cp\u003e2026\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 36px;\"\u003e\n \u003cp\u003e5703.49\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e5404.72\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e6002.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 9px;\"\u003e\n \u003cp\u003e2027\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 36px;\"\u003e\n \u003cp\u003e5779.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e5273.77\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e6285.71\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 9px;\"\u003e\n \u003cp\u003e2028\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 36px;\"\u003e\n \u003cp\u003e5828.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e5180.48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e6476.16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 9px;\"\u003e\n \u003cp\u003e2029\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 36px;\"\u003e\n \u003cp\u003e5870.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e5108.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e6632.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 9px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e2030\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 36px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e5876.80\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e5017.65\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e6735.95\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e\u003cstrong\u003ePeak\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 9px;\"\u003e\n \u003cp\u003e2031\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 36px;\"\u003e\n \u003cp\u003e5868.73\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e4923.76\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e6813.70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 9px;\"\u003e\n \u003cp\u003e2032\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 36px;\"\u003e\n \u003cp\u003e5789.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e4767.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e6811.55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 9px;\"\u003e\n \u003cp\u003e2033\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 36px;\"\u003e\n \u003cp\u003e5657.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e4564.44\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e6749.63\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 9px;\"\u003e\n \u003cp\u003e2034\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 36px;\"\u003e\n \u003cp\u003e5509.97\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e4352.37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e6667.57\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 9px;\"\u003e\n \u003cp\u003e2035\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 36px;\"\u003e\n \u003cp\u003e5426.33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e4208.29\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 20px;\"\u003e\n \u003cp\u003e6644.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cstrong\u003eTable 2: Summary of Granger Causality Tests for GCRs Levels and Viral Outbreak Events across 12 Lags\u003c/strong\u003e\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"3\" cellpadding=\"0\" width=\"99%\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 7px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eLag\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eRadiation \u0026rarr; Events (p-value)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eEvents \u0026rarr; Radiation (p-value)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 7px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e1\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.0000***\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.8422\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 7px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.0000***\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.8007\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 7px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e3\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.0000***\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.2750\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 7px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e4\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.0000***\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.3552\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 7px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e5\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.0003***\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.3473\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 7px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e6\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.0008***\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.4236\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 7px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e7\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.0014**\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.4635\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 7px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e8\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.0010**\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.5079\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 7px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e9\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.0032**\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.3634\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 7px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e10\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.0030**\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.4197\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 7px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e11\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.0059**\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.5030\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 7px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e12\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.0375*\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.2140\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cstrong\u003eTable 3: Spectral Coherence Analysis Identifying Significant Periodicities and Possibly Associated with Solar/Atmospheric Cycles\u003c/strong\u003e\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"3\" cellpadding=\"0\" width=\"99%\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 22px;\"\u003e\n \u003cp\u003e\u003cstrong\u003ePeriod (Years)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eCoherence\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eP-Value\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003e\u003cstrong\u003ePossible Cycle Description\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 22px;\"\u003e\n \u003cp\u003e21.33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.91\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eHale Cycle (Solar Magnetic)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 22px;\"\u003e\n \u003cp\u003e10.67\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e0.007\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eSchwabe Cycle (11-Year Solar)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 22px;\"\u003e\n \u003cp\u003e2.37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.81\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e0.010\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eQuasi-Biennial Oscillation (QBO)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 22px;\"\u003e\n \u003cp\u003e2.13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.83\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e0.003\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eQuasi-Biennial Oscillation (QBO)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 22px;\"\u003e\n \u003cp\u003e1.94\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.89\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e0.003\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eQuasi-Biennial Oscillation (QBO)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 22px;\"\u003e\n \u003cp\u003e1.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.84\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e0.004\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eAnnual Cycle\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 22px;\"\u003e\n \u003cp\u003e0.97\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.81\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eAnnual Variation\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 22px;\"\u003e\n \u003cp\u003e0.65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.81\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e0.007\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eIntra-annual signal\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 22px;\"\u003e\n \u003cp\u003e0.51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e0.005\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eSemi-annual signal\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 22px;\"\u003e\n \u003cp\u003e0.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e0.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eSemi-annual Cycle\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 22px;\"\u003e\n \u003cp\u003e0.37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.82\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e0.003\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eseasonal harmonic\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 22px;\"\u003e\n \u003cp\u003e0.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.83\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e0.003\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eseasonal harmonic\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 22px;\"\u003e\n \u003cp\u003e0.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.91\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eseasonal harmonic\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 22px;\"\u003e\n \u003cp\u003e0.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.92\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e0.002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eseasonal harmoni\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 22px;\"\u003e\n \u003cp\u003e0.29\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.91\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e0.002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eHigh-frequency variation\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 22px;\"\u003e\n \u003cp\u003e0.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.89\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e0.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eQuarterly signal (~3 months)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 22px;\"\u003e\n \u003cp\u003e0.21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.84\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e0.009\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eHigh-frequency jitter\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 22px;\"\u003e\n \u003cp\u003e0.21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e0.009\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 46px;\"\u003e\n \u003cp\u003eHigh-frequency jitter\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Viral outbreaks, galactic cosmic rays, global viral pandemics, synchronization, solar cycle and Hale cycle","lastPublishedDoi":"10.21203/rs.3.rs-8834986/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8834986/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cstrong\u003eBackground\u003c/strong\u003e: The temporal emergence of major viral outbreaks has traditionally been regarded as largely stochastic, with limited capacity for long-range anticipation. Increasing evidence from heliophysics and atmospheric science suggests that Galactic Cosmic Ray (GCRs) flux—modulated by solar magnetic activity and Earth–atmosphere coupling—constitutes a persistent background source of ionizing radiation and may represent an overlooked environmental driver capable of organizing biological phenomena across multiple timescales. As a ubiquitous component of the planetary radiation environment, GCRs continuously interact with biological systems, providing a plausible environmental context for large-scale temporal modulation without implying direct deterministic causation.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMethods\u003c/strong\u003e: A total of 514 viral outbreak events (EM-DAT, 1964 to 2025) and GCRs intensity data (Oulu Cosmic Ray Station) were analyzed using SARIMA forecasting, PELT change-point detection, Granger causality, cross-spectral and Wavelet Transform Coherence (WTC), and a Vector Error Correction Model with exogenous harmonic components (VECMX). These methods were applied within an environmental–ecological time-series framework to evaluate whether large-scale GCRS variability aligns with population-level viral outbreak dynamics. Harmonic structures corresponding to the Hale (~22-year), Schwabe (~11-year), annual/semi-annual, and Quasi-Biennial Oscillation (QBO) cycles were incorporated to assess phase synchronization, ecological timing cues, and long-range temporal alignment between cosmic radiation variability and viral emergence patterns.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eResults\u003c/strong\u003e: GCRs variability significantly Granger-caused viral outbreak occurrence across all tested lags up to 12 months (p \u0026lt; 0.05), with maximal significance within the first four months (p \u0026lt; 0.0001), while no reverse causality was detected. Spectral coherence revealed robust phase-locked coupling at the Hale and Schwabe solar cycles (coherence = 0.91 and 0.85, respectively), indicating long-term synchronization. Additional statistically significant coherence was identified at quasi-biennial, annual, and semi-annual timescales, consistent with GCRs secondary particles modulation by the Quasi-Biennial Oscillation and seasonal atmospheric shielding. WTC demonstrated sustained coherence at the ≈11-year Schwabe periodicity. Burst detection analysis further showed clustering of viral outbreak onsets during periods of low solar activity, notably around the 2009 and 2019 solar minima. Conditional harmonic VECMX and SARIMA projections indicate a renewed increase in GCRs intensity toward ~2030, coinciding with the anticipated solar cycle A\u0026lt;0, 25/26 minimum and a corresponding phase-aligned rise in viral outbreak activity.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConclusions\u003c/strong\u003e: Global viral outbreak dynamics exhibit statistically robust, multi-scale synchronization with GCRs variability. While GCRs are unlikely to act as direct causal agents, they may function as environmental timing cues or permissive triggers that modulate viral emergence or ecological susceptibility windows. Incorporation of heliophysical indicators as contextual environmental risk modifiers may enhance early-warning systems and global outbreak preparedness when integrated with conventional epidemiological surveillance frameworks.\u003c/p\u003e","manuscriptTitle":"Environmental Synchronization Between Background Galactic Cosmic Radiation and the Non-Random Timing of Viral Outbreak Emergence","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-11 05:19:34","doi":"10.21203/rs.3.rs-8834986/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"b2048d16-610a-4fde-81da-6795b6acb853","owner":[],"postedDate":"February 11th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":62622270,"name":"Ecological Modeling"},{"id":62622271,"name":"Astrobiology"},{"id":62622272,"name":"Atmospheric Sciences"},{"id":62622273,"name":"Epidemiology"}],"tags":[],"updatedAt":"2026-02-11T05:19:35+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-11 05:19:34","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8834986","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8834986","identity":"rs-8834986","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}