Is the worst of the COVID-19 global pandemic yet to come? Application of financial mathematics as candidate predictive tools

The study hypothesizes that the Elliott Wave Principle, originally developed to explain market movements as manifestations of crowd psychology, can describe and predict the epidemiological evolution of COVID-19. The authors argue that human emotions and behaviors—such as adherence to mask-wearing, social distancing, and willingness to vaccinate—shape pandemic dynamics analogously to how sentiment influences asset prices. A thought experiment contrasts strictly compliant individuals with those whose compliance fluctuates with emotions and external cues, positing that collective behavioral oscillations generate wave-like patterns in case trajectories. The purpose is to test whether Elliott Wave patterns and associated Fibonacci relationships can explain observed trends and support scenario-based projections for the pandemic, providing an alternative, sentiment-driven lens to anticipate future surges and declines.

Background is provided on Ralph N. Elliott’s Wave Principle and its use in technical analysis to interpret sentiment-driven market cycles across multiple time scales. The fractal nature of impulse (five-wave) and corrective (three-wave) structures and their quantitative relationships via Fibonacci ratios (retracements and extensions) are summarized as the theoretical basis for applying the approach to other domains of mass human behavior. The paper does not present a formal, separate literature review on epidemiological modeling but references the Elliott foundational works and standard Fibonacci-based methods used in finance.

- Conceptual framework: Apply Elliott Wave analysis to 7-day moving averages of daily new COVID-19 cases, positing that public sentiment and policy adherence produce impulse (growth) and corrective (decline) waves across nested time scales. - Elliott Wave structure: Identify impulse waves (i, iii, v at lower degree; 1, 3, 5 at higher degree; I at still higher) and corrective waves (ii, iv; 2, 4; II), leveraging the fractal hierarchy and the rule that impulses subdivide into five sub-waves and corrections into three sub-waves (a, b, c). - Fibonacci Pinball technique: Use Fibonacci retracement and extension levels to estimate support/resistance and project future case trajectories. • Retracement formulas (using last two time points Pt and Pt-1): - Uptrend: Pt+1 = Pt − (Pt − Pt−1) · Fib - Downtrend: Pt+1 = Pt + (Pt−1 − Pt) · Fib • Extension formulas (using last three time points Pt, Pt−1, Pt−2): - Uptrend: Pt+1 = Pt + (Pt−1 − Pt−2) · Fib - Downtrend: Pt+1 = Pt − (Pt−2 − Pt−1) · Fib Common Fibonacci levels include 23.6%, 50%, 61.8%, 100%, 138.2%, 261.8%, etc., used to define potential support/resistance. - Data: Publicly available daily new cases from Our World in Data (JHU source): https://github.com/owid/covid-19-data/blob/master/public/data/jhu/new_cases.csv. - Processing and tools: Analyses performed in MATLAB R2018a; 7-day moving averages used for trend identification; code available from the corresponding author upon request. - Case studies: Apply the framework to the USA, European Economic Area (EEA), India, Brazil, and the world. Annotate timelines with major policy events (restrictive and permissive) to align observed impulses/corrections with shifts in public health measures and behavior. - Scenario modeling: Construct best-, intermediate-, and worst-case projections based on vaccination availability/speed and strength of restrictions, using Fibonacci Pinball to bound possible paths and turning points.

- Observational fit to Elliott patterns: • USA: Case trajectory (to 3/22/2021) aligns with a complete higher-dimensional impulsive super-wave I comprising waves 1, 2, extended 3 (with five sub-waves i–v), 4, and 5; current movement interpreted as corrective wave A of II. Wave 3 and sub-wave iii exhibit the strongest growth, consistent with Elliott theory. • EEA: Initial wave 1 followed by an extended corrective wave 2 (spring–summer 2020 restrictions). A strong wave 3 surge after summer holidays, then corrective wave 4 (a–b–c) with vaccination start; loosening restrictions and slow vaccinations in early 2021 likely initiated wave 5. • India and Brazil: Early stringent restrictions delayed wave 1. Subsequent easing in June 2020 triggered wave 1; mask use and distancing led to corrective wave 2. Brazil showed a strong wave 3 following reopening of tourism and venues since October 2020. India experienced a prolonged correction, potentially influenced by biological factors (evidence of stronger innate immunity in the population). - Quantitative context: As of March 2021, >124 million infections and >2.7 million deaths worldwide provide a high-emotion environment conducive to sentiment-driven dynamics. - Policy-behavior alignment: Corrective phases align with restrictions (lockdowns, mask mandates), while impulsive phases align with policy relaxation (business/school reopenings, holidays) and behavioral fatigue. - Projections via Fibonacci Pinball: • World: Interpreted as in impulsive wave B of super-wave II undergoing downtrend retracement with resistance near common Fibonacci levels (e.g., 50%, 61.8%, 100% R), followed by downtrend extensions leading to mild/moderate/strong correction by the end of super-wave II around August 2021, contingent on vaccine availability and policy adherence. • USA: In corrective wave A of super-wave II with possible support near ~300% retracement; anticipated impulsive wave B (due to policy relaxation, spring gatherings, slow vaccination) to retrace to 23.6–100% R levels, then corrective wave C (renewed restrictions or improved vaccination) to downtrend extension supports. The magnitude of correction (mild to strong) depends on vaccination pace and adherence. - Scenario outcomes: • Scenario 1 (worst): Vaccine mostly unavailable, highly transmissible variants, minimal restrictions → large extensions and higher peaks. • Scenario 2 (intermediate): Partial vaccine availability with limited restrictions. • Scenario 3 (best): Broad vaccine availability with stringent restrictions → truncated impulses and stronger corrections. - Pandemic outlook: Without rapid mass vaccination and strong, sustained adherence to public health measures, higher-dimensional waves II–V may unfold in 2021–2022, potentially causing unprecedented infection levels; conversely, strong interventions could truncate future impulses.

The findings support the hypothesis that collective behavioral oscillations during the pandemic manifest as Elliott-type impulse and corrective waves. The observed alignment between policy-driven behavioral shifts and wave phases, along with approximate adherence to Fibonacci retracement/extension ratios, suggests sentiment-sensitive predictability in case trajectories. This framework offers a heuristic tool to anticipate turning points under varying policy and vaccination scenarios. It addresses the research question by demonstrating that a financial sentiment model can reproduce and interpret pandemic dynamics across regions, linking increases to relaxation/fatigue and decreases to restrictions/vaccination. The significance lies in providing an alternative, behavior-centric predictive lens that can inform timing and stringency of interventions, with projections highlighting risks of resurgence (e.g., anticipated wave III) if vaccination is slow or measures are relaxed, especially amid more transmissible variants.

This work presents, to the authors’ knowledge, the first application of the Elliott Wave Principle and Fibonacci Pinball to epidemiological time series, showing that COVID-19 case trajectories for multiple regions exhibit impulse/corrective structures consistent with crowd-psychology-driven dynamics. Using this framework, the authors generate scenario-based projections for the world and USA, indicating that the pandemic would likely persist through 2021 and could escalate without rapid, widespread vaccination and sustained restrictions, whereas strong measures could truncate future waves. Future research should quantitatively integrate biological factors (e.g., immunity heterogeneity, emerging variants), vaccination rollout dynamics, and granular mobility/compliance data; validate the approach prospectively against mechanistic epidemiological models; and explore hybrid models that blend sentiment-based signals with traditional transmission parameters.

- Dependence on the assumption that case dynamics are primarily driven by crowd psychology and policy adherence; biological heterogeneity (e.g., population immunity differences, variant fitness) may alter patterns, as noted for India. - Use of aggregated reported case data subject to testing/reporting biases and delays; 7-day averages may still reflect structural artifacts. - Elliott Wave identification and Fibonacci level selection can be subjective, and overfitting to past patterns may occur; turning points are sensitive to chosen levels. - Scenario projections are contingent on uncertain external factors (vaccine availability/uptake, emergence of variants, policy changes), limiting forecast precision. - Affiliation and data limitations prevent comprehensive validation across all regions and time scales within the study period.