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Integrating Persuasion Theory into the Epidemiological Modelling of Health Misinformation Spread on Social Media

Mkululi Sikosana, Sean Maudsley-Barton, Oluwaseun Ajao

arXiv:2608.15689v1cs.SIcs.AIcs.CLcs.LG

TL;DR

Health misinformation models often omit the changing psychological signals that shape online diffusion. This paper integrates persuasion-related signals into a six-compartment epidemiological model, improving empirical alignment when those signals vary meaningfully over time, though benefits are weak when they do not.

  • Problem

    Continuous-time misinformation models rarely incorporate real-time behavioural signals, leaving structural diffusion models and psychological research insufficiently integrated.

  • Method

    The ELM-SIRMMM framework extends SIR to six misinformation lifecycle compartments and modulates transmission with time-varying sentiment, engagement, and cognitive-effort signals.

  • Results

    Across three Twitter datasets, behavioural enrichment improved empirical alignment when psychological signals varied meaningfully, while Monant showed comparatively weak modulation.

  • Takeaways & Limitations

    Misinformation diffusion can be modelled more realistically when structural propagation is conditioned on temporally varying behavioural information.

  • Takeaways & Limitations

    When psychological inputs lack variance, the model reverts toward static SIR-like dynamics and loses the benefits of ELM modulation.

Abstract

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This study presents a hybrid epidemiological and behavioural framework to simulate the spread of health misinformation on social media. We extend the classical Susceptible--Infected--Recovered (SIR) model to a six-compartment structure (SIRMMM), incorporating Misinformed Susceptible (MS), Misinformed Infected (MI), and Misinformed Recovered (MR) compartments to better reflect the dynamics of the misinformation lifecycle. To account for individual-level behavioural variation, we extend the SIRMMM model by integrating psychological signals from the Elaboration Likelihood Model (ELM), including sentiment polarity, engagement metrics, and cognitive effort, which dynamically modulate the misinformation transmission rate, yielding the ELM-SIRMMM framework. Model parameters were estimated using the FibVID dataset, which captures COVID-19 misinformation on Twitter. Generalisability was tested on two additional datasets: MC-Fake (emotional misinformation) and Monant (general health misinformation). Results show that the ELM-SIRMMM model enhances both predictive accuracy and dynamic realism. On FibVID, it decreases RMSE by 5.5%, delays the misinformation peak from day 150 to day 160, and increases its peak prevalence from 6% to 7%. On MC-Fake, it accurately reproduces a flash-rumour pattern, infecting 38% of users by day 45 and achieving 97% misinformation recovery, all while maintaining model accuracy. In contrast, minimal behavioural signal variability in the Monant dataset leads to marginal benefit, with only a 3% peak and 57% of users remaining susceptible. These findings suggest that structural elaboration alone is insufficient. Functional realism in modelling misinformation spread requires dynamic psychological inputs that vary meaningfully across time and contexts.

I. INTRODUCTION · A. RESEARCH AIMS & HYPOTHESES

The paper argues that structural epidemic models lack behavioural realism for social-media misinformation and proposes ELM-SIRMMM to integrate persuasion cues into propagation dynamics. It compares SIRMMM and ELM-SIRMMM and tests hypotheses about recovery mechanisms, realistic dynamics, and empirical cascade fit.

  • I. INTRODUCTION: COVID-19 misinformation can spread rapidly and unpredictably on social media, affecting public-health interventions and individual behaviour.
  • I. INTRODUCTION: Traditional SIR models simplify misinformation diffusion through homogeneous mixing, constant transmission rates, and instantaneous recovery.
  • I. INTRODUCTION: Behavioural realism is needed because psychological factors, message framing, and presentation shape how individuals share and interpret contested information.
  • I. INTRODUCTION: ELM-SIRMMM extends SIR to six states by adding Misinformed Susceptible (MS), Misinformed Infected (MI), and Misinformed Recovered (MR).These compartments distinguish exposure, active sharing, and cessation.
  • I. INTRODUCTION: Its transmission coefficient varies over time using sentiment, engagement, and cognitive-effort measures to represent user-level behavioural heterogeneity and dual-route persuasion.
  • I. INTRODUCTION: The modelling approach is motivated by cross-dataset differences in linguistic complexity, emotional tone, and rhetorical structure.The paper expects behavioural enrichment to be most informative when sentiment, engagement, or cognition signals fluctuate.
  • A. RESEARCH AIMS & HYPOTHESES: The study compares SIRMMM with ELM-SIRMMM and hypothesizes that SIR overestimates prevalence, SIRMMM improves peak and decay dynamics, and ELM-SIRMMM best fits empirical cascades.H3 specifies lower RMSE and improved peak timing relative to SIR and SIRMMM.

II. STATE OF THE ART … 1) Classical SIR

Prior work has developed epidemiological and behavioural approaches to misinformation diffusion, but their integration remains limited. This paper unifies these strands through SIRMMM with an ELM-inspired behavioural layer, while using classical SIR as a conceptual baseline for diffusion dynamics.

  • II. STATE OF THE ART: Misinformation-diffusion research has bifurcated into epidemiological compartmental extensions and behavioural modulation of message and user attributes.Epidemiological work includes fact-checking compartments and complex-contagion variants, while behavioural work considers emotional, linguistic, semantic, and network influences.
  • II. STATE OF THE ART: Dual-process persuasion theory remains relatively underdeveloped in dynamic misinformation models, despite evidence supporting integrative approaches to classification and emotional-contagion analysis.The cited literature motivates combining complementary representations and examining how emotional contagion interacts with meme lifecycles.
  • II. STATE OF THE ART: The proposed framework enriches SIR with three misinformation-specific compartments and embeds an ELM-inspired behavioural layer in the transmission coefficient.This unified design captures structural diffusion patterns alongside real-time user-level persuasion dynamics, building on prior multi-compartment and psychological-feature studies.
  • III. MATERIALS & METHODS: The materials-and-methods section covers datasets, engineered behavioural features, the ELM-integrated compartmental model, and parameter-estimation procedures for simulating misinformation propagation.These components define the empirical and computational basis for the model dynamics.
  • A. EPIDEMIOLOGICAL MODELS OF MISINFORMATION: All model variants assume homogeneous population mixing, a single-wave outbreak window, and no reinfection, prioritising explanatory fit to observed cascades over recurrent or long-horizon rumour cycles.The analysed period is therefore treated as a single outbreak window rather than a recurrent diffusion process.
  • 1) Classical SIR: The SIR component serves as a conceptual diffusion baseline for comparing curve shape and saturation behaviour, without coupled disease–misinformation co-dynamics or cross-terms.Its role is comparative rather than a joint epidemiological model.
  • 1) Classical SIR: β and γ are fixed transmission and recovery rates, with R0 = β/γ quantifying expected secondary sharers generated by one active sharer in a fully susceptible population.The model maintains N = S+I+R, where γ represents the rate at which users stop sharing false claims.
  • 1) Classical SIR: When R0 > 1, classical SIR predicts saturation and near-universal exposure, motivating SIRMMM because misinformation often spreads slowly and incompletely.For FibVID, β and γ are fitted to daily misinformation incidence using solve_ivp and curve_fit.

2) Extended SIRMMM · MS · MI · 3) ELM-Integrated SIRMMM

The framework extends SIR with misinformed states to model misinformation lifecycles, then introduces time-varying transmission driven by ELM-inspired behavioural signals. This addresses the constant-rate assumption by representing sentiment, engagement, and cognition in persuasion dynamics.

  • 2) Extended SIRMMM: The extended model adds Misinformed Susceptible (MS), Misinformed Infected (MI), and Misinformed Recovered (MR) states to represent misinformation engagement.These compartments capture the full misinformation lifecycle within the SIR framework.
  • MS · MI: SIRMMM simulates real-world misinformation cascades through delayed peaks and slow declines.Its structure is intended to reflect temporal patterns in misinformation spread.
  • MS · MI: The extended structure assumes a constant misinformation transmission rate βm, limiting representation of psychological and contextual variability.The cited variability includes sentiment and engagement.
  • 3) ELM-Integrated SIRMMM: ELM-SIRMMM allows the misinformation transmission rate βm(t) to vary over time using ELM-inspired behavioural signals.This makes transmission responsive to changing behavioural inputs.
  • 3) ELM-Integrated SIRMMM: Sentiment measures emotional polarity, Engagement measures likes and retweets, and Cognition proxies content complexity.Together, these signals operationalize behavioural variation in the integrated model.
  • 3) ELM-Integrated SIRMMM: These behavioural features correspond to peripheral- and central-route persuasion dynamics in the Elaboration Likelihood Model.The mapping links observable social-media signals with distinct persuasion routes.
  • 3) ELM-Integrated SIRMMM: For model stability, the integrated formulation fixes βd = 0.3 and γd = 0.1.These fixed parameters constrain the resulting equations.

B. PARAMETERISATION & MODEL FITTING (FIBVID

The FibVID model was initialized with seeded misinformation and disease states, then fitted using static and behaviourally varying misinformation-transmission parameters. Because behavioural-input collinearity permits similar trajectories, fitted coefficients are interpreted by direction and stability rather than as unique causal effects.

  • Model initialization: Misinformation was seeded with MI0 on day 1, with MS0 = N −MI0 and MR0 = 0, while disease was seeded with I0 = 1.
  • Behavioural fitting: The time-varying transmission rate βm(t) = β0 + βszs + βeze + βczc was fitted by estimating all parameters with curve_fit.
  • Interpretation and limitation: Collinearity between behavioural inputs can produce similar trajectories, so fitted coefficients are interpreted mainly by direction and stability, not as unique or causal effects.

C. GENERALISATION TO MC–FAKE AND MONANT … A. COMPARATIVE INTERPRETATION OF SIMULATIONS

Across MC–Fake, Monant, and comparative simulations, ELM-SIRMMM’s gains depend on temporally variable behavioural signals. It improves fit and diffusion realism for dynamic contexts but offers limited benefit when signals are flat or sparse.

  • C. GENERALISATION TO MC–FAKE AND MONANT: Generalisability testing applied the same least-squares fitting to MC–Fake and Monant, deriving sentiment from polarity, engagement from platform metrics, and cognition from word count.Compartments were reinitialised using observed incidence.
  • D. DATASETS & FEATURES: Behavioural features were organised by category and applied across all three datasets to support cross-dataset model evaluation.The datasets and behavioural features are summarised in Table 2.
  • IV. RESULTS: The study evaluated classical SIR, plain SIRMMM, and ELM-integrated SIRMMM across datasets using compartment trajectories, RMSE, incidence curves, and peak-misinformation parameters.Figure 1 tracks misinformation-specific MS, MI, and MR alongside disease-related S, I, and R compartments.
  • A. COMPARATIVE INTERPRETATION OF SIMULATIONS: RMSE falls from 906 to 856, while peak MI day moves from 150 to 160 and peak misinformation intensity rises from 6% to 7% on FibVID with ELM modulation.The approximately 5.5% fit improvement accompanies a more sustained diffusion process than the plain variant.
  • A. COMPARATIVE INTERPRETATION OF SIMULATIONS: 38% peak MI at approximately day 45 is followed by 97% in the misinformation-recovered state on MC–Fake, producing a sharp flash-rumour pattern.Correction occurs after substantial early uptake.
  • A. COMPARATIVE INTERPRETATION OF SIMULATIONS: 3% peak MI around day 80, 40% in the misinformation-recovered state, and 57% remaining misinformation-susceptible indicate weak misinformation activation on Monant.The muted trajectory corresponds to comparatively flat or sparse behavioural signals over time.
  • A. COMPARATIVE INTERPRETATION OF SIMULATIONS: ELM-SIRMMM outperforms the plain variant when sentiment, engagement, or cognition fluctuate, but reverts toward classical behaviour when psychologically relevant signals are scarce.These results indicate that psychologically informed modelling requires rich and variable inputs.

B. ELM LIMITATIONS IN MONANT: STRUCTURAL · C. PERFORMANCE ANALYSIS · 1) ELM Coefficient Estimates

The ELM–SIRMMM model generalises functionally only when psychological inputs vary enough to modulate βm(t), while its evaluation combines predictive fit, trajectory diagnostics, and fitted behavioural coefficients. Monant’s low signal variance suppresses ELM effects, whereas the coefficient estimates show distinct sentiment and cognitive-load influences.

  • B. ELM LIMITATIONS IN MONANT: STRUCTURAL: Sparse engagement signals and weakly varying sentiment and length profiles in Monant constrain the dynamic range available to modulate βm(t).Monant’s web-forum signals provide limited behavioural variation over time.
  • B. ELM LIMITATIONS IN MONANT: STRUCTURAL: Limited psychological-input variance suppresses βm(t) adaptation, causing the ELM-integrated model to revert toward static, traditional SIR-like misinformation dynamics.Structural or parameter alignment alone cannot produce behavioural effects without sufficiently varying signals.
  • B. ELM LIMITATIONS IN MONANT: STRUCTURAL: FibVID’s βm(t) varies with sentiment, engagement, and cognition, whereas Monant’s remains flat because behavioural inputs are insufficiently variable.The contrasting curves indicate ELM-driven responses in FibVID but limited ELM activation in Monant.
  • B. ELM LIMITATIONS IN MONANT: STRUCTURAL: Similar β coefficients in Monant do not activate persuasion pathways when psychological features lack variance, reducing the model’s behavioural explanatory power.The resulting dynamics follow a standard epidemic curve despite architectural similarity.
  • C. PERFORMANCE ANALYSIS: Within-dataset evaluation compares RMSE with peak timing, peak magnitude, and end-state composition to assess predictive fit and epidemiological plausibility.The analysis tests whether behavioural enrichment produces materially different dynamics.
  • 1) ELM Coefficient Estimates: Table 5 reports fitted sentiment, engagement, and cognition weights for each dataset, which shape βm(t).These weights constitute the behavioural coefficient estimates used in the ELM-integrated model.
  • 1) ELM Coefficient Estimates: βsm = −14.35 (FibVID), −11.84 (MC–Fake) and −14.92 (Monant), while βcm ≈−59 to −64, making cognitive load the strongest dampening cue.The negative sentiment coefficients are associated with faster spread through peripheral-route processing, whereas increased word count reduces transmission more than other cues.

2) Coefficient sign interpretation, identifiability, and robustness

The negative engagement coefficient is a model-implied, conditional association whose interpretation is limited by omitted processes, covariate relationships, and behavioural-input identifiability. Cross-dataset directional stability supports only a bounded robustness claim, while the proposed robustness checks were not executed.

  • Coefficient sign interpretation: The engagement coefficient is negative across datasets, representing its partial effect on βm(t) conditional on sentiment, cognition, feature construction, and the time grid.Its sign may appear counterintuitive when engagement is interpreted as social proof.
  • Coefficient sign interpretation: A negative engagement sign may reflect unmodelled moderation or corrective exposure, temporal ordering, or residual variation after adjustment for correlated sentiment.Correlated covariates can cause the sign to change under adjustment.
  • Identifiability: Identifiability is limited by collinearity among sentiment, engagement, and cognition, low signal variance in Monant, and the linear additive specification of βm(t).Accordingly, coefficient signs are model-implied associations rather than causal effects.
  • Robustness: The robustness protocol proposes alternative proxy definitions and scaling, lagged engagement, and behavioural-input ablations to test coefficient and trajectory stability.The checks were not executed in the current experiments, so causal validation is not claimed.
  • Robustness: The engagement coefficient remains negative across FibVID, MC–Fake, and Monant despite dataset-specific engagement operationalisations, supporting directional stability rather than causal interpretation.Engagement was operationalised as interaction counts, retweets plus replies, and vote-based activity, respectively.

3) Comparative fit and trajectory summaries across contexts

Behavioural enrichment improves within-dataset fit on FibVID, but its benefits vary across contexts with the temporal variability of psychological inputs. The ELM-conditioned model therefore supports context-sensitive rather than universally portable misinformation trajectories.

  • FibVID: 5.5% lower RMSE (906→856), a ten-day peak delay (150→160), and a peak-prevalence increase (6%→7%) result when sentiment, engagement, and cognition are added on FibVID.MRend also rises from 56% to 60%, while the correction efficiency ratio decreases from 9.3 to 8.6 because MImax is higher.
  • MC–Fake: ≈38% peak prevalence at day ≈45 in MC–Fake reproduces a sharp rumour spike, but correction efficiency remains low at 2.6.The front-loaded exposure pattern makes corrective dynamics less effective.
  • Monant: 3% peak prevalence and MSend = 57% in Monant indicate limited behavioural benefit under flat psychological signals.The result matches the dataset’s low-variance signal limitation and flat βm(t) pattern.
  • Cross-context interpretation: Peak timing, peak magnitude, and end-state composition anchor cross-corpus comparison, showing that structural portability is insufficient without psychological variance.The same ELM specification behaves differently depending on whether psychological inputs vary meaningfully over time.

D. HYPOTHESIS TESTING

Hypothesis testing supports explicit recovery and persuasion-informed, time-varying transmission as important for reproducing FibVID’s cascade dynamics. The ELM-augmented model improves fit, peak timing, and early-surge shape when psychological signals vary over time.

  • H1 (Recovery mechanism): 44% of users remain in MSend at the FibVID end state, while MRend reaches 56%, supporting H1’s explicit recovery mechanism.The non-saturating composition is consistent with MR representing cessation from misinformation exposure.
  • H2 (Peak and decay dynamics): MImax = 6% around day 150, followed by smooth decay, reproducing FibVID’s empirical hump-shaped cascade and supporting H2.Plain SIRMMM captures both peak timing and qualitative decline behaviour.
  • H3 (ELM augmentation): 5.5% RMSE reduction (906→856), a ten-day peak delay (150→160), and peak prevalence growth (6% to 7%) support H3.These changes occur when βm(t) varies with sentiment, engagement, and cognition on FibVID.
  • Overall hypothesis assessment: Explicit recovery and persuasion-informed time-varying transmission are both necessary to reproduce key FibVID cascade properties under the stated model.The hypothesis tests connect the theoretical propositions to observed fit behaviour.
  • Model comparison: ELM-integrated transmission better captures the timing and shape of FibVID’s early misinformation surge than classical SIR and plain SIRMMM.The baseline models underestimate early sharer counts and delay the peak, whereas ELM conditioning aligns more closely with the observed incidence.

V. DISCUSSION

The ELM-SIRMMM framework improves epidemic-model explanations and predictions when behavioural cues vary substantially. Its interpretable compartments and time-varying transmission coefficients connect misinformation trajectories to observable psychological inputs and actionable interventions.

  • Discussion: Behaviourally modulated transmission enhances explanatory power only when user cues vary significantly.The framework operationalises sentiment, engagement, and cognition as time-varying influences on βm(t).
  • Discussion: 5.5% RMSE reduction (906 →856), a ten-day apex delay, and peak growth from 6% to 7% improved FibVID modelling.The gains occurred on a base of fortyfive thousand daily observations.
  • Discussion: Negative sentiment and social validation accelerate diffusion, whereas higher cognitive load suppresses the effective transmission rate.Sentiment and engagement represent peripheral-route cues, while cognition represents central-processing effort.
  • Discussion: Intervention within two days of a sentiment surge could reduce total exposure by one-third in the MC–Fake simulation.The result supports real-time throttling, factcheck prompts, and counter-rumour stress testing under varied engagement scenarios.
  • Explainability & Interpretability: Explicit SIRMMM compartments and fitted βm(t) coefficients make outcomes traceable to behavioural meanings, psychological inputs, and transition dynamics.The six compartments are S, I, R, MS, MI, and MR; local explanations relate MI(t) and βm(t) changes to sentiment, engagement, and cognition.
  • Explainability & Interpretability: Parameter sensitivity and cross-dataset trajectories show when ELM enrichment is functionally active and how coefficient directions, βm(t) profiles, MI trajectories, and end states diverge.Increasing βs steepens and advances the MI peak, whereas increasing γm reduces MR lag and lowers the residual MS reservoir.

B. LIMITATIONS · C. FUTURE DIRECTIONS · VI. CONCLUSION

The study identifies limitations in behavioural, emotional, and network modelling, while concluding that ELM–SIRMMM improves realism when psychological signals vary meaningfully over time. Future work targets richer features, dynamic networks, longer observation windows, and cross-cultural validation.

  • B. LIMITATIONS: βm(t) is linear and assumes additive effects, while implicit network topology and coarse sentiment polarity limit modelling of interaction, structure, and affect.Proposed improvements include interaction terms, agent-based or graph neural layers, and fine-grained emotions such as anger or fear.
  • C. FUTURE DIRECTIONS: Future work will add stance and credibility features, dynamic reply-graph contact networks, longer time windows, and cross-cultural datasets.These extensions are intended to examine repeated resurgence and whether central-route dominance increases in high-literacy contexts.
  • VI. CONCLUSION: ELM–SIRMMM combines interpretable epidemic compartments with time-varying sentiment, engagement, and cognitive-effort signals.It replaces a fixed misinformation transmission coefficient with a behaviourally modulated function.
  • VI. CONCLUSION: 906 to 856: ELM–SIRMMM reduced FibVID RMSE by approximately 5.5%.The model also shifted peak misinformation prevalence from day 150 to day 160.
  • VI. CONCLUSION: 56% to 60%: ELM–SIRMMM increased the final misinformation-recovered proportion on FibVID.This result accompanied the FibVID reduction in RMSE and delayed peak prevalence.
  • VI. CONCLUSION: Behavioural enrichment is most effective when psychological signals exhibit meaningful temporal variation.The explanatory value of the ELM layer depends on signal variability, quality, and temporal resolution, and fitted coefficients are conditional associations rather than causal parameters.
  • VI. CONCLUSION: ELM–SIRMMM demonstrates more realistic misinformation diffusion modelling without claiming universally superior prediction.Its framework retains explicit compartmental states and traceable transmission mechanisms while integrating persuasion-related signals.
  • VI. CONCLUSION: Future extensions should address richer affective and stance features, dynamic network structure, repeated resurgence, and cross-cultural validation.These directions aim to determine when psychologically informed transmission models generalise beyond the examined settings.
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