pith. sign in

arxiv: 2604.17368 · v1 · submitted 2026-04-19 · 📡 eess.SY · cs.SY

Stochastic Delayed Dynamics of Rumor Propagation with Awareness and Fact-Checking

Lamia Alyami , Anis Hamadouche , Amir Hussain This is my paper

Pith reviewed 2026-05-10 05:58 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords rumor propagationstochastic differential equationstime delayfact-checkingawarenessstability analysisreproduction numberinfodemic
0
0 comments X

The pith

A stochastic delayed model for rumor spread with awareness and fact-checking converges to stability when the reproduction number stays below one.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper builds a mathematical model using stochastic differential equations that include a fixed time delay to represent lags in how people process information and respond to rumors. It adds random noise terms to capture unpredictable fluctuations in social contacts and incorporates compartments for awareness, skepticism, and active fact-checking. The analysis proves that the rumor-free state is stable under a basic reproduction number threshold of less than one, with simulations showing how longer delays increase both outbreak size and outcome variability. This matters for predicting when interventions can reliably stop misinformation during events such as pandemics. The work supplies explicit conditions linking faster fact-checking and shorter response lags to reduced rumor persistence.

Core claim

The authors introduce a stochastic delayed differential model for rumor propagation that accounts for human behavioral responses, public skepticism, and fact-checking mechanisms. A discrete time delay models natural lags in information processing and institutional response, while additive stochastic perturbations represent random fluctuations in social interactions and exposure. Rigorous stability analysis establishes global asymptotic stability of the rumor-free equilibrium and derives convergence guarantees whenever the basic reproduction number is less than one. Numerical simulations quantify outbreak severity and uncertainty as functions of variable information processing delays, undersc

What carries the argument

The stochastic delayed differential equation system with awareness and fact-checking compartments, whose long-term behavior is controlled by the basic reproduction number threshold.

Load-bearing premise

The model assumes that a single discrete time delay and simple additive noise terms can capture the full range of lags and random fluctuations that occur in real human information processing and social interactions.

What would settle it

Real-world data from an infodemic in which the rumor persists and grows even after the model's reproduction number is computed below one, despite measured awareness and fact-checking rates, would contradict the stability and convergence claims.

Figures

Figures reproduced from arXiv: 2604.17368 by Amir Hussain, Anis Hamadouche, Lamia Alyami.

Figure 1
Figure 1. Figure 1: Mean spreader population I(t) (100-run Monte Carlo simulation) with 95% confidence intervals, showing a sharp outbreak peak and subsequent decay. Stochastic perturbations drive increased variability around the peak. implies that the delay does not destroy stability when the removal rates (γ + ρ) and the exposure transition rate σ dominate the effective delayed transmission intensity. Remark 1. Condition (1… view at source ↗
Figure 2
Figure 2. Figure 2: The average trajectory of all compartments shows the spreader popu [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
read the original abstract

This paper presents a stochastic delayed differential model for rumor propagation during infodemic that incorporates human behavioral response, public skepticism and fact-checking mechanisms. A discrete time delay is introduced to model natural lags in information processing and institutional response. Additionally, we adopt additive stochastic perturbations to model random fluctuations in social interaction and exposure. We present a rigorous stability analysis of the proposed rumor transmission model and derive convergence guarantees under reproduction number conditions. We also validate the model by numerical simulations and analyze the outbreak severity and quantify uncertainty under variable information processing delays. The results highlight the importance of timely awareness and fact-checking interventions for mitigating misinformation spread during pandemics

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 0 minor

Summary. The manuscript develops a stochastic delayed differential equation model for rumor propagation incorporating awareness, fact-checking, discrete time delays modeling information-processing lags, and additive stochastic perturbations for random fluctuations in social interactions. It performs stability analysis of equilibria, derives a reproduction number via the next-generation matrix on the deterministic skeleton, establishes convergence guarantees under threshold conditions on this number using standard Lyapunov–Razumikhin or Itô-formula techniques for SDDEs, and validates the results through numerical simulations that quantify outbreak severity and uncertainty under varying delays.

Significance. If the derivations hold, the work provides a useful extension of rumor models by integrating behavioral responses and stochastic effects, with potential implications for timing awareness and fact-checking interventions during infodemics. The explicit bound on noise intensity that preserves the threshold and the numerical exploration of delay effects are strengths; the approach follows established methods for SDDEs and next-generation matrices, adding to the literature on stochastic social dynamics.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive and accurate summary of our stochastic delayed model for rumor propagation, including the stability analysis, reproduction number derivation, and numerical validation of intervention timing. The recommendation for minor revision is noted. No specific major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper derives a stochastic delayed differential equation model for rumor spread incorporating awareness and fact-checking, then performs stability analysis via standard Lyapunov-Razumikhin or characteristic equation methods for SDDEs. The reproduction number is obtained from the next-generation matrix on the deterministic skeleton, a non-circular construction that does not presuppose the stability result. Stochastic terms are bounded explicitly via Itô's formula without reducing predictions to fitted inputs. No self-definitional steps, self-citation load-bearing premises, ansatz smuggling, or renaming of known results appear; the convergence guarantees are independent of the model inputs and externally falsifiable via the stated noise-intensity threshold.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard assumptions from mathematical biology applied to social phenomena, with the reproduction number serving as a key threshold parameter that may be fitted or estimated from data.

free parameters (1)
  • Reproduction number
    Conditions for convergence are based on this number, which is typically calculated from transmission and recovery rates in such models.
axioms (2)
  • domain assumption Rumor propagation can be modeled using stochastic delayed differential equations with additive noise.
    This is the foundational modeling choice for capturing delays and randomness in information spread.
  • domain assumption Awareness and fact-checking mechanisms can be incorporated as behavioral responses in the model.
    Assumed to influence the transmission dynamics.

pith-pipeline@v0.9.0 · 5401 in / 1397 out tokens · 58896 ms · 2026-05-10T05:58:40.515912+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

14 extracted references · 14 canonical work pages

  1. [1]

    Infodemic management: protecting people from harmful health information in emergencies,

    W. H. Organizationet al., “Infodemic management: protecting people from harmful health information in emergencies,” inInfodemic manage- ment: protecting people from harmful health information in emergencies, 2024

    work page 2024

  2. [2]

    Framework for managing the covid-19 infodemic: methods and results of an online, crowdsourced who technical consultation,

    V . Tangcharoensathien, N. Calleja, T. Nguyen, T. Purnat, M. D’Agostino, S. Garcia-Saiso, M. Landry, A. Rashidian, C. Hamilton, A. AbdAllah et al., “Framework for managing the covid-19 infodemic: methods and results of an online, crowdsourced who technical consultation,”Journal of medical Internet research, vol. 22, no. 6, p. e19659, 2020

    work page 2020

  3. [3]

    Tomes and M

    N. Tomes and M. S. Parry,What are the historical roots of the COVID-19 infodemic? Lessons from the past. World Health Organization. Regional Office for Europe, 2022

    work page 2022

  4. [4]

    A deadly infodemic: social media and the power of covid-19 misinformation,

    M. A. Gisondi, R. Barber, J. S. Faust, A. Raja, M. C. Strehlow, L. M. Westafer, and M. Gottlieb, “A deadly infodemic: social media and the power of covid-19 misinformation,” p. e35552, 2022

    work page 2022

  5. [5]

    In- fodemics and health misinformation: a systematic review of reviews,

    I. J. B. Do Nascimento, A. B. Pizarro, J. M. Almeida, N. Azzopardi- Muscat, M. A. Gonc ¸alves, M. Bj ¨orklund, and D. Novillo-Ortiz, “In- fodemics and health misinformation: a systematic review of reviews,” Bulletin of the World Health Organization, vol. 100, no. 9, p. 544, 2022

    work page 2022

  6. [6]

    The impact of misinformation on the covid-19 pandemic,

    M. M. F. Caceres, J. P. Sosa, J. A. Lawrence, C. Sestacovschi, A. Tidd- Johnson, M. H. U. Rasool, V . K. Gadamidi, S. Ozair, K. Pandav, C. Cuevas-Louet al., “The impact of misinformation on the covid-19 pandemic,”AIMS public health, vol. 9, no. 2, p. 262, 2022

    work page 2022

  7. [7]

    Beyond misinformation: devel- oping a public health prevention framework for managing information ecosystems,

    A. Ishizumi, J. Kolis, N. Abad, D. Prybylski, K. A. Brookmeyer, C. V oegeli, C. Wardle, and H. Chiou, “Beyond misinformation: devel- oping a public health prevention framework for managing information ecosystems,”The Lancet Public Health, vol. 9, no. 6, pp. e397–e406, 2024

    work page 2024

  8. [8]

    Epidemic modeling for mis- information spread in digital networks through a social intelligence approach,

    S. Govindankutty and S. P. Gopalan, “Epidemic modeling for mis- information spread in digital networks through a social intelligence approach,”Scientific Reports, vol. 14, no. 1, p. 19100, 2024

    work page 2024

  9. [9]

    Epidemics and rumours,

    D. J. Daley and D. G. Kendall, “Epidemics and rumours,”Nature, vol. 204, no. 4963, pp. 1118–1118, 1964

    work page 1964

  10. [10]

    Stochastic rumours,

    ——, “Stochastic rumours,”Journal of the Institute of Mathematics and Its Applications, vol. 1, no. 1, pp. 42–55, 1965

    work page 1965

  11. [11]

    An uncertain sir rumor spreading model,

    H. Sun, Y . Sheng, and Q. Cui, “An uncertain sir rumor spreading model,” Advances in Difference Equations, vol. 2021, no. 1, p. 286, 2021

    work page 2021

  12. [12]

    Social media rumor refutation effectiveness: Evaluation, modelling and enhancement,

    Z. Li, Q. Zhang, X. Du, Y . Ma, and S. Wang, “Social media rumor refutation effectiveness: Evaluation, modelling and enhancement,”In- formation Processing & Management, vol. 58, no. 1, p. 102420, 2021

    work page 2021

  13. [13]

    Detecting health misinformation in online health communities: Incorporating behavioral features into machine learning based approaches,

    Y . Zhao, J. Da, and J. Yan, “Detecting health misinformation in online health communities: Incorporating behavioral features into machine learning based approaches,”Information Processing & Management, vol. 58, no. 1, p. 102390, 2021

    work page 2021

  14. [14]

    A scoping review of digital health interventions for combating covid-19 misinformation and disinformation,

    K. Czerniak, R. Pillai, A. Parmar, K. Ramnath, J. Krocker, and S. My- neni, “A scoping review of digital health interventions for combating covid-19 misinformation and disinformation,”Journal of the American Medical Informatics Association, vol. 30, no. 4, pp. 752–760, 2023

    work page 2023