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<p>Understanding how narratives spread across social media platforms requires a framework that captures both the stochastic generation of posts and the gradual evolution of user engagement. This study proposes a cross-platform diffusion model that integrates a marked multivariate Hawkes process with a bounded exposure–adoption ordinary differential equation (ODE). The Hawkes component models event arrivals and cross-platform excitation, while the ODE captures how exposure translates into active engagement over time. Applied to the 2025 U.S. tariff-war discourse spanning 30,493 Instagram, 11,218 TikTok, 12,252 X, and 30,493 YouTube posts collected between January and May 2025, the model reveals interpretable and stable cross-platform influence dynamics. The estimated branching matrix (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\rho (B) = 0.523\)</EquationSource> </InlineEquation>) lies well below the critical threshold (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\rho (B) = 1\)</EquationSource> </InlineEquation>), indicating a stable, self-damped diffusion regime in which cross-platform cascades persist but do not explode, with dominant pathways from short-form and real-time platforms toward long-form commentary channels. The exposure–adoption ODE was validated through a forward-prediction experiment, training on a percentage of each trajectory and evaluating on the future, demonstrating accurate extrapolation of engagement trends and confirming the model’s predictive coherence. Together, these results demonstrate that the proposed framework provides a mathematically grounded and interpretable lens for analyzing how narratives emerge, propagate, and stabilize across interconnected media ecosystems.</p>

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Modeling cross-platform narrative diffusion: a stable Hawkes–ODE framework for exposure and adoption dynamics

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月6日

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  • Ridwan Amure,
  • Nitin Agarwal

摘要

Understanding how narratives spread across social media platforms requires a framework that captures both the stochastic generation of posts and the gradual evolution of user engagement. This study proposes a cross-platform diffusion model that integrates a marked multivariate Hawkes process with a bounded exposure–adoption ordinary differential equation (ODE). The Hawkes component models event arrivals and cross-platform excitation, while the ODE captures how exposure translates into active engagement over time. Applied to the 2025 U.S. tariff-war discourse spanning 30,493 Instagram, 11,218 TikTok, 12,252 X, and 30,493 YouTube posts collected between January and May 2025, the model reveals interpretable and stable cross-platform influence dynamics. The estimated branching matrix ( \(\rho (B) = 0.523\) ) lies well below the critical threshold ( \(\rho (B) = 1\) ), indicating a stable, self-damped diffusion regime in which cross-platform cascades persist but do not explode, with dominant pathways from short-form and real-time platforms toward long-form commentary channels. The exposure–adoption ODE was validated through a forward-prediction experiment, training on a percentage of each trajectory and evaluating on the future, demonstrating accurate extrapolation of engagement trends and confirming the model’s predictive coherence. Together, these results demonstrate that the proposed framework provides a mathematically grounded and interpretable lens for analyzing how narratives emerge, propagate, and stabilize across interconnected media ecosystems.