Emotional contagion on social media and the simulation of intervention strategies after a disaster event: a modeling study

The study addresses how emotions spread on social media following natural disasters, focusing on the 8-13 flash flood in Pengzhou (Longcaogou Scenic Area), Sichuan, China. In a context of high internet penetration and active social platforms such as Sina Weibo, disaster-related discourse can trigger strong public emotions that influence behavior and may escalate into cyber violence. The purpose is to characterize the temporal trends of public emotions (positive, neutral, negative) in posts and comments, to model the mechanism by which emotions spread from posts to comments, and to evaluate intervention strategies to guide public opinion. The importance lies in mitigating negative psychological impacts and supporting disaster governance through data-informed public sentiment management.

Theoretical and empirical background spans several themes: (1) Temporal emotional orientations after disasters: Emotions fluctuate with disaster phases, often peaking in negativity during acute phases and moderating as response progresses; Chinese Weibo studies show initial neutrality followed by negative expressions and later emergence of positive sentiments (e.g., prayers, gratitude). (2) Social influence and emotion spread mechanisms: Emotional contagion arises via imitation-feedback and category activation; on social media, users perceive emotional content, process it, and express potentially mutated emotions; posters' emotions influence comment volume and tone. (3) Modeling approaches: Data-driven (time series, ML) and mechanism-driven (transmission dynamics, agent-based) models have been used. Infectious-disease-inspired models (SIR, SIRS, E-SIR/E-SFI/MNE-SFI, SOSa-SPSa) capture generation, variation, and evolution of emotions but often rely heavily on curve-fitting and lack real-world parameter extraction, sensitivity/stability testing, or intervention simulation. (4) Mechanism-driven advances: Refining by emotional valence and users’ choices improves realism; however, parameter estimation uncertainty remains a challenge. (5) Chinese context: Sina Weibo serves as a major channel for sentiment diffusion; models incorporating spreading probability, emotion mutation, and transforming weights have shown improved performance with Weibo data. (6) Flood-focused analyses: Prior studies examined spatiotemporal sentiment distributions and factors affecting message virality during floods, but few simulated emotion evolution via mechanism-based models or tested interventions. This study contributes by estimating key parameters directly from data (proportions of comment emotions attributable to post emotions and post-to-comment time intervals) and by simulating interventions relevant to governance.

Study design: Five steps—(1) data collection and sentiment labeling; (2) conceptualization of emotion spread from posters to commenters; (3) development of a mechanism-driven PSCR (post–susceptible–comment–removed) dynamic model; (4) parameter estimation via firsthand data analysis, curve-fitting, and assumptions; (5) transmission quantification and intervention simulation. Event and data: Case topic #Pengzhou flash floods# on Sina Weibo, covering August 13–20, 2021 (Pengzhou/Longcaogou flash flood). Data fields included usernames/IDs, timestamps, and text for original posts and first-level comments. After cleaning (removing stop words, typos, garbled/special characters, duplicates), the final dataset comprised 556 posts and 12,447 first-level comments. Text processing and keyword extraction used GooSeeker; sentiment analysis categorized items as negative (-1), neutral (0), or positive (1). Model (PSCR): Population N represents Weibo users potentially involved. Compartments: S (susceptible, no emotion), C_i (commenters expressing emotion i ∈ {-1,0,1}), R_i (removed from emotion i), and P_j (posters with emotion j ∈ {-1,0,1}). Susceptible users exposed to posts may comment and transition to C_i at a transmission rate b, with force of infection λ_i driven by time-varying post waves P_j convolved with a kernel k to reflect decaying influence of posts. Two empirically derived modifiers govern risk from P_j to C_i: q_ij (proportion of comments of type i attributable to posts of type j) and σ_ij (time elapsed from a post of type j to a comment of type i). Commenters remain in C_i for an average duration 1/γ_i before moving to R_i. The model equations define dynamics for S, C_i, and R_i with convolution to capture temporal decay of post influence. Parameter estimation: Key parameters obtained from data: (a) q_ij via bootstrap—1,000 iterations each sampling 400 of 556 posts; for each, compute proportions of comment emotions under posts by emotion, yielding 25th/50th/75th percentiles. Median proportions: neutral comments under negative/neutral/positive posts 0.44 [0.34–0.56], 0.49 [0.39–0.58], 0.57 [0.26–0.70]; negative comments 0.39 [0.25–0.49], 0.32 [0.21–0.39], 0.22 [0.09–0.38]; positive comments 0.17 [0.11–0.24], 0.20 [0.13–0.25], 0.22 [0.08–0.39]. (b) σ_ij (post-to-comment time in hours) computed as time differences; negative posts had longer medians to comment emotions (e.g., to negative: 8.24 [3.13–17.23]; to neutral: 7.35 [2.38–16.68]; to positive: 7.04 [2.53–15.95]); σ_ij fit exponential distributions. Assumptions: N=200,000 (susceptible population). Parameters estimated by curve-fitting due to lack of direct observability: transmission rate b, removal rates γ_i, and initial C_i(0). Model implemented in Anylogic 8.7.0; goodness-of-fit assessed by RMSE. Transmission quantification: Defined Secondary Attack Rate (SAR_ij) for transmission from post emotion j to comment emotion i as SAR_ij = b_ij × q_ij / γ_i (operationalized in study as b/γ scaled by q_ij), enabling comparison of transmissibility across routes. Intervention simulations: Three scenarios evaluated via cumulative numbers of negative, neutral, and positive comments, using a scale factor x to modify targeted components: (I) interrupting individual transmission routes from posts to comments; (II) altering counts of negative or positive posts separately; (III) simultaneously changing both negative and positive post counts. Sensitivity analysis varied N from 20,000 to 240,000 to assess robustness.

- Temporal trends: Overall poster sentiment was negative with three peaks. Comment sentiment was mostly neutral (5,786), followed by negative (4,063), with three corresponding peaks (~6 h with 2,752 comments; ~24 h with 5,802; ~24 h with 2,892). Negative posts triggered more intense discussions than neutral or positive posts. - Data-derived parameters: Median q_ij showed that neutral comments dominated under all post types (negative 0.44, neutral 0.49, positive 0.57). Negative comments were most prevalent under negative posts (0.39), then neutral (0.32), and least under positive (0.22). Positive comments were lowest overall (0.17–0.22 across post types). Post-to-comment median intervals from negative posts were longer (e.g., to negative comments 8.24 h; to neutral 7.35 h; to positive 7.04 h) than from neutral/positive posts; σ_ij fit exponential distributions. - Model validity: PSCR reproduced real-time comment curves for all three emotions with RMSE < 51. - Transmissibility (SAR): Neutral posts exhibited the highest transmissibility to comments across emotions (examples: SAR0→-1 ≈ 12.17; SAR0→0 ≈ 18.86; SAR0→1 ≈ 7.46), exceeding negative-post-driven routes (≈ 4.77, 6.03, 2.43) and positive-post-driven routes (≈ 1.39, 5.85, 1.79). Abundant negative comments were driven primarily by neutral and negative posts. - Intervention I (route interruption): Fully interrupting negative-post routes reduced negative comments by 30.04% (vs. interrupting positive-post routes: 15.42%). Neutral comments were most reduced by interrupting neutral-post routes (39.37%) versus negative (25.67%) or positive (15.72%) routes. Positive comments fell by 18.87% when interrupting positive-post routes and by 14.53% when interrupting negative-post routes. Primary sources for each emotional comment type are posts with the same emotion. - Intervention II (change post counts separately): Reducing negative posts from 100% to 50% lowered negative comments by 14.97% and positive comments by 7.17%. Increasing positive posts from 100% to 150% increased positive comments by 9.40% and negative comments by 7.64%. - Intervention III (change both): To reduce negative comments, decreasing negative posts has a larger effect than decreasing positive posts (e.g., a 20% reduction in negative posts ≈ a 40% reduction in positive posts). To increase positive comments, adjusting positive posts has a larger effect (e.g., +27% positive posts ≈ −21% negative posts). Simultaneously increasing positive posts and reducing negative posts decreased the negative-to-positive comment ratio. - Sensitivity: Varying N from 20,000 to 240,000 did not materially alter emotional curves, supporting robustness of N=200,000 assumption.

The findings address the research questions by showing (RQ1) distinct temporal patterns of emotion after the flood with mostly neutral comments but a strong presence and persistence of negative affect, and three synchronized peaks for posts and comments. (RQ2) The PSCR model explains how emotions propagate from posts to comments with explicit routes and timing, revealing higher transmissibility from neutral posts and demonstrating that negative comments are primarily fueled by neutral and negative post streams; negative posts exhibit longer post-to-comment delays and greater persistence/contagiousness than positive posts. The SAR metric provides a practical, comparable measure of route-specific transmissibility for emotion spread. (RQ3) Intervention simulations indicate that curbing negative posts most effectively reduces negative comments, while boosting positive posts increases positive comments but may also slightly raise negative comments. Combining reductions in negative posts with increases in positive posts optimally lowers the negative-to-positive ratio. These results underscore the role of original posters’ emotional choices in shaping downstream public sentiment and offer actionable levers for social media managers and emergency authorities to guide public opinion, while highlighting the need to balance moderation with freedom of expression and transparency in the public sphere.

The study characterizes post-disaster emotional dynamics on Weibo and introduces a mechanism-driven PSCR model that captures transmission from posts to comments using empirically estimated proportions of emotion-specific infection (q_ij) and post-to-comment intervals (σ_ij), with decaying post influence via convolution. Negative emotions were more persistent and contagious than positive ones. Reducing negative posts decreases overall and negative comments; increasing positive posts raises positive comments. Coordinated adjustments to reduce negative posts and increase positive posts can control harmful emotional spread and foster a healthier online environment. The PSCR framework and the SAR metric fill a methodological gap and can support the design of effective, real-time communication strategies after disasters and similar high-salience events.

- Emotion granularity: Emotions were grouped into three categories; finer granularity could improve precision but would substantially increase model complexity and parameterization demands. - Homogeneous exposure assumption: The model assumes equal likelihood of reading posts across susceptible users, omitting individual-level heterogeneity (e.g., age, routines). - Single-event dataset: Findings are based on the 8-13 Pengzhou flood; generalizability to other contexts may be limited, though the event shares features common to public emergencies. - Parameter estimation: Several parameters (e.g., b, γ_i, initial C_i) were obtained via curve-fitting, potentially yielding non-unique solutions; future surveys could reduce uncertainty. - Scope of interactions: Analysis focused on post-to-first-level comment transmission, excluding contagion among commenters (comment-to-comment cascades). - Network structure: The model does not account for follower networks or user influence (e.g., fan counts), which can affect normative pressure and contagion strength.