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Tracking mob Dynamics in online social networks Using epidemiology model based on Mobility Equations

Jumana H. S. Alkhalissi, Ahmed Al-Taweel

TL;DR

The paper tackles mob dynamics in online social networks by embedding mobility into an epidemiological framework (the SQCIR model) and calibrating it to Twitter data related to COVID-19 from April to June 2020. It derives a basic reproduction number $R_0=\frac{\Lambda \epsilon}{\Phi(\Phi+v)}$ and analyzes the stability of the mob-free equilibrium, proving a transcritical bifurcation at $R_0=1$ with an endemic state $E^{\star}$ arising for $R_0>1$. Numerical simulations using real Twitter data validate the model and reveal that mob-related mobility increases peak infections and total spread, while sensitivity analyses highlight parameters $\Lambda$ and $\epsilon$ as key drivers of transmission. The work provides a quantitative tool to understand and potentially mitigate misinformation spread and mob-like dynamics on social platforms, with implications for interventions targeting skeptical users and mobility-driven contact rates. Future work includes incorporating additional data sources, extending controls, and accounting for neutral sentiments to better capture online contagion dynamics.

Abstract

Nowadays, social media is the main tool in our new lives. The outbreak news and all related obtained from social media, and mob events affect the of spread these news fast. Recently, epidemiological models to study disease spread and analyze the behavior of mob groups by dealing with "contagions" that propagate through user networks. In this research, we introduced a mathematical model to analyze social behavior related to COVID-19 spread by examining Twitter activity from April 2020 to June 2020. The main feature of this model is the integration of mobility dynamics that be derived from the above real data, to adjust the rate of outbreak based on the response of social interactions. Consider mobility as a parameter of time-varying, and fluctuations in the rate of contact that is driven by factors like personal behavior or external affecting such as "lockdown" and "quarantine" etc., to track public sentiment and engagement trends during the pandemic. The threshold number is derived, and the existence of bifurcation and the stability of the steady states are established. Numerical simulations and sensitivity analysis of relevant parameters are also carried out.

Tracking mob Dynamics in online social networks Using epidemiology model based on Mobility Equations

TL;DR

The paper tackles mob dynamics in online social networks by embedding mobility into an epidemiological framework (the SQCIR model) and calibrating it to Twitter data related to COVID-19 from April to June 2020. It derives a basic reproduction number and analyzes the stability of the mob-free equilibrium, proving a transcritical bifurcation at with an endemic state arising for . Numerical simulations using real Twitter data validate the model and reveal that mob-related mobility increases peak infections and total spread, while sensitivity analyses highlight parameters and as key drivers of transmission. The work provides a quantitative tool to understand and potentially mitigate misinformation spread and mob-like dynamics on social platforms, with implications for interventions targeting skeptical users and mobility-driven contact rates. Future work includes incorporating additional data sources, extending controls, and accounting for neutral sentiments to better capture online contagion dynamics.

Abstract

Nowadays, social media is the main tool in our new lives. The outbreak news and all related obtained from social media, and mob events affect the of spread these news fast. Recently, epidemiological models to study disease spread and analyze the behavior of mob groups by dealing with "contagions" that propagate through user networks. In this research, we introduced a mathematical model to analyze social behavior related to COVID-19 spread by examining Twitter activity from April 2020 to June 2020. The main feature of this model is the integration of mobility dynamics that be derived from the above real data, to adjust the rate of outbreak based on the response of social interactions. Consider mobility as a parameter of time-varying, and fluctuations in the rate of contact that is driven by factors like personal behavior or external affecting such as "lockdown" and "quarantine" etc., to track public sentiment and engagement trends during the pandemic. The threshold number is derived, and the existence of bifurcation and the stability of the steady states are established. Numerical simulations and sensitivity analysis of relevant parameters are also carried out.

Paper Structure

This paper contains 15 sections, 2 theorems, 34 equations, 7 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Data Collection
  4. The SQCIR Mob propagation model
  5. Model analysis
  6. Equilibrium points
  7. Basic reproduction number $\Re_{0}$
  8. Local Stability Analysis of Mob Free Equilibrium
  9. Existence of Endemic Equilibrium State
  10. Bifurcation of endemic equilibrium point
  11. Sensitivity analysis
  12. Numerical simulations and discussions
  13. Analyzing the Reproduction Number $\Re_0$
  14. Simulation of The SQCIR Model
  15. Conclusions

Key Result

Theorem 3.1

The MFE point is locally asymptotically stable if $\Re_{0}<1$ and unstable otherwise.

Figures (7)

  • Figure 2.1: SQCIR compartment model of mob propagation.
  • Figure 3.1: The figure shows the sensitivity indices of $\Re_0$ for the dependent parameters of the COVID19 model \ref{['eq1']}.
  • Figure 3.2: Best fit modeling for mob Dynamics in social media networks. The figure shows the estimated infected case data fitting with the real infected case data of the SQCIR model \ref{['eq111']}.
  • Figure 4.1: Dynamics of $\Re_0$ on different parameters.
  • Figure 4.2: Simulation of the proposed model \ref{['eq111']} with mobility and disease dynamics over the time.
  • ...and 2 more figures

Theorems & Definitions (3)

  • Remark 1
  • Theorem 3.1
  • Theorem 3.2