Modeling Misinformation Spread on Twitter/X

ISEF Category: Mathematics

Subcategory: Other  ·  Difficulty: Advanced  ·  Setup: Home Setup  ·  Time: Full Year

The Hook

A rumor can travel faster than the truth, and social media gives it a rocket boost. On Twitter/X, one post can jump from a tiny group to a huge crowd in hours. If you like math, you can model that spread the way people model disease. The cool part is that you can test whether confirmation bias changes the outcome.

What Is It?

This project treats misinformation like something that spreads through a network. In a basic SIR model, people move from Susceptible to Infected to Recovered. Here, the words mean something social instead of medical. Susceptible means a person has not seen the rumor or has not decided what to think. Infected means they accept or share it. Recovered means they stop sharing it, or they correct their belief.

The fractional-order part adds memory. In plain language, the model remembers past behavior, not just the current moment. That matters because people do not react like particles. They may keep trusting a source, keep doubting a correction, or keep sharing something they saw earlier. Confirmation bias coupling adds another layer. It means people are more likely to accept rumors that match what they already believe. You can think of it like a filter that lets some claims in more easily than others.

Bifurcation analysis asks when the system changes behavior. A small change in one parameter can move the model from slow spread to rapid spread, or from a rumor that fades out to one that keeps circulating. That gives you a clean math question with real-world meaning.

Why This Is a Good Topic

This is a strong science fair topic because the core question is mathematical, testable, and tied to a real social problem. You can use public datasets, build a model, fit parameters, and compare versions of the model with and without memory or confirmation bias. You do not need a wet lab, but you do need careful thinking, clean code, and honest statistics. That makes it a good fit for a student who wants a serious research-style project.

Research Questions

• How does adding a fractional-order term change the fit to public election-rumor diffusion data?
• What is the effect of confirmation-bias coupling on the predicted peak size of misinformation spread?
• Does a model with memory predict a longer rumor tail than a standard SIR model?
• To what extent does the best-fit fractional order vary across different public rumor datasets?
• Which parameter changes create a tipping point from rumor fade-out to sustained spread?
• How does the model error compare when you fit early-stage data versus full-curve data?

Basic Materials

• Laptop or desktop computer with Python installed.
• Spreadsheet software for organizing dataset columns.
• Public rumor diffusion dataset from a government, university, or peer-reviewed source.
• Text editor or notebook for tracking model assumptions.
• Graphing tool such as Python Matplotlib or Desmos for visualizing curves.
• Basic calculator for quick parameter checks.

Advanced Materials

• Laptop or desktop computer with Python and scientific libraries.
• Public election-rumor diffusion dataset with timestamps and engagement counts.
• Symbolic or numerical math software for fractional differential equations.
• Version control tool such as Git for tracking model changes.
• Statistical package for parameter fitting and uncertainty estimates.
• Access to peer-reviewed papers on fractional epidemic models and opinion dynamics.

Software & Tools

• Python: Runs your simulations, parameter fitting, and plots for the model.
• Jupyter Notebook: Keeps code, notes, and figures together in one place.
• NumPy: Handles arrays and numerical calculations.
• SciPy: Supports optimization, curve fitting, and differential equation tools.
• Matplotlib: Makes publication-style graphs for model comparison.

Experiment Steps

1. Define the exact rumor dataset you will study and decide what counts as spread, recovery, and exposure.
2. Choose the baseline SIR structure, then decide where fractional memory and confirmation bias will enter the equations.
3. Plan the parameters you will estimate from data and the parameters you will hold fixed.
4. Build a comparison set of models, including a standard SIR version and your fractional version.
5. Set up a fitting plan that tests how well each model matches the full curve and the early growth phase.
6. Design a bifurcation study that changes one key parameter at a time and tracks when the model behavior shifts.

Common Pitfalls

• Using a dataset with unclear timestamps, which makes it impossible to compare model output to real spread speed.
• Treating retweets, likes, and replies as the same signal, which blurs the meaning of infection in the model.
• Fitting too many free parameters at once, which makes several different models look equally good.
• Ignoring the difference between early growth and late decay, which hides whether memory actually improves the fit.
• Skipping sensitivity checks, which leaves you unable to tell whether the tipping point is real or just a tuning artifact.

What Makes This Competitive

A stronger project does more than fit one curve. It compares several model structures, reports uncertainty, and explains why one version works better than another. You can stand out by testing a real bifurcation point, not just drawing a smooth line through data. Careful validation on separate datasets, plus a clear interpretation of confirmation bias, will push the work past a class project.

Project Variations

• Use health misinformation datasets instead of election rumors to see whether the same model structure still fits.
• Compare Twitter/X diffusion with Reddit or Facebook post cascades to test whether platform structure changes the fractional order.
• Replace confirmation-bias coupling with a trust or source-credibility term and compare which model explains the data better.

Learn More

• PubMed: Search for review articles on misinformation diffusion, opinion dynamics, and social contagion models.
• Google Scholar: Find recent peer-reviewed papers on fractional-order SIR models and rumor spread.
• NIH PubMed Central: Read full-text articles on network models and behavioral spread when available.
• MIT OpenCourseWare: Use mathematics and differential equations course materials for modeling ideas and notation.
• NOAA Data and Tools: Practice cleaning and plotting real public datasets before you work with social media data.
• arXiv: Search for preprints on fractional differential equations and social network diffusion models.