Modeling Dynamic Social Distancing in 3D

A Behavioral Extension of the Kermack–McKendrick SIR Model

By Aaron Loh | Top 300 Thermo Fisher Scientific Junior Innovator | 2nd Place, Florida State Science and Engineering Fair (SSEF)

Overview

The COVID-19 pandemic revealed how public behavior and government policy interact in complex ways during disease outbreaks. To explore this relationship, I developed a 3D agent-based simulation in Unity (C#) based on the classic Kermack–McKendrick SIR (Susceptible–Infected–Recovered) model.

Unlike traditional models, my version introduces two new behavioral parameters:

λ₁ (Fatigue Rate): how quickly people tire of following distancing guidelines.
λ₂ (Reaction Velocity): how fast governments respond to rising infections.

By combining mathematical modeling, computer simulation, and statistical analysis, my goal was to visualize how real-time behavior changes affect epidemic curves — offering insights that could help policymakers craft more effective responses in future public-health crises.

Research Question

How do public fatigue (λ₁) and government reaction velocity (λ₂) influence infection peaks and timing in epidemic dynamics?

Methodology

Platform: Unity Engine with C# scripting
Mathematics: Differential equations solved via the fourth-order Runge–Kutta method
Data Collection: CSV logging of susceptible, infected, and recovered populations over time
Analysis Tools: MATLAB for two-way ANOVA and polynomial regression
Controlled Variables: infection rate, recovery rate, simulation length, and population size

Each simulation tracked thousands of autonomous agents interacting in 3D space. The model dynamically adjusted each individual’s preferred distance based on infection prevalence, fatigue rate, and government reaction speed.

Results & Insights

Increasing λ₂ (faster response) reduced infection peaks and accelerated recovery.
Increasing λ₁ (faster fatigue) raised peaks and caused delayed secondary waves.
Statistical analysis confirmed λ₂ had a stronger effect on infection size than λ₁.
At extreme values, both parameters showed diminishing returns—suggesting that balanced, sustainable policy is more effective than reaction speed alone.

These findings emphasize the importance of maintaining public trust and consistent communication during health crises.

Impact

Awards:
• Top 300 Thermo Fisher Scientific Junior Innovators Challenge (Society for Science)
• 2nd Place – State Science and Engineering Fair of Florida (SSEF)
Mentorship: Guided by faculty from Florida Atlantic University and mentors from A.D. Henderson University School.
Applications: The model framework can extend to topics such as AI policy, social behavior modeling, and system resilience under stress.

Technologies Used

Future Directions

Next, I plan to expand this model using machine learning to automatically tune λ₁ and λ₂ based on real epidemiological data. This would create adaptive simulations capable of predicting optimal intervention timing in both disease and policy modeling contexts.

Learn More

Watch the demonstration on my YouTube Channel → 🎥