Calculation of epidemic arrival time distributions using branching processes.

Area of Science:

• Epidemiology
• Network Science
• Mathematical Biology

Background:

• Global air travel networks have reshaped disease spread dynamics.
• Predicting pathogen arrival times is crucial for public health preparedness.
• Existing models may overestimate their predictive accuracy.

Purpose of the Study:

• To derive the probability distribution of epidemic arrival times using a branching process model.
• To validate the model's robustness against parameter variations and errors.
• To compare the predictive power of branching process models with real-world data.

Main Methods:

• Modeling early epidemic spread as a simple branching process.
• Deriving the full probability distribution of pathogen arrival times.
• Comparing model predictions with empirical data and established "effective distance" metrics.

Main Results:

• The branching process model successfully rederived known arrival time results.
• The approach demonstrated robustness to parameter values outside traditional ranges.
• Real-world data analysis revealed significantly lower predictive power than previously reported for similar methods.

Conclusions:

• Branching process models offer a theoretical basis for "effective distance" in disease spread.
• Current models, including this one, may not accurately predict epidemic arrival times in practice.
• Further research is needed to improve the accuracy of epidemic spread prediction models.