Disentangling reporting and disease transmission.

Area of Science:

• Epidemiology
• Mathematical Biology
• Statistical Modeling

Background:

• Second-order statistics can indicate system stability and predict critical transitions.
• Early warning indicators are crucial for infectious disease surveillance and epidemic threshold detection.
• Previous work lacked analytical treatment of imperfect observation effects on these indicators.

Purpose of the Study:

• To develop and analyze early warning indicators for infectious disease emergence.
• To analytically treat the impact of imperfect observation (reporting probability) on indicator behavior.
• To identify indicators insensitive to reporting probability for distinguishing transmission vs. reporting trends.

Main Methods:

• Calculating expected values for moments of reported cases using binomial/negative binomial distributions.
• Modeling reported cases based on a birth-death-immigration process with deaths.
• Employing simulation studies to validate indicator performance and assess variance reduction strategies.

Main Results:

• The normalized second factorial moment and decay time are identified as reporting probability-insensitive indicators.
• Simulation demonstrated the ability to differentiate increased transmission from increased reporting using these indicators.
• High variance in estimates was observed, but ensemble averaging across multiple time series can reduce this variance.

Conclusions:

• Reporting probability-insensitive indicators offer a robust tool for infectious disease surveillance.
• These indicators can help distinguish genuine changes in disease transmission from changes in reporting practices.
• Ensemble averaging is a viable strategy to improve the reliability of these early warning signals.