The R = 1 threshold can misclassify epidemic stability

Area of Science:

• Epidemiology
• Mathematical Biology
• Public Health

Background:

• The effective reproduction number (R) is a key statistic for tracking infectious disease spread and guiding public health policy.
• An R value of 1 is traditionally interpreted as a critical threshold, separating epidemic growth (R > 1) from disease control (R < 1).

Purpose of the Study:

• To identify limitations in the interpretation of R=1 as a universal stability threshold in infectious disease dynamics.
• To introduce and validate a new statistic, E, as a more robust and practical real-time threshold for disease control and policy.

Main Methods:

• Analysis of the limitations of R, particularly when averaging over heterogeneous populations.
• Evaluation of an alternative transmissibility definition using next-generation matrices and its shortcomings.
• Adaptation and application of a novel statistic, E, derived from R using experimental design theory.

Main Results:

• The traditional R=1 threshold frequently fails, masking early warning signs of resurgence and misclassifying complex dynamics.
• Alternative methods, such as those using next-generation matrices, can overcorrect, leading to false negative stability signals.
• The statistic E effectively constrains stability scenarios, remains robust to noise, and establishes E=1 as a superior real-time threshold.

Conclusions:

• R=1 is an unreliable indicator of disease stability due to population heterogeneity.
• The novel statistic E offers a more precise and reliable real-time threshold for assessing and managing infectious disease outbreaks.
• Implementing E=1 as a stability threshold can improve the predictive value and effectiveness of public health policies.