Resolving the impact of waiting time distributions on the persistence of measles

Area of Science:

• Epidemiology
• Population Biology
• Mathematical Modeling

Background:

• Measles exhibits a well-defined stochastic persistence threshold, with a critical community size (CCS) around 250,000-500,000.
• Factors like immunity, susceptible recruitment, seasonality, age, and spatial coupling influence measles persistence.
• Previous models struggled to agree on CCS prediction and the mechanisms driving measles persistence.

Purpose of the Study:

• To investigate whether simple models can accurately predict the critical community size (CCS) for measles persistence.
• To determine which mechanisms are most crucial for measles persistence across various population sizes.
• To assess the impact of different waiting time distributions (WTDs) on measles persistence models.

Main Methods:

• Introduced two novel statistical measures for assessing persistence: fade-outs post-epidemic and fade-outs post-invasion.
• Compared persistence patterns between models with varying WTDs using different statistical criteria.
• Utilized appropriately parameterized measles models to analyze CCS predictions.

Main Results:

• The relative patterns of measles persistence across models are highly sensitive to the chosen statistical measure of persistence.
• Contrary to prior research, this study demonstrates that model predictions for CCS are consistent regardless of the persistence measure used.
• Appropriately parameterized models yield similar CCS predictions irrespective of WTD variations.

Conclusions:

• The critical community size for measles persistence is robust across different statistical measures and waiting time distributions.
• Simple, well-parameterized models can effectively predict the CCS for measles.
• Understanding the interplay of epidemiological factors and stochastic dynamics is key to predicting infectious disease persistence.