Understanding the persistence of measles: reconciling theory, simulation and observation

Area of Science:

• Epidemiology
• Mathematical Biology
• Infectious Disease Modeling

Background:

• Localized extinction patterns in measles, first observed in 1957, have spurred the development of numerous mathematical models.
• Recent models using constant infectious and incubation periods suggest realistic persistence levels, contrasting with established mathematical theory.

Purpose of the Study:

• To reconcile the apparent discrepancy between recent modeling approaches and established mathematical theory regarding measles persistence.
• To compare the persistence of stochastic measles models under different parameterizations and theoretical frameworks.

Main Methods:

• Utilizing a deterministic approach to parameterize various models, fitting them to the observed biennial attractor of measles.
• Determining seasonality levels based on model selection and comparing the persistence of stochastic model versions using best-fit parameters.
• Analyzing the differences between observed disease fade-out patterns and the theoretical 'first passage time' concept.

Main Results:

• Reconciliation of differences between constant and exponential period models in reproducing measles extinction patterns.
• Seasonality levels are directly influenced by the choice of mathematical model used.
• Stochastic model persistence varies significantly based on parameterization and theoretical assumptions.

Conclusions:

• The choice of model structure significantly impacts the representation of measles dynamics and persistence.
• Understanding the nuances between deterministic and stochastic approaches is crucial for accurate infectious disease modeling.
• Further investigation into the 'first passage time' concept may offer deeper insights into disease fade-out mechanisms.