A beta-Poisson model for infectious disease transmission

Area of Science:

• Epidemiology
• Mathematical Biology
• Infectious Disease Modeling

Background:

• Emerging and zoonotic infections pose significant global health threats.
• Stochastic transmission dynamics and varying transmission potential characterize these outbreaks.
• The negative binomial distribution is a standard model for early epidemic transmission.

Purpose of the Study:

• To introduce and evaluate a novel beta-Poisson mixture model for infectious disease transmission.
• To compare the performance of the beta-Poisson model against the negative binomial and zero-inflated Poisson models.
• To assess the applicability of the beta-Poisson model in intervention modeling scenarios.

Main Methods:

• Development of a beta-Poisson mixture model where transmission probability is beta-distributed.
• Demonstration that the negative binomial and zero-inflated Poisson distributions are limiting cases of the beta-Poisson model.
• Fitting the beta-Poisson model to secondary case distributions from diverse real-world outbreaks.

Main Results:

• The beta-Poisson model can provide a closer fit to secondary case data than the negative binomial distribution.
• However, the negative binomial model is consistently preferred based on the Akaike Information Criterion, indicating better parsimony.
• Both models effectively capture key transmission features like overdispersion and superspreading.

Conclusions:

• The beta-Poisson model, while flexible, is generally outperformed by the negative binomial model on parsimonious grounds.
• The negative binomial distribution remains a robust and often preferable model for analyzing secondary case distributions.
• The beta-Poisson model's structure offers potential utility in simulating specific public health interventions affecting contact rates or infectivity.