Year: 2026
Type: preprint
Abstract: Probability generating functions (PGFs) are a fundamental tool in mathematical epidemiology to characterize the stochastic evolution of epidemics via branching process theory. However, they are rarely used as operational tools in real-time during an outbreak, the main barrier being a lack of a systematic, computational methodology to describe epidemiological time series, such as cases or hospital admissions over time. Here, we introduce a general and computationally efficient framework for outbreak analytics based on PGFs. We first develop a method to encode joint distributions of incidences and their noisy measurements by realistic surveillance systems. Then, by transforming PGFs to cumulant generating functions (CGFs), we enable efficient evaluation of these joint distributions. We demonstrate the practicality of our approach for Bayesian inference and short-term forecasts, offering a significant computational advantage over simulation-based methods. Altogether, our framework operationalizes generating functions and paves the way for their broader adoption in computational epidemiology.
Source: arXiv (Cornell University)
Authors: Boudreau, Mariah C., St-Onge, Guillaume
Institutions: Northeastern University, University of Ottawa
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: Northeastern University - to ensure optimal, resilient, cost-effective sampling frameworks for wastewater surveillance globally, Northeastern University - To inform global public health by improving wastewater surveillance system design for early pathogen detection in low- and middle-income countries., G962744442
OpenAlex ID: W7221811668