A generating function perspective on the transmission forest

• Main Authors: Thakkar, Niket, Famulare, Mike
• Format: Journal Article
• Language: English
• Published: 27-11-2023
• Subjects: Quantitative Biology - Populations and Evolution
• DOI: 10.48550/arxiv.2311.16317

In a previous paper, we showed that a compartmental stochastic process model
of SARS-CoV-2 transmission could be fit to time series data and then
reinterpreted as a collection of interacting branching processes drawn from a
dynamic degree distribution. We called this reinterpretation a transmission
forest. This paper builds on that idea. Specifically, leveraging generating
function methods from analytic combinatorics, we develop a theory describing
the transmission forest's properties, allowing us to show for example that
transmission tree interactions fade with increasing disease prevalence. We then
validate the theory by computing forest statistics, like the tree survival
function, which we compare to estimates based on the sampling method developed
previously. The accuracy and flexibility of the analytic approach is clear, and
it allows us to comment on multi-scale features of more general transmission
processes.