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Population-level survival analysis from individual-level transmission models

Banff International Research Station for Mathematical Innovation and Discovery

In a recent paper KhudaBukhsh et al., we showed that solutions to Ordinary Differential Equations (ODEs) describing the large-population limits of Markovian stochastic compartmental dynamical systems can be interpreted as survival or hazard functions when analyzing data from individuals sampled from the population. An earlier paper by Kenah showed that likelihoods from individual-level mass-action transmission models simplify in the limit of a large population when the depletion of susceptibles is negligible. In this paper, we unify and generalize these results by deriving population-level survival and hazard functions from explicit individual-level models. This allows population-level survival analysis to be applied to a more general class of epidemic models and allows the asymptotic pairwise likelihoods to be applied throughout the course of an epidemic. In practice, this will provide a logically consistent framework for the analysis of both high-resolution outbreak investigations or household studies and population-level surveillance or sentinel data.

Mathematics; Probability theory and stochastic processes; Statistics

video/mp4

Author affiliation: The Ohio State University

2019-11-19

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/72313

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/