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Discrete stochastic analogs of Erlang epidemic models

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Version 2 2020-06-05, 11:32
Version 1 2017-11-21, 03:16
journal contribution
posted on 2020-06-05, 11:32 authored by Wayne M. Getz, Eric R. Dougherty

Erlang differential equation models of epidemic processes provide more realistic disease-class transition dynamics from susceptible (S) to exposed (E) to infectious (I) and removed (R) categories than the ubiquitous SEIR model. The latter is itself is at one end of the spectrum of Erlang SEmInR models with m1 concatenated E compartments and n1 concatenated I compartments. Discrete-time models, however, are computationally much simpler to simulate and fit to epidemic outbreak data than continuous-time differential equations, and are also much more readily extended to include demographic and other types of stochasticity. Here we formulate discrete-time deterministic analogs of the Erlang models, and their stochastic extension, based on a time-to-go distributional principle. Depending on which distributions are used (e.g. discretized Erlang, Gamma, Beta, or Uniform distributions), we demonstrate that our formulation represents both a discretization of Erlang epidemic models and generalizations thereof. We consider the challenges of fitting SEmInR models and our discrete-time analog to data (the recent outbreak of Ebola in Liberia). We demonstrate that the latter performs much better than the former; although confining fits to strict SEIR formulations reduces the numerical challenges, but sacrifices best-fit likelihood scores by at least 7%.

Funding

This work in part was thus supported by South African Center for Epidemiological Modeling and Analysis and also by NIH Grant GM117617 to Jason Blackburn with WMG as subcontractor.

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