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Abstract
<p class="first" id="d6426146e64">Most current Bayesian SEIR (Susceptible, Exposed,
Infectious, Removed (or Recovered))
models either use exponentially distributed latent and infectious periods, allow for
a single distribution on the latent and infectious period, or make strong assumptions
regarding the quantity of information available regarding time distributions, particularly
the time spent in the exposed compartment. Many infectious diseases require a more
realistic assumption on the latent and infectious periods. In this article, we provide
an alternative model allowing general distributions to be utilized for both the exposed
and infectious compartments, while avoiding the need for full latent time data. The
alternative formulation is a path-specific SEIR (PS SEIR) model that follows individual
paths through the exposed and infectious compartments, thereby removing the need for
an exponential assumption on the latent and infectious time distributions. We show
how the PS SEIR model is a stochastic analog to a general class of deterministic SEIR
models. We then demonstrate the improvement of this PS SEIR model over more common
population averaged models via simulation results and perform a new analysis of the
Iowa mumps epidemic from 2006.
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