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Abstract:
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Over the course of an epidemic, the infection rate may naturally vary over time as a result of changes in behavior, new policies, or other factors. However, existing methods for incorporating time-varying rates within stochastic epidemic models do not scale well to data from large outbreaks; as a result, many practitioners resort to simplifying assumptions with rigid forms on the infection rate. In this paper, we present a new class of flexible time-varying stochastic epidemic models amenable to scalable Bayesian inference under the exact model posterior. Drawing on ideas from volatility modeling, we model the time-varying infection rate with a discrete-time gamma process. This model can track changes in the infection rate and, through the use of time-specific discount factors, allows for abrupt variations. We show the practicality of this model by developing an efficient Gibbs sampler for the infection rate under a discrete-time stochastic SEIR model, enabling Bayesian inference for large outbreaks with missing data. We apply the method to assess the impact of interventions on the effective reproduction number during the 1995 Ebola pandemic in Congo.
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