Unifying Epidemic Models with Mixtures

Abstract

The COVID-19 pandemic has emphasized the need for a robust understanding of epidemic models. Current models of epidemics are classified as either mechanistic or non-mechanistic: mechanistic models make explicit assumptions on the dynamics of disease, whereas non-mechanistic models make assumptions on the form of observed time series. Here, we introduce a simple mixture-based model which bridges the two approaches while retaining benefits of both. The model represents time series of cases and fatalities as a mixture of Gaussian curves, providing a flexible function class to learn from data compared to traditional mechanistic models. Although the model is non-mechanistic, we show that it arises as the natural outcome of a stochastic process based on a networked SIR framework. This allows learned parameters to take on a more meaningful interpretation compared to similar non-mechanistic models, and we validate the interpretations using auxiliary mobility data collected during the COVID-19 pandemic. We provide a simple learning algorithm to identify model parameters and establish theoretical results which show the model can be efficiently learned from data. Empirically, we find the model to have low prediction error. * Ultimately, this allows us to systematically understand the impacts of interventions on COVID-19, which is critical in developing data-driven solutions to controlling epidemics.

Modeling and Forecasting COVID-19 Cases using Latent Subpopulations

“…Very relevant to our approach is the work of Sarker et al (2022), who also consider latent sub-populations, where the learner can only observe a single time-series that is the aggregate of the different sub-populations. They model the number of infected people over time as a mixture of Gaussians, and propose using a peak-finding heuristic to determine the number of sub-populations (each modeled as a Gaussian) to use in their mixture.…”