Modeling and Forecasting COVID-19 Cases using Latent Subpopulations

TL;DR

This paper introduces two novel methods for modeling and forecasting COVID-19 cases by representing the population as a mixture of latent subpopulations, improving accuracy over traditional models.

Contribution

The authors propose dictionary-based and mixture-of-curves methods to model heterogeneous populations without known subpopulation identities, applicable with various parametric models.

Findings

Dictionary approach outperforms classical SIR models in accuracy.

Methods effectively model observed data and forecast infections 1-4 weeks ahead.

Proposed models show lower error and variance across 187 countries.

Abstract

Classical epidemiological models assume homogeneous populations. There have been important extensions to model heterogeneous populations, when the identity of the sub-populations is known, such as age group or geographical location. Here, we propose two new methods to model the number of people infected with COVID-19 over time, each as a linear combination of latent sub-populations -- i.e., when we do not know which person is in which sub-population, and the only available observations are the aggregates across all sub-populations. Method #1 is a dictionary-based approach, which begins with a large number of pre-defined sub-population models (each with its own starting time, shape, etc), then determines the (positive) weight of small (learned) number of sub-populations. Method #2 is a mixture-of-$M$ fittable curves, where $M$, the number of sub-populations to use, is given by the user. Both methods are compatible with any parametric model; here we demonstrate their use with first (a)~Gaussian curves and then (b)~SIR trajectories. We empirically show the performance of the proposed methods, first in (i) modeling the observed data and then in (ii) forecasting the number of infected people 1 to 4 weeks in advance. Across 187 countries, we show that the dictionary approach had the lowest mean absolute percentage error and also the lowest variance when compared with classical SIR models and moreover, it was a strong baseline that outperforms many of the models developed for COVID-19 forecasting.