Modeling and Forecasting COVID-19 Cases using Latent Subpopulations

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 subpopulations -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 subpopulations. 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.

COVID-19 trends across borders: Identifying correlations among countries

“…These methods have shown promising performance in modeling and forecasting COVID-19 cases. [12][13][14] In other research, methods for forecasting COVID-19 cases and trends have included manual fitting, where initial model parameters are chosen based on historical data, and automated fitting, where parameters are chosen based on candidate case trajectory simulations. 15 Polynomial regression, ARIMA, deep learning techniques, such as recurrent neural network (RNN), and generalized space-time (GST) ARIMA models have been used for COVID-19 forecasting.…”