  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.
