  Epidemiological models for the spread of pathogens in a population are
usually only able to describe a single pathogen. This makes their application
unrealistic in cases where multiple pathogens with similar symptoms are
spreading concurrently within the same population. Here we describe a method
which makes possible the application of multiple single-strain models under
minimal conditions. As such, our method provides a bridge between theoretical
models of epidemiology and data-driven approaches for modeling of influenza and
other similar viruses.
  Our model extends the Susceptible-Infected-Recovered model to higher
dimensions, allowing the modeling of a population infected by multiple viruses.
We further provide a method, based on an overcomplete dictionary of feasible
realizations of SIR solutions, to blindly partition the time series
representing the number of infected people in a population into individual
components, each representing the effect of a single pathogen.
  We demonstrate the applicability of our proposed method on five years of
seasonal influenza-like illness (ILI) rates, estimated from Twitter data. We
demonstrate that our method describes, on average, 44\% of the variance in the
ILI time series. The individual infectious components derived from our model
are matched to known viral profiles in the populations, which we demonstrate
matches that of independently collected epidemiological data. We further show
that the basic reproductive numbers ($R0$) of the matched components are in
range known for these pathogens.
  Our results suggest that the proposed method can be applied to other
pathogens and geographies, providing a simple method for estimating the
parameters of epidemics in a population.
