  Current epidemics in the biological and social domains are challenging the
standard assumptions of mathematical contagion models. Chief among them are the
complex patterns of transmission caused by heterogeneous group sizes and
infection risk varying by orders of magnitude in different settings, like
indoor versus outdoor gatherings in the COVID-19 pandemic or different
moderation practices in social media communities. However, quantifying these
heterogeneous levels of risk is difficult and most models typically ignore
them. Here, we include these novel features in an epidemic model on weighted
hypergraphs to capture group-specific transmission rates. We study analytically
the consequences of ignoring the heterogeneous transmissibility and find an
induced superlinear infection rate during the emergence of a new outbreak, even
though the underlying mechanism is a simple, linear contagion. The dynamics
produced at the individual and group levels are therefore more similar to
complex, nonlinear contagions, thus blurring the line between simple and
complex contagions in realistic settings. We support this claim by introducing
a Bayesian inference framework to quantify the nonlinearity of contagion
processes. We show that simple contagions on real weighted hypergraphs are
systematically biased toward the superlinear regime if the heterogeneity of the
weights is ignored, greatly increasing the risk of erroneous classification as
complex contagions. Our results provide an important cautionary tale for the
challenging task of inferring transmission mechanisms from incidence data. Yet,
it also paves the way for effective models that capture complex features of
epidemics through nonlinear infection rates.
