  The recent outbreak of COVID-19 in Mainland China is characterized by a
distinctive algebraic, sub-exponential increase of confirmed cases during the
early phase of the epidemic, contrasting an initial exponential growth expected
for an unconstrained outbreak with sufficiently large reproduction rate.
Although case counts vary significantly between affected provinces in Mainland
China, the scaling law $t^{\mu}$ is surprisingly universal, with a range of
exponents $\mu=2.1\pm0.3$. The universality of this behavior indicates that
despite social, regional, demographical, geographical, and socio-economical
heterogeneities of affected Chinese provinces, this outbreak is dominated by
fundamental mechanisms that are not captured by standard epidemiological
models. We show that the observed scaling law is a direct consequence of
containment policies that effectively deplete the susceptible population. To
this end we introduce a parsimonious model that captures both, quarantine of
symptomatic infected individuals as well as population wide isolation in
response to mitigation policies or behavioral changes. For a wide range of
parameters, the model reproduces the observed scaling law in confirmed cases
and explains the observed exponents. Quantitative fits to empirical data permit
the identification of peak times in the number of asymptomatic or
oligo-symptomatic, unidentified infected individuals, as well as estimates of
local variations in the basic reproduction number. The model implies that the
observed scaling law in confirmed cases is a direct signature of effective
contaiment strategies and/or systematic behavioral changes that affect a
substantial fraction of the susceptible population. These insights may aid the
implementation of containment strategies in potential export induced COVID-19
secondary outbreaks elsewhere or similar future outbreaks of other emergent
infectious diseases.
