  Containment measures implemented by some countries to suppress the spread of
COVID-19 have resulted in a slowdown of the epidemic characterized by time
series of daily infections plateauing over extended periods of time. We prove
that such a dynamical pattern is compatible with critical
Susceptible-Infected-Removed (SIR) dynamics. In traditional analyses of the
critical SIR model, the critical dynamical regime is started from a single
infected node. The application of containment measures to an ongoing epidemic,
however, has the effect to make the system enter in its critical regime with a
number of infected individuals potentially large. We describe how such
non-trivial starting conditions affect the critical behavior of the SIR model.
We perform a theoretical and large-scale numerical investigation of the model.
We show that the expected outbreak size is an increasing function of the
initial number of infected individuals, while the expected duration of the
outbreak is a non-monotonic function of the initial number of infected
individuals. Also, we precisely characterize the magnitude of the fluctuations
associated with the size and duration of the outbreak in critical SIR dynamics
with non-trivial initial conditions. Far from heard immunity, fluctuations are
much larger than average values, thus indicating that predictions of plateauing
time series may be particularly challenging.
