  The worldwide outbreak of the coronavirus was first identified in 2019 in
Wuhan, China. Since then, the disease has spread worldwide. As it currently
spreading in the United States, policy makers, public health officials and
citizens are racing to understand the impact of this virus on the United States
healthcare system. They fear that the rapid influx of patients will overwhelm
the healthcare system leading to unnecessary fatalities. Most countries and
states in America have introduced mitigation strategies, such as social
distancing, to decrease the rate of newly infected people, i.e. flattening the
curve.In this paper, we analyze the time evolution of the number of people
hospitalized due to the coronavirus using the methods of queueing theory. Given
that the rate of new infections varies over time as the pandemic evolves, we
model the number of coronavirus patients as a dynamical system based on the
theory of infinite server queues with non-stationary Poisson arrival rates.
With this model we are able to quantify how flattening the curve affects the
peak demand for hospital resources. This allows us to characterize how
aggressively society must flatten the curve in order to avoid overwhelming the
capacity of healthcare system. We also demonstrate how flattening the curve
impacts the elapsed time between the peak rate of hospitalizations and the time
of the peak demand for the hospital resources. Finally, we present empirical
evidence from China, South Korea, Italy and the United States that supports the
insights from the model.
