  At the time of writing, the ongoing COVID-19 pandemic, caused by severe acute
respiratory syndrome coronavirus 2 (SARS-CoV-2), had already resulted in more
than thirty-two million cases infected and more than one million deaths
worldwide.
  Given the fact that the pandemic is still threatening health and safety, it
is in the urgency to understand the COVID-19 contagion process and know how it
might be controlled. With this motivation in mind, in this paper, we consider a
version of a stochastic discrete-time
Susceptible-Infected-Recovered-Death~(SIRD)-based epidemiological model with
two uncertainties: The uncertain rate of infected cases which are undetected or
asymptomatic, and the uncertain effectiveness rate of control. Our aim is to
study the effect of an epidemic control policy on the uncertain model in a
control-theoretic framework. We begin by providing the closed-form solutions of
states in the modified SIRD-based model such as infected cases, susceptible
cases, recovered cases, and deceased cases. Then, the corresponding expected
states and the technical lower and upper bounds for those states are provided
as well. Subsequently, we consider two epidemic control problems to be
addressed: One is almost sure epidemic control problem and the other average
epidemic control problem. Having defined the two problems, our main results are
a set of sufficient conditions on a class of linear control policy which
assures that the epidemic is "well-controlled"; i.e., both of the infected
cases and deceased cases are upper bounded uniformly and the number of infected
cases converges to zero asymptotically. Our numerical studies, using the
historical COVID-19 contagion data in the United States, suggest that our
appealingly simple model and control framework can provide a reasonable
epidemic control performance compared to the ongoing pandemic situation.
