  We propose a versatile model with a flexible choice of control for an
early-pandemic outbreak prevention when vaccine/drug is not yet available. At
that stage, control is often limited to non-medical interventions like social
distancing and other behavioral changes. For the SIR optimal control problem,
we show that the running cost of control satisfying mild, practically justified
conditions generates an optimal strategy, $u(t)$, $t \in [0, T]$, that is
sustainable up until some moment $\tau \in [0 ,T)$. However, for any $t \in
[\tau, T]$, the function $u(t)$ will decline as $t$ approaches $T$, which may
cause the number of newly infected people to increase. So, the window from $0$
to $\tau$ is the time for public health officials to prepare alternative
mitigation measures, such as vaccines, testing, antiviral medications, and
others. In addition to theoretical study, we develop a fast and stable
computational method for solving the proposed optimal control problem. The
efficiency of the new method is illustrated with numerical examples of optimal
control trajectories for various cost functions and weights. Simulation results
provide a comprehensive demonstration of the effects of control on the epidemic
spread and mitigation expenses, which can serve as invaluable references for
public health officials.
