  In this study, we first develop SIV model by incorporating the intercellular
time delay and analyze the stability of the equilibrium points. The model
dynamics admits disease-free equilibrium and the infected equilibrium with
their stability, based on the value of basic reproduction number $R_0$. We then
frame an optimal control problem with antiviral drugs and second-line drugs as
control measures and study their roles in reducing the infected cell count and
the viral load. The comparative study done in the optimal control problem
suggests that when the first line antiviral drugs shows adverse events,
considering these drugs in reduced quantity along with the second line drug
would be highly effective in reducing the infected cell and viral load in a
COVID infected patients. Later, we formulate a time-optimal control problem
with the objective to drive the system from any given initial state to the
desired infection-free equilibrium state in minimal time. Using Pontryagin's
Minimum Principle the optimal control strategy is shown to be of bang-bang type
with possibility of switches between two extreme values of the optimal
controls. Numerically, it is shown that the desired infection-free state is
achieved in less time when the higher values of both the optimal controls are
chosen.
