Over the past few decades, researchers have paid more focus to finding
the optimal method for controlling infectious diseases. Recently, the
idea of optimal control has widely been used to discuss the spread of
COVD-19 pandemic. In this article, we consider a mathematical model to
show the transmission of this virus with constant rates. Then, the
optimal control technique is applied on the model with two different
scenarios. The first scenario contains two different controls such as
treatment and vaccination rate. However, the second scenario is dealing
with treatment and vaccination effect. Accordingly, this study
identifies the impact of these control mechanisms as time-dependent
interventions using mathematical modeling and an optimal control method
with Hamilton technique and Pontryagin's maximum principle.
Computational results show that the use of treatment in the high level
has the biggest impact in the minimizing the total infected people.
Furthermore, the suggested mathematical model with and without control
variables are accurately analyzed using the forward-backward Runge Kutta
method in MATLAB for initial states and parameters. The findings of
optimal control here indicate that the suggested scenarios may effective
use for reducing the number of infected individuals and improving public
health strategies more widely.