Abstract
To understand dynamics of the COVID‐19 disease realistically, a new SEIAPHR model has been proposed in this article where the infectious individuals have been categorized as symptomatic, asymptomatic, and super‐spreaders. The model has been investigated for existence of a unique solution. To measure the contagiousness of COVID‐19, reproduction number
R
0
is also computed using next generation matrix method. It is shown that the model is locally stable at disease‐free equilibrium point when
R
0
<
1
and unstable for
R
0
>
1
. The model has been analyzed for global stability at both of the disease‐free and endemic equilibrium points. Sensitivity analysis is also included to examine the effect of parameters of the model on reproduction number
R
0
. A couple of optimal control problems have been designed to study the effect of control strategies for disease control and eradication from the society. Numerical results show that the adopted control approaches are much effective in reducing new infections.