Let us consider the standard SEIR model with additional vaccination compartment:
\begin{eqnarray*} \frac{dS}{dt}&=& -\beta \frac{SI}{N} - bS \\ \frac{dV}{dt}&=& bS - \epsilon(\beta \frac{VI}{N}) \\ \frac{dE}{dt}&=& \beta \frac{SI}{N} + \epsilon(\beta \frac{VI}{N}) - \alpha E \\ \frac{dI}{dt}&=& \alpha E - \gamma I\\ \frac{dR}{dt}&=& f\gamma I\\ \end{eqnarray*}
Here I assume that $V$ is the number of healthcare and frontline workers who are vaccinated. Now, in reality, there are only a limited number of such individuals. Thus, I want to alter the parameter $b$ so that the number of vaccinated persons cannot exceed a specific number, say $K.$ Your suggestions are so much appreciated.
This is an answer to my question: Take $$b = r \left( 1 - \frac{V}{K} \right)$$ where $r$ is some constant.