  In this paper, the SIR dynamics is extended by considering another
compartmental which represents hospitalization of the critical cases. So a
system of differential equations with four blocks is considered when there is
intensive care unit (ICU) to cure critical cases. Outgoing rate of survived
infected individuals is divided into $nI$ and $\frac{bI}{I+b}$. The second term
represents the rate of critical cases who enter ICUs. It is proved that there
are forward, backward and Hopf bifurcations in different regimes of parameters.
