Emergence of Hopf bifurcation in an extended SIR dynamic

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.

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