Emergence of Hopf bifurcation in an extended SIR dynamic

Abstract

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.

arXiv comment21 pages, 7 figures