Emergence of Hopf bifurcation in an extended SIR dynamic

TL;DR

This paper extends the SIR epidemic model by adding a hospitalization compartment for critical cases, analyzing complex bifurcation phenomena including Hopf bifurcations under various parameter regimes.

Contribution

It introduces a four-compartment SIR model with ICU considerations and proves the existence of forward, backward, and Hopf bifurcations in the system.

Findings

Existence of Hopf bifurcation in the extended SIR model.

Identification of parameter regimes for different bifurcation types.

Analysis of system dynamics with critical case hospitalization.

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.