Emergence of Hopf bifurcation in an extended SIR dynamic

Abstract

In this paper, the original SIR model is improved by considering a new compartment, representing the hospitalization of critical cases. A system of differential equations with four blocks is developed to analyze the treatment of severe cases in an Intensive Care Unit (ICU). The outgoing rate of the infected individuals who survive is divided into nI and bI/1+b where the second term represents the transition rate of critical cases that are hospitalized in ICU. The findings demonstrate the existence of forward, backward and Hopf bifurcations in various ranges of parameters.