Stability analysis of delayed SIR model with logistic growth and bilinear incidence rate

Abstract

We look at a system of delay differential equations for an SIR model with logistic and bilinear incidence rates in this study. The model demonstrates bifurcation, where a stable disease-free equilibrium (DFE) coexists with a stable endemic equilibrium, according to the research (EE). When the reproduction number determines the requirements for local equilibrium stability and Hopf bifurcation’s existence. In order to preserve the stability behaviour, we also performed a bifurcation analysis with an anticipated duration of delay. We used numerical simulations to demonstrate the theoretical results’ relevance and effectiveness.