Stability and bifurcation analysis of a SIR model with saturated incidence rate and saturated treatment

TL;DR

This paper analyzes a SIR epidemic model incorporating saturated incidence and treatment rates, examining stability, bifurcations, and disease control implications through theoretical analysis and numerical simulations.

Contribution

It introduces a comprehensive analysis of backward and Hopf bifurcations in a nonlinear SIR model with resource limitations and vaccination effects.

Findings

Existence of backward bifurcation under certain conditions

Stability and direction of Hopf bifurcation determined

Numerical simulations support theoretical results

Abstract

We study the dynamics of a SIR epidemic model with nonlinear incidence rate, vertical transmission vaccination for the newborns and the capacity of treatment, that takes into account the limitedness of the medical resources and the efficiency of the supply of available medical resources. Under some conditions we prove the existence of backward bifurcation, the stability and the direction of Hopf bifurcation. We also explore how the mechanism of backward bifurcation affects the control of the infectious disease. Numerical simulations are presented to illustrate the theoretical findings.