Bistability in a SIRS model with general nonmonotone and saturated incidence rate

TL;DR

This paper analyzes a SIRS epidemiological model with a complex incidence rate, revealing bistability and bifurcation phenomena, and provides critical thresholds for different dynamical behaviors.

Contribution

It introduces a SIRS model with a nonmonotone, saturated incidence rate and thoroughly analyzes its stability and bifurcation properties, including the existence of bistability.

Findings

The system exhibits saddle-node bifurcation.

The model always has a stable disease-free equilibrium.

Numerical simulations confirm theoretical results.

Abstract

In this paper, we consider a SIRS model with general nonmonotone and saturated incidence rate and perform stability and bifurcation analysis. We show that the system has saddle-node bifurcation and displays bistable behavior. We obtain the critical thresholds that characterize the dynamical behaviors of the model. We find with surprise that the system always admits a disease free equilibrium E0 which is always asymptotically stable. Numerical simulations are carried out to verify our results.