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

2019/11/29 by Shaoli Wang, Wang, Shaoli, Xiyan Bai +3
Computer Science · Mathematics · Medicine · #FOS: Biological sciences #Fractional Differential Equations Solutions #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Dynamics and Pattern Formation #Populations and Evolution (q-bio.PE)

paper · pdf · doi:10.48550/arxiv.1911.13002

openalex publication_date 2019/11/29 · openalex created_date 2019/12/05 · openalex updated_date 2026/07/28

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.

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