Global dynamics of a delayed SEIS infectious disease model with logistic growth and saturation incidence. (30th October 2015)

• Record Type: Journal Article
• Authors: Xu, Rui; Zhang, Shihua; Zhang, Fengqin
• Is Part Of: Mathematical methods in the applied sciences. Volume 39:Number 12(2016:Aug. 15)
• Page Start: 3294
• Page End: 3308
• Publication Date: 2015-10-30
• Subjects: Infectious disease model -- saturation incidence -- delay -- stability -- Hopf bifurcation; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3774
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, a delayed Susceptible‐Exposed‐Infectious‐Susceptible (SEIS) infectious disease model with logistic growth and saturation incidence is investigated, where the time delay describes the latent period of the disease. By analyzing corresponding characteristic equations, the local stability of a disease‐free equilibrium and an endemic equilibrium is discussed. The existence of Hopf bifurcations at the endemic equilibrium is established. By using the persistence theory for infinite dimensional dynamic systems, it is proved that if the basic reproduction number is greater than unity, the system is permanent. By means of suitable Lyapunov functionals and LaSalle's invariance principle, sufficient conditions are obtained for the global stability of the disease‐free equilibrium and the endemic equilibrium, respectively. Numerical simulations are carried out to illustrate the theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.