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Global dynamics of a delayed SEIS infectious disease model with logistic growth and saturation incidence
Author(s) -
Xu Rui,
Zhang Shihua,
Zhang Fengqin
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3774
Subject(s) - mathematics , basic reproduction number , invariance principle , lyapunov function , epidemic model , logistic function , saturation (graph theory) , stability (learning theory) , infectious disease (medical specialty) , stability theory , mathematical economics , nonlinear system , disease , statistics , demography , computer science , combinatorics , medicine , physics , population , linguistics , philosophy , pathology , quantum mechanics , machine learning , sociology
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.