title: Global Hopf bifurcation analysis of an susceptible-infective-removed epidemic model incorporating media coverage with time delay.
abstract: An susceptible-infective-removed epidemic model incorporating media coverage with time delay is proposed. The stability of the disease-free equilibrium and endemic equilibrium is studied. And then, the conditions which guarantee the existence of local Hopf bifurcation are given. Furthermore, we show that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of delay. The obtained results show that the time delay in media coverage can not affect the stability of the disease-free equilibrium when the basic reproduction number is less than unity. However, the time delay affects the stability of the endemic equilibrium and produces limit cycle oscillations while the basic reproduction number is greater than unity. Finally, some examples for numerical simulations are included to support the theoretical prediction.
authors.affiliation: a College of Mathematics and Statistics , Zhoukou Normal University , Zhoukou Henan , People's Republic of China.
authors.forename: Huitao
authors.initials: H
authors.lastname: Zhao
authors.affiliation: a College of Mathematics and Statistics , Zhoukou Normal University , Zhoukou Henan , People's Republic of China.
authors.forename: Miaochan
authors.initials: M
authors.lastname: Zhao
mesh_terms: D050936:Basic Reproduction Number; D003146:Communications Media; D003198:Computer Simulation; D058872:Epidemics; D006801:Humans; D008954:Models, Biological; D013997:Time Factors
keywords: 34C23; 34G20; SIR epidemic model; global Hopf bifurcation; media coverage; stability