An SIRS epidemic model incorporating media coverage with time delay.
An SIRS epidemic model incorporating media coverage with time delay is proposed. The positivity and boundedness are studied firstly. The locally asymptotical stability of the disease-free equilibrium and endemic equilibrium is studied in succession. And then, the conditions on which periodic orbits bifurcate are given. Furthermore, we show that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of the 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 R 0 < 1. However, when R 0 > 1, the stability of the endemic equilibrium will be affected by the time delay; there will be a family of periodic orbits bifurcating from the endemic equilibrium when the time delay increases through a critical value. Finally, some examples for numerical simulations are also included.
Department of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650093, China ; Department of Mathematics and Information Science, Zhoukou Normal University, Zhoukou, Henan 466001, China.
Huitao
0000-0002-0656-702X
H
Zhao
Department of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650093, China.
Yiping
Y
Lin
Department of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650093, China.
Yunxian
Y
Dai
D000465:Algorithms; D050936:Basic Reproduction Number; D003198:Computer Simulation; D058872:Epidemics; D006801:Humans; D008954:Models, Biological; D012984:Software; D018746:Systemic Inflammatory Response Syndrome / Q000453:epidemiology*