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2014 Dynamical Behavior of a New Epidemiological Model
Zizi Wang, Zhiming Guo
J. Appl. Math. 2014: 1-9 (2014). DOI: 10.1155/2014/854528


A new epidemiological model is introduced with nonlinear incidence, in which the infected disease may lose infectiousness and then evolves to a chronic noninfectious disease when the infected disease has not been cured for a certain time τ. The existence, uniqueness, and stability of the disease-free equilibrium and endemic equilibrium are discussed. The basic reproductive number R0 is given. The model is studied in two cases: with and without time delay. For the model without time delay, the disease-free equilibrium is globally asymptotically stable provided that R01; if R0>1, then there exists a unique endemic equilibrium, and it is globally asymptotically stable. For the model with time delay, a sufficient condition is given to ensure that the disease-free equilibrium is locally asymptotically stable. Hopf bifurcation in endemic equilibrium with respect to the time τ is also addressed.


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Zizi Wang. Zhiming Guo. "Dynamical Behavior of a New Epidemiological Model." J. Appl. Math. 2014 1 - 9, 2014.


Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07010778
MathSciNet: MR3178975
Digital Object Identifier: 10.1155/2014/854528

Rights: Copyright © 2014 Hindawi


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