Global Behaviors of a Class of Discrete SIRS Epidemic Models with Nonlinear Incidence Rate
Joint Authors
Zhang, Long
Teng, Zhidong
Wang, Lei
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-03-17
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
We study a class of discrete SIRS epidemic models with nonlinear incidence rate F ( S ) G ( I ) and disease-induced mortality.
By using analytic techniques and constructing discrete Lyapunov functions, the global stability of disease-free equilibrium and endemic equilibrium is obtained.
That is, if basic reproduction number ℛ 0 < 1 , then the disease-free equilibrium is globally asymptotically stable, and if ℛ 0 > 1 , then the model has a unique endemic equilibrium and when some additional conditions hold the endemic equilibrium also is globally asymptotically stable.
By using the theory of persistence in dynamical systems, we further obtain that only when ℛ 0 > 1 , the disease in the model is permanent.
Some special cases of F ( S ) G ( I ) are discussed.
Particularly, when F ( S ) G ( I ) = β S I / ( 1 + λ I ) , it is obtained that the endemic equilibrium is globally asymptotically stable if and only if ℛ 0 > 1 .
Furthermore, the numerical simulations show that for general incidence rate F ( S ) G ( I ) the endemic equilibrium may be globally asymptotically stable only as ℛ 0 > 1 .
American Psychological Association (APA)
Wang, Lei& Teng, Zhidong& Zhang, Long. 2014. Global Behaviors of a Class of Discrete SIRS Epidemic Models with Nonlinear Incidence Rate. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-18.
https://search.emarefa.net/detail/BIM-1033632
Modern Language Association (MLA)
Wang, Lei…[et al.]. Global Behaviors of a Class of Discrete SIRS Epidemic Models with Nonlinear Incidence Rate. Abstract and Applied Analysis No. 2014 (2014), pp.1-18.
https://search.emarefa.net/detail/BIM-1033632
American Medical Association (AMA)
Wang, Lei& Teng, Zhidong& Zhang, Long. Global Behaviors of a Class of Discrete SIRS Epidemic Models with Nonlinear Incidence Rate. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-18.
https://search.emarefa.net/detail/BIM-1033632
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1033632