Dynamic Behavior for an SIRS Model with Nonlinear Incidence Rate and Treatment

Dynamic Behavior for an SIRS Model with Nonlinear Incidence Rate and Treatment

This paper considers an SIRS model with nonlinear incidence rate and treatment. It is assumed that susceptible and infectious individuals have constant immigration rates. We investigate the existence of equilibrium and prove the global asymptotical stable results of the endemic equilibrium. We then...

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Main Authors: Junhong Li, Ning Cui
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:The Scientific World Journal
Online Access:http://dx.doi.org/10.1155/2013/209256
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spelling doaj-6c0e5ccd6310419c91665055ab5388312020-11-24T22:05:15ZengHindawi LimitedThe Scientific World Journal1537-744X2013-01-01201310.1155/2013/209256209256Dynamic Behavior for an SIRS Model with Nonlinear Incidence Rate and TreatmentJunhong Li0Ning Cui1Department of Mathematics and Sciences, Hebei Institute of Architecture & Civil Engineering, Zhangjiakou, Hebei 075000, ChinaDepartment of Mathematics and Sciences, Hebei Institute of Architecture & Civil Engineering, Zhangjiakou, Hebei 075000, ChinaThis paper considers an SIRS model with nonlinear incidence rate and treatment. It is assumed that susceptible and infectious individuals have constant immigration rates. We investigate the existence of equilibrium and prove the global asymptotical stable results of the endemic equilibrium. We then obtained that the model undergoes a Hopf bifurcation and existences a limit cycle. Some numerical simulations are given to illustrate the analytical results.http://dx.doi.org/10.1155/2013/209256
collection DOAJ
language English
format Article
sources DOAJ
author Junhong Li
Ning Cui
spellingShingle Junhong Li
Ning Cui
Dynamic Behavior for an SIRS Model with Nonlinear Incidence Rate and Treatment
The Scientific World Journal
author_facet Junhong Li
Ning Cui
author_sort Junhong Li
title Dynamic Behavior for an SIRS Model with Nonlinear Incidence Rate and Treatment
title_short Dynamic Behavior for an SIRS Model with Nonlinear Incidence Rate and Treatment
title_full Dynamic Behavior for an SIRS Model with Nonlinear Incidence Rate and Treatment
title_fullStr Dynamic Behavior for an SIRS Model with Nonlinear Incidence Rate and Treatment
title_full_unstemmed Dynamic Behavior for an SIRS Model with Nonlinear Incidence Rate and Treatment
title_sort dynamic behavior for an sirs model with nonlinear incidence rate and treatment
publisher Hindawi Limited
series The Scientific World Journal
issn 1537-744X
publishDate 2013-01-01
description This paper considers an SIRS model with nonlinear incidence rate and treatment. It is assumed that susceptible and infectious individuals have constant immigration rates. We investigate the existence of equilibrium and prove the global asymptotical stable results of the endemic equilibrium. We then obtained that the model undergoes a Hopf bifurcation and existences a limit cycle. Some numerical simulations are given to illustrate the analytical results.
url http://dx.doi.org/10.1155/2013/209256
work_keys_str_mv AT junhongli dynamicbehaviorforansirsmodelwithnonlinearincidencerateandtreatment
AT ningcui dynamicbehaviorforansirsmodelwithnonlinearincidencerateandtreatment
_version_ 1725826626942402560

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