Lyapunov Functions for a Class of Discrete SIRS Epidemic Models with Nonlinear Incidence Rate and Varying Population Sizes

Lyapunov Functions for a Class of Discrete SIRS Epidemic Models with Nonlinear Incidence Rate and Varying Population Sizes

We investigate the dynamical behaviors of a class of discrete SIRS epidemic models with nonlinear incidence rate and varying population sizes. The model is required to possess different death rates for the susceptible, infectious, recovered, and constant recruitment into the susceptible class, infec...

Full description

Bibliographic Details
Main Authors: Ying Wang, Zhidong Teng, Mehbuba Rehim
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2014/472746
id doaj-381a143cf65741178a967651c8d63c2b
record_format Article
spelling doaj-381a143cf65741178a967651c8d63c2b2020-11-25T00:22:41ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/472746472746Lyapunov Functions for a Class of Discrete SIRS Epidemic Models with Nonlinear Incidence Rate and Varying Population SizesYing Wang0Zhidong Teng1Mehbuba Rehim2College of Mathematics and Model Sciences, Xinjiang University, Urumqi 830046, ChinaCollege of Mathematics and Model Sciences, Xinjiang University, Urumqi 830046, ChinaCollege of Mathematics and Model Sciences, Xinjiang University, Urumqi 830046, ChinaWe investigate the dynamical behaviors of a class of discrete SIRS epidemic models with nonlinear incidence rate and varying population sizes. The model is required to possess different death rates for the susceptible, infectious, recovered, and constant recruitment into the susceptible class, infectious class, and recovered class, respectively. By using the inductive method, the positivity and boundedness of all solutions are obtained. Furthermore, by constructing new discrete type Lyapunov functions, the sufficient and necessary conditions on the global asymptotic stability of the disease-free equilibrium and endemic equilibrium are established.http://dx.doi.org/10.1155/2014/472746
collection DOAJ
language English
format Article
sources DOAJ
author Ying Wang
Zhidong Teng
Mehbuba Rehim
spellingShingle Ying Wang
Zhidong Teng
Mehbuba Rehim
Lyapunov Functions for a Class of Discrete SIRS Epidemic Models with Nonlinear Incidence Rate and Varying Population Sizes
Discrete Dynamics in Nature and Society
author_facet Ying Wang
Zhidong Teng
Mehbuba Rehim
author_sort Ying Wang
title Lyapunov Functions for a Class of Discrete SIRS Epidemic Models with Nonlinear Incidence Rate and Varying Population Sizes
title_short Lyapunov Functions for a Class of Discrete SIRS Epidemic Models with Nonlinear Incidence Rate and Varying Population Sizes
title_full Lyapunov Functions for a Class of Discrete SIRS Epidemic Models with Nonlinear Incidence Rate and Varying Population Sizes
title_fullStr Lyapunov Functions for a Class of Discrete SIRS Epidemic Models with Nonlinear Incidence Rate and Varying Population Sizes
title_full_unstemmed Lyapunov Functions for a Class of Discrete SIRS Epidemic Models with Nonlinear Incidence Rate and Varying Population Sizes
title_sort lyapunov functions for a class of discrete sirs epidemic models with nonlinear incidence rate and varying population sizes
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2014-01-01
description We investigate the dynamical behaviors of a class of discrete SIRS epidemic models with nonlinear incidence rate and varying population sizes. The model is required to possess different death rates for the susceptible, infectious, recovered, and constant recruitment into the susceptible class, infectious class, and recovered class, respectively. By using the inductive method, the positivity and boundedness of all solutions are obtained. Furthermore, by constructing new discrete type Lyapunov functions, the sufficient and necessary conditions on the global asymptotic stability of the disease-free equilibrium and endemic equilibrium are established.
url http://dx.doi.org/10.1155/2014/472746
work_keys_str_mv AT yingwang lyapunovfunctionsforaclassofdiscretesirsepidemicmodelswithnonlinearincidencerateandvaryingpopulationsizes
AT zhidongteng lyapunovfunctionsforaclassofdiscretesirsepidemicmodelswithnonlinearincidencerateandvaryingpopulationsizes
AT mehbubarehim lyapunovfunctionsforaclassofdiscretesirsepidemicmodelswithnonlinearincidencerateandvaryingpopulationsizes
_version_ 1725358815316017152

Similar Items