Stability and Asymptotic Behavior of a Regime-Switching SIRS Model with Beddington–DeAngelis Incidence Rate

Stability and Asymptotic Behavior of a Regime-Switching SIRS Model with Beddington–DeAngelis Incidence Rate

A regime-switching SIRS model with Beddington–DeAngelis incidence rate is studied in this paper. First of all, the property that the model we discuss has a unique positive solution is proved and the invariant set is presented. Secondly, by constructing appropriate Lyapunov functionals, global stocha...

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Main Authors: Shan Wang, Youhua Peng, Feng Wang
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2020/7181939
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spelling doaj-accf69e0844647888ce2c8646cf9b3b32020-11-25T03:28:54ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472020-01-01202010.1155/2020/71819397181939Stability and Asymptotic Behavior of a Regime-Switching SIRS Model with Beddington–DeAngelis Incidence RateShan Wang0Youhua Peng1Feng Wang2Department of Mathematics, Pingxiang University, Pingxiang 337000, ChinaDepartment of Mathematics, Pingxiang University, Pingxiang 337000, ChinaDepartment of Mathematics, Pingxiang University, Pingxiang 337000, ChinaA regime-switching SIRS model with Beddington–DeAngelis incidence rate is studied in this paper. First of all, the property that the model we discuss has a unique positive solution is proved and the invariant set is presented. Secondly, by constructing appropriate Lyapunov functionals, global stochastic asymptotic stability of the model under certain conditions is proved. Then, we leave for studying the asymptotic behavior of the model by presenting threshold values and some other conditions for determining disease extinction and persistence. The results show that stochastic noise can inhibit the disease and the behavior will have different phenomena owing to the role of regime-switching. Finally, some examples are given and numerical simulations are presented to confirm our conclusions.http://dx.doi.org/10.1155/2020/7181939
collection DOAJ
language English
format Article
sources DOAJ
author Shan Wang
Youhua Peng
Feng Wang
spellingShingle Shan Wang
Youhua Peng
Feng Wang
Stability and Asymptotic Behavior of a Regime-Switching SIRS Model with Beddington–DeAngelis Incidence Rate
Mathematical Problems in Engineering
author_facet Shan Wang
Youhua Peng
Feng Wang
author_sort Shan Wang
title Stability and Asymptotic Behavior of a Regime-Switching SIRS Model with Beddington–DeAngelis Incidence Rate
title_short Stability and Asymptotic Behavior of a Regime-Switching SIRS Model with Beddington–DeAngelis Incidence Rate
title_full Stability and Asymptotic Behavior of a Regime-Switching SIRS Model with Beddington–DeAngelis Incidence Rate
title_fullStr Stability and Asymptotic Behavior of a Regime-Switching SIRS Model with Beddington–DeAngelis Incidence Rate
title_full_unstemmed Stability and Asymptotic Behavior of a Regime-Switching SIRS Model with Beddington–DeAngelis Incidence Rate
title_sort stability and asymptotic behavior of a regime-switching sirs model with beddington–deangelis incidence rate
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2020-01-01
description A regime-switching SIRS model with Beddington–DeAngelis incidence rate is studied in this paper. First of all, the property that the model we discuss has a unique positive solution is proved and the invariant set is presented. Secondly, by constructing appropriate Lyapunov functionals, global stochastic asymptotic stability of the model under certain conditions is proved. Then, we leave for studying the asymptotic behavior of the model by presenting threshold values and some other conditions for determining disease extinction and persistence. The results show that stochastic noise can inhibit the disease and the behavior will have different phenomena owing to the role of regime-switching. Finally, some examples are given and numerical simulations are presented to confirm our conclusions.
url http://dx.doi.org/10.1155/2020/7181939
work_keys_str_mv AT shanwang stabilityandasymptoticbehaviorofaregimeswitchingsirsmodelwithbeddingtondeangelisincidencerate
AT youhuapeng stabilityandasymptoticbehaviorofaregimeswitchingsirsmodelwithbeddingtondeangelisincidencerate
AT fengwang stabilityandasymptoticbehaviorofaregimeswitchingsirsmodelwithbeddingtondeangelisincidencerate
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