Stability and asymptotic behavior of a regime-switching SIRS model with Beddington-DeAngelis incidence rate
type: Item
instance of: scholarly article
title: Stability and asymptotic behavior of a regime-switching SIRS model with Beddington-DeAngelis incidence rate
zbMATH Open document ID: 1459.92149
DOI: 10.1155/2020/7181939
author: Shan Wang
author: Youhua Peng
author: Feng Wang
published in: Mathematical Problems in Engineering
publication date: 2020-07-30T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60J28
zbMATH DE Number: 7226156
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2020/7181939
OpenAlex ID: W3043352593
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description: scientific article; zbMATH DE number 7226156