Global dynamics analysis of a stochastic SIRS epidemic model with vertical transmission and different periods of immunity
type: Item
instance of: scholarly article
title: Global dynamics analysis of a stochastic SIRS epidemic model with vertical transmission and different periods of immunity
zbMATH Open document ID: 1474.37121
DOI: 10.1504/IJDSDE.2020.111485
author: Driss Kiouach
author: Yassine Sabbar
published in: International Journal of Dynamical Systems and Differential Equations
publication date: 2021-05-07T00:00:00Z
review text: Summary: In this work, we analyse a stochastic susceptible-infected-recovered-susceptible (SIRS) epidemic model with vertical transmission and different periods of immunity. This model has a global positive solution. Firstly, we establish sufficient conditions for extinction and persistence in the mean of a disease. Then, we prove the global stability of the system under a suitable condition of perturbation intensity. In the case of the non-autonomous system, we show that there exists at least one positive periodic solution. Finally, some numerical examples are introduced to show the validity of our results.
Mathematics Subject Classification ID: 37N25
Mathematics Subject Classification ID: 92D30
zbMATH DE Number: 7345600
zbMATH Keywords: stochastic SIRS model
zbMATH Keywords: vertical transmission
zbMATH Keywords: global stability
zbMATH Keywords: extinction
zbMATH Keywords: persistence
zbMATH Keywords: periodic solution
MaRDI profile type: Publication
full work available at URL: ijdsde.2020.111485
OpenAlex ID: W4231608747
description: scientific article; zbMATH DE number 7345600