Dynamics of a stochastic SIS epidemic model with saturated incidence
type: Item
instance of: scholarly article
title: Dynamics of a stochastic SIS epidemic model with saturated incidence
zbMATH Open document ID: 1474.92097
DOI: 10.1155/2014/723825
author: Can Chen
author: Yan-Mei Kang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We introduce stochasticity into the SIS model with saturated incidence. The existence and uniqueness of the positive solution are proved by employing the Lyapunov analysis method. Then, we carry out a detailed analysis on both its almost sure exponential stability and its \(p\)th moment exponential stability, which indicates that the \(p\)th moment exponential stability implies the almost sure exponential stability. Additionally, the results show that the conditions for the disease to become extinct are much weaker than those in the corresponding deterministic model. The conditions for the persistence in the mean and the existence of a stationary distribution are also established. Finally, we derive the expressions for the mean and variance of the stationary distribution. Compared with the corresponding deterministic model, the threshold value for the disease to die out is affected by the half saturation constant. That is, increasing the saturation effect can reduce the disease transmission. Computer simulations are presented to illustrate our theoretical results.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 34F05
zbMATH DE Number: 7022951
Wikidata QID: Q59040931
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/723825
OpenAlex ID: W2053948560
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description: scientific article; zbMATH DE number 7022951