Asymptotic behavior and stationary distribution of a nonlinear stochastic epidemic model with relapse and cure
type: Item
instance of: scholarly article
title: Asymptotic behavior and stationary distribution of a nonlinear stochastic epidemic model with relapse and cure
zbMATH Open document ID: 1489.92166
DOI: 10.1155/2020/4307083
author: Jiying Ma
author: Qing Yi
published in: Journal of Mathematics
publication date: 2021-01-07T00:00:00Z
review text: Summary: In this paper, by introducing environmental perturbation, we extend an epidemic model with graded cure, relapse, and nonlinear incidence rate from a deterministic framework to a stochastic differential one. The existence and uniqueness of positive solution for the stochastic system is verified. Using the Lyapunov function method, we estimate the distance between stochastic solutions and the corresponding deterministic system in the time mean sense. Under some acceptable conditions, the solution of the stochastic system oscillates in the vicinity of the disease-free equilibrium if the basic reproductive number \(R_0\leq 1\), while the random solution oscillates near the endemic equilibrium, and the system has a unique stationary distribution if \(R_0>1\). Moreover, numerical simulation is conducted to support our theoretical results.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 34F05
zbMATH DE Number: 7290890
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2020/4307083
OpenAlex ID: W3046629421
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description: scientific article; zbMATH DE number 7290890