Asymptotic Behavior and Stationary Distribution of a Nonlinear Stochastic Epidemic Model with Relapse and Cure
Joint Authors
Source
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-08-01
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
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 R0≤1, while the random solution oscillates near the endemic equilibrium, and the system has a unique stationary distribution if R0>1.
Moreover, numerical simulation is conducted to support our theoretical results.
American Psychological Association (APA)
Ma, Jiying& Yi, Qing. 2020. Asymptotic Behavior and Stationary Distribution of a Nonlinear Stochastic Epidemic Model with Relapse and Cure. Journal of Mathematics،Vol. 2020, no. 2020, pp.1-12.
https://search.emarefa.net/detail/BIM-1188044
Modern Language Association (MLA)
Ma, Jiying& Yi, Qing. Asymptotic Behavior and Stationary Distribution of a Nonlinear Stochastic Epidemic Model with Relapse and Cure. Journal of Mathematics No. 2020 (2020), pp.1-12.
https://search.emarefa.net/detail/BIM-1188044
American Medical Association (AMA)
Ma, Jiying& Yi, Qing. Asymptotic Behavior and Stationary Distribution of a Nonlinear Stochastic Epidemic Model with Relapse and Cure. Journal of Mathematics. 2020. Vol. 2020, no. 2020, pp.1-12.
https://search.emarefa.net/detail/BIM-1188044
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1188044