Stability analysis of a discrete SIRS epidemic model with vaccination. Issue 3 (3rd March 2020)

• Record Type: Journal Article
• Authors: Xiang, Lei; Zhang, Yuyue; Huang, Jicai
• Is Part Of: Journal of difference equations and applications. Volume 26:Issue 3(2020)
• Page Start: 309
• Page End: 327
• Publication Date: 2020-03-03
• Subjects: Discrete SIRS epidemic model -- vaccination -- basic reproduction number -- stability; 37N25 -- 37G10; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2020.1725497
• Languages: English
• ISSNs: 1023-6198

Abstract

ABSTRACT: A discrete SIRS epidemic model with vaccination and a general infection probability function is investigated in this paper. The basic reproduction number ℜ 0 of the model is calculated. It is proven that the disease-free equilibrium is locally asymptotically stable if ℜ 0 < 1 and globally asymptotically stable for some additional conditions, and the endemic equilibrium is locally asymptotically stable if ℜ 0 > 1 . Numerical simulations are presented to illustrate the stability results, and the sensitivity analysis of the basic reproduction number ℜ 0 shows that the proportionality coefficient of unvaccinated susceptible, the probability that infected individuals do not recover, and the probability of survival have much more effect on ℜ 0 .