Analysis of stochastic delayed SIRS model with exponential birth and saturated incidence rate. (September 2020)

• Record Type: Journal Article
• Authors: Ali, Ishtiaq; Ullah Khan, Sami
• Is Part Of: Chaos, solitons and fractals. Volume 138(2020)
• Publication Date: 2020-09
• Subjects: Stochastic delayed SIRS model -- Legendre spectral collocation method -- Endemic equilibrium -- Error analysis; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2020.110008
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: In this paper, we investigate numerically a stochastic delayed SIRS model with exponential structure and saturated incidence. A Legendre collocation method which convert the given model to a nonlinear algebraic system of equations is applied for the approximate solution. The general dynamics of the model is analyzed for relatively small noise and it is shown that large noise will cause the eradication, which will control the spreading of the disease further. Stability of the endemic equilibrium with delay is analyzed with imposing some conditions on the intensity of the noise for both stochastic and deterministic SIRS models. Some numerical test are performed to justify the mathematical conclusions.