Numerical Analysis of Stochastic SIRS Model Population Transfer from Infectious class to Susceptible class with Saturated Incidence Rate

In this article, stochastic SIRS model is formulated with saturated incidence rate. Stochastic effects of special transfer from infectious to susceptible and the spread of infectious disease are confabulated. The fringe dynamic is analyzed in case of imaginably limited noise. The loud noise would spectacle the elimination of disease, which would restraint transmission of the disease. We also analyzed the stability of the endemic equilibrium with delay and observed that under some condition on delay, it is stable. Deterministic and stochastic SIRS both models are discussed in this study. The Legendre polynomials are used to convert the stochastic delayed SIRS model to a nonlinear algebraic system, which is solvable using Legendre spectral collocation method. Finally, we have proposed a test sample of stochastic delayed SIRS model to establish our mathematical conclusions.