Higher order stochastically perturbed SIRS epidemic model with relapse and media impact

This is the authors' abstract. We don't add key points for this paper.

Elaborate and intensive studies have been already made on nonlinear incidence, temporary immunity, and relapse. We propose that instead of nonlinear incidence the effective utilization of media propaganda about the communicable diseases, though could not be contained, may create an awareness and give an exposure among the public mass. Thus, scopes may exist to avoid and reduce communicable disease. This paper is intended to probe higher order stochastically perturbed stochastic SIRS model with relapse and media impact. The stochastic SIRS discloses sufficient conditions for the existence of the ergodic stationary distribution and sufficient conditions for the extinction of the infectious disease are deduced. The results of our model have got various implications in enumerable nonlinear infection forces with colored noise.