Analysis of a stochastic SIR model with media effects

TL;DR

This paper analyzes a stochastic SIR epidemic model incorporating media effects, establishing conditions for disease extinction or persistence, and highlighting the influence of environmental noise and media on disease dynamics.

Contribution

It introduces a stochastic SIR model with media effects, deriving the basic reproduction number and analyzing the impact of environmental noise and media on disease thresholds.

Findings

Large environmental noise can lead to disease extinction with probability 1.

Media effects do not alter the basic reproduction number.

Numerical simulations show media reduces infection levels.

Abstract

In this study, we investigate a stochastic SIR model with media effects. The uniqueness and the existence of a global positive solution are studied. The sufficient conditions of extinction and persistence of the disease are established. We obtain the basic reproduction number $R_0^S$ for stochastic system, which can act as the threshold given small environmental noise. Note that large noise can induce the disease extinction with probability of 1, suggesting that environmental noises can not be ignored when investigating threshold dynamics. Further, inclusion of media induced behaviour changes does not affect the threshold itself, which is similar to the conclusion of the deterministic models. However, numerical simulations suggest that media impacts induce the disease infection decline.