In this paper, a new SIRS epidemic model which considers the influence of information intervention and environmental noise is studied. The study shows that information intervention and white noise have great effects on the disease. First, we show that there is global existence and positivity of the solution. Then, we prove that the stochastic basic production \(\mathscr{R}_{s}\) is a threshold which determines the extinction or persistence of the disease. When the intensity of noise is large, we obtain \(\mathscr{R}_{s}1\) and a sufficient condition for the existence of stationary distribution is obtained, which means the disease is prevalent. Finally, the main results are illustrated by numerical simulations.
11 June 2018 in Mathematical Methods in the Applied Sciences