Stochastic permanence of an SIQS epidemic model with saturated incidence and independent random perturbations

• An SIQS epidemic model with independent random perturbations is formulated and studied.
• The unique solution is shown to remain in the positive cone with possibility 1.
• The study shows the stochastic permanence and ultimate boundedness.
• Numerical simulations illustrate the main theoretical results.

This article discusses a stochastic SIQS epidemic model with saturated incidence. We assume that random perturbations always fluctuate at the endemic equilibrium. The existence of a global positive solution is obtained by constructing a suitable Lyapunov function. Under some suitable conditions, we derive the stochastic boundedness and stochastic permanence of the solutions of a stochastic SIQS model. Some numerical simulations are carried out to check our results.