Dynamical Behaviors Of A Stochastic SIQR Epidemic Model With Quarantine-adjusted Incidence

In this paper,we focus on the dynamical behaviors of a stochastic SIQR epidemic model with quarantine-adjusted incidence.In order to give the model the error and the sufficient conditions for extinction,firstly,we obtain the existence and uniqueness of the positive solution of the model through Lyapunov analysis.Then,through the Has' minskii theory,we prove that the model has a unique stationary distribution with ergodicity.This indicates that the disease is prevalent;subsequently,the conditions for disease disappearance are obtained by random analysis and the results of the random SIQR epidemiological model are given.The results show that when the white noise is relatively large,the infectious disease will be extinct,which also indicates that the intervention of white noise plays an important role in controlling the spread of the disease.Finally,we verify the results obtained by numerical simulation.