Vaccination effect on a stochastic epidemic model with healing and relapse

In this work, we consider a stochastic epidemic model with vaccination, healing and relapse. We prove the existence and the uniqueness of the positive solution. We establish sufficient conditions for the extinction and the persistence in mean of the stochastic system. Moreover, we also establish sufficient conditions for the existence of ergodic stationary distribution to the model, which reveals that the infectious disease will persist. The graphical illustrations of the approximate solutions of the stochastic epidemic model have been performed.

Automated summary

In this work, a stochastic epidemic model with vaccination, healing and relapse is studied. The existence and uniqueness of the positive solution are proven. Sufficient conditions for extinction and persistence in mean of the stochastic system are established. Additionally, sufficient conditions for the existence of an ergodic stationary distribution to the model are also established, indicating the persistence of the infectious disease. Graphical illustrations of the approximate solutions of the stochastic epidemic model are presented.