Resumen de Disease Dynamics of a Probabilistic Model with Vaccination Under Regime Switching

Tomás Caraballo Garrido , A. Nait Brahim, A. Settat, A. Lahrouz, T. Amtout

• The dynamics of a SIS epidemic model with vaccination and a saturated incidence rate in specific stochastic environments are examined with vaccination and a saturated incidence rate in specific stochastic environments. The study focuses on the system’s long-term behavior and aims to establish sufficient conditions for disease extinction and persistence. In cases where persistence occurs, a stationary distribution is investigated. Additionally, it is proven that the density functions converge in L1 to an invariant density under certain conditions. These results enhance understanding of the SIS epidemic model with vaccination, building upon and extending previous research in this field.