Abstract
This paper is concerned with the dynamical behavior of a hybrid switching SVIR epidemic model with vaccination and Lévy noise. Besides a standard geometric Brownian motion, another two driving processes are considered: a stationary Poisson point process and a continuous time finite-state Markov chain. To begin with, we obtain sufficient conditions for persistence in the mean of the disease. Then we establish sufficient conditions for extinction of the disease. Furthermore, in the case of persistence, we also obtain sufficient conditions for the existence of positive recurrence of the solutions by constructing a suitable stochastic Lyapunov function with regime switching.
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