Dynamical behavior of a hybrid switching SIS epidemic model with vaccination and Lévy jumps

Abstract

In this paper, the dynamical behavior of a hybrid switching SIS epidemic model with vaccination and Lévy jumps is considered. Besides a standard geometric Brownian motion, another two driving processes are taken into account: a stationary Poisson point process and a continuous time finite-state Markov chain. Firstly, we establish sufficient conditions for persistence in the mean of the disease. Then we obtain sufficient conditions for extinction of the disease. In addition, we also establish sufficient conditions for the existence of positive recurrence of the solutions to the model by constructing a suitable stochastic Lyapunov function with regime switching.

Keywords:

• Vaccination; persistence and extinction; positive recurrence; Markov switching; Lévy jumps

MATHEMATICS SUBJECT CLASSIFICATION:

• 34E10
• 60H10
• 92B05

Additional information

Funding

This work was supported by the National Natural Science Foundation of P.R. China (No. 11871473), Natural Science Foundation of Guangxi Province (No. 2016GXNSFBA380006), the Fundamental Research Funds for the Central Universities (No. 15CX08011A), KY2016YB370 and 2016CSOBDP0001.